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Relativistic mean-field mass models
NASA Astrophysics Data System (ADS)
Peña-Arteaga, D.; Goriely, S.; Chamel, N.
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented.
Relativistic mean field models for finite nuclei and neutron stars
NASA Astrophysics Data System (ADS)
Chen, Wei-Chia
In this dissertation we have created theoretical models for finite nuclei, nuclear matter, and neutron stars within the framework of relativistic mean field (RMF) theory, and we have used these models to investigate the elusive isovector sector and related physics, in particular, the neutron-skin thickness of heavy nuclei, the nuclear symmetry energy, and the properties of neutron stars. To build RMF models that incorporate collective excitations in finite nuclei in addition to their ground-state properties, we have extended the non-relativistic sum rule approach to the relativistic domain. This allows an efficient estimate of giant monopole energies. Moreover, we have combined an exact shell-model-like approach with the mean-field calculation to describe pairing correlations in open-shell nuclei. All the ingredients were then put together to establish the calibration scheme. We have also extended the transformation between model parameters and pseudo data of nuclear matter within the RMF context. Performing calibration in this pseudo data space can not only facilitate the searching algorithm but also make the pseudo data genuine model predictions. This calibration scheme is also supplemented by a covariance analysis enabling us to extract the information content of a model, including theoretical uncertainties and correlation coefficients. A series of RMF models subject to the same isoscalar constraints but one differing isovector assumption were then created using this calibration scheme. By comparing their predictions of the nuclear matter equation of state to both experimental and theoretical constraints, we found that a small neutron skin of about 0.16 fm in Pb208 is favored, indicating that the symmetry energy should be soft. To obtain stronger evidence, we proceeded to examine the evolution of the isotopic chains in both oxygen and calcium. Again, it was found that the model with such small neutron skin and soft symmetry energy can best describe both isotopic
Relativistic mean-field models and nuclear matter constraints
Dutra, M.; Lourenco, O.; Carlson, B. V.; Delfino, A.; Menezes, D. P.; Avancini, S. S.; Stone, J. R.; Providencia, C.; Typel, S.
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear {sigma}{sup 3}+{sigma}{sup 4} models, (iii) {sigma}{sup 3}+{sigma}{sup 4}+{omega}{sup 4} models, (iv) models containing mixing terms in the fields {sigma} and {omega}, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the {sigma} ({omega}) field. The isospin dependence of the interaction is modeled by the {rho} meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Relativistic mean-field hadronic models under nuclear matter constraints
NASA Astrophysics Data System (ADS)
Dutra, M.; Lourenço, O.; Avancini, S. S.; Carlson, B. V.; Delfino, A.; Menezes, D. P.; Providência, C.; Typel, S.; Stone, J. R.
Background: The microscopic composition and properties of infinite hadronic matter at a wide range of densities and temperatures have been subjects of intense investigation for decades. The equation of state (EoS) relating pressure, energy density, and temperature at a given particle number density is essential for modeling compact astrophysical objects such as neutron stars, core-collapse supernovae, and related phenomena, including the creation of chemical elements in the universe. The EoS depends not only on the particles present in the matter, but, more importantly, also on the forces acting among them. Because a realistic and quantitative description of infinite hadronic matter and nuclei from first principles in not available at present, a large variety of phenomenological models has been developed in the past several decades, but the scarcity of experimental and observational data does not allow a unique determination of the adjustable parameters. Purpose: It is essential for further development of the field to determine the most realistic parameter sets and to use them consistently. Recently, a set of constraints on properties of nuclear matter was formed and the performance of 240 nonrelativistic Skyrme parametrizations was assessed [M. Dutra et al., Phys. Rev. C 85, 035201 (2012), 10.1103/PhysRevC.85.035201] in describing nuclear matter up to about three times nuclear saturation density. In the present work we examine 263 relativistic-mean-field (RMF) models in a comparable approach. These models have been widely used because of several important aspects not always present in nonrelativistic models, such as intrinsic Lorentz covariance, automatic inclusion of spin, appropriate saturation mechanism for nuclear matter, causality, and, therefore, no problems related to superluminal speed of sound in medium. Method: Three different sets of constraints related to symmetric nuclear matter, pure neutron matter, symmetry energy, and its derivatives were used. The
Hadronic matter at finite temperature and density within an effective relativistic mean-field model
NASA Astrophysics Data System (ADS)
Lavagno, A.
We study hot and dense hadronic matter by means of an effective relativistic mean-field model with the inclusion of the full octet of baryons, the Δ-isobar degrees of freedom and the lightest pseudoscalar and vector mesons. These last particles are considered by taking into account an effective chemical potential and an effective mass depending on the self-consistent interaction between baryons. The analysis is performed by requiring the Gibbs conditions on the global conservation of baryon number, electric charge fraction and zero net strangeness.
Cluster decay in very heavy nuclei in a relativistic mean field model
NASA Astrophysics Data System (ADS)
Bhattacharya, Madhubrata; Gangopadhyay, G.
Exotic cluster decay of very heavy nuclei was studied in the microscopic Super-Asymmetric Fission Model. The Relativistic Mean Field model with the force FSU Gold was employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction were used in the double folding model to obtain the potential between the cluster and the daughter. Half-life values were calculated in the WKB approximation and the spectroscopic factors were extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions were made for some possible decays.
Relativistic mean-field model with energy dependent self-energies
Antic, S.; Typel, S.
Conventional relativistic mean-field theory is extended with the introduction of higher-order derivative couplings of nucleons with the meson fields. The Euler-Lagrange equations follow from the principle of stationary action. From invariance principles of the Lagrangian density the most general expressions for the conserved current and energy-momentum tensor are derived. The nucleon self-energies show the explicit dependence on the meson fields. They contain additional regulator functions which describe the energy dependence. The density dependence of meson-nucleon couplings causes the apperance of additional rearrangement contributions in the self-energies. The equation of state of infinite nuclear matter is obtained and the thermodynamical consistency of the model is demonstrated. This model is applied to the description of spherical, non-rotating stars in β-equilibrium. Stellar structure is calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations. The results for neutron stars are shown in terms of mass-radius relations.
Building Relativistic Mean-Field Models for Atomic Nuclei and Neutron Stars
NASA Astrophysics Data System (ADS)
Chen, Wei-Chia; Piekarewicz, Jorge
Nuclear energy density functional (EDF) theory has been quite successful in describing nuclear systems such as atomic nuclei and nuclear matter. However, when building new models, attention is usually paid to the best-fit parameters only. In recent years, focus has been shifted to the neighborhood around the minimum of the chi-square function as well. This powerful covariance analysis is able to provide important information bridging experiments, observations, and theories. In this work, we attempt to build a specific type of nuclear EDFs, the relativistic mean-field models, which treat atomic nuclei, nuclear matter, and neutron stars on the same footing. The application of covariance analysis can reveal correlations between observables of interest. The purpose is to elucidate the alleged relations between the neutron skin of heavy nuclei and the size of neutron stars, and to develop insight into future investigations.
Nuclear reaction cross sections of exotic nuclei in the Glauber model for relativistic mean field densities
Patra, S. K.; Panda, R. N.; Arumugam, P.; Gupta, Raj K.
We have calculated the total nuclear reaction cross sections of exotic nuclei in the framework of the Glauber model, using as inputs the standard relativistic mean field (RMF) densities and the densities obtained from the more recently developed effective-field-theory-motivated RMF (the E-RMF). Both light and heavy nuclei are taken as the representative targets, and the light neutron-rich nuclei as projectiles. We found the total nuclear reaction cross section to increase as a function of the mass number, for both the target and projectile nuclei. The differential nuclear elastic scattering cross sections are evaluated for some selected systems at various incident energies. We found a large dependence of the differential elastic scattering cross section on incident energy. Finally, we have applied the same formalism to calculate both the total nuclear reaction cross section and the differential nuclear elastic scattering cross section for the recently discussed superheavy nucleus with atomic number Z=122.
Caloric curve for nuclear liquid-gas phase transition in relativistic mean-field hadronic model
NASA Astrophysics Data System (ADS)
Parvan, A. S.
The main thermodynamical properties of the first order phase transition of the relativistic mean-field (RMF) hadronic model were explored in the isobaric, the canonical and the grand canonical ensembles on the basis of the method of the thermodynamical potentials and their first derivatives. It was proved that the first order phase transition of the RMF model is the liquid-gas type one associated with the Gibbs free energy G. The thermodynamical potential G is the piecewise smooth function and its first order partial derivatives with respect to variables of state are the piecewise continuous functions. We have found that the energy in the caloric curve is discontinuous in the isobaric and the grand canonical ensembles at fixed values of the pressure and the chemical potential, respectively, and it is continuous, i.e. it has no plateau, in the canonical and microcanonical ensembles at fixed values of baryon density, while the baryon density in the isotherms is discontinuous in the isobaric and the canonical ensembles at fixed values of the temperature. The general criterion for the nuclear liquid-gas phase transition in the canonical ensemble was identified.
The effect of inclusion of Δ resonances in relativistic mean-field model with scaled hadron masses and coupling constants
NASA Astrophysics Data System (ADS)
Maslov, K. A.; Kolomeitsev, E. E.; Voskresensky, D. N.
Knowledge of the equation of state of the baryon matter plays a decisive role in the description of neutron stars. With an increase of the baryon density the filling of Fermi seas of hyperons and Δ isobars becomes possible. Their inclusion into standard relativistic mean-field models results in a strong softening of the equation of state and a lowering of the maximum neutron star mass below the measured values. We extend a relativistic mean-field model with scaled hadron masses and coupling constants developed in our previous works and take into account now not only hyperons but also the Δ isobars. We analyze available empirical information to put constraints on coupling constants of Δs to mesonic mean fields. We show that the resulting equation of state satisfies majority of presently known experimental constraints.
Ground State Properties of Z=126 Isotopes within the Relativistic Mean Field Model
NASA Astrophysics Data System (ADS)
Yu, Qi-Xin; Li, Jun-Qing; Zhang, Hong-Fei
The ground state properties of Z = 126 isotopes with neutron numbers N = 174-244 are calculated by the relativistic mean field (RMF) theory with effective interactions NL-Z2. In order to make a comprehensive understanding of the possible proton magic number Z = 126, we also perform the calculations in the vicinity of Z = 126, such as Z = 114,116,118,120,122,124,128 and 130 isotopic chains. The calculated results show there exist evident magicity for proton number Z = 120 and relatively weak magicity for proton number Z = 126. Supported by the National Natural Science Foundation of China under Grant Nos. 11675066, 11475050, 11265013, and the CAS Knowledge Innovation under Grant No. KJCX2-EW-N02
Vlasov formalism for extended relativistic mean field models: The crust-core transition and the stellar matter equation of state
NASA Astrophysics Data System (ADS)
Pais, Helena; Providência, Constança
The Vlasov formalism is extended to relativistic mean field hadron models with nonlinear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear ω ρ and σ ρ coupling terms on the crust-core transition density and pressure and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6 ±0.3 km and a crust thickness of 1.36 ±0.06 km for a 1.4 M⊙ star.
Relativistic mean field description of cluster radioactivity
NASA Astrophysics Data System (ADS)
Bhagwat, A.; Gambhir, Y. K.
Comprehensive investigations of the observed cluster radioactivity are carried out. First, the relativistic mean field (RMF) theory is employed for the calculations of the ground-state properties of relevant nuclei. The calculations reproduce the experiment well. The calculated RMF point densities are folded with the density-dependent M3Y nucleon-nucleon interaction to obtain the cluster-daughter interaction potential. This, along with the calculated and experimental Q values, is used in the WKB approximation for estimating the half-lives of the parent nuclei against cluster decay. The calculations qualitatively agree with the experiment. Sensitive dependence of the half-lives on Q values is explicitly demonstrated.
Investigation of the Mg isotopes using the shell-model-like approach in relativistic mean field theory
NASA Astrophysics Data System (ADS)
Bai, Hong-Bo; Zhang, Zhen-Hua; Li, Xiao-Wei
Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations. Supported by NSFC (11465001,11275098, 11275248, 11505058,11165001) and Natural Science Foundation of Inner Mongolia of China (2016BS0102)
Application of the relativistic mean-field mass model to the r-process and the influence of mass uncertainties
Sun, B.; Montes, F.; Geng, L. S.; Geissel, H.; Litvinov, Yu. A.; Meng, J.
A new mass table calculated by the relativistic mean-field approach with the state-dependent BCS method for the pairing correlation is applied for the first time to study r-process nucleosynthesis. The solar r-process abundance is well reproduced within a waiting-point approximation approach. Using an exponential fitting procedure to find the required astrophysical conditions, the influence of mass uncertainty is investigated. The r-process calculations using the FRDM, ETFSI-Q, and HFB-13 mass tables have been used for that purpose. It is found that the nuclear physical uncertainty can significantly influence the deduced astrophysical conditions for the r-process site. In addition, the influence of the shell closure and shape transition have been examined in detail in the r-process simulations.
Beyond the relativistic mean-field approximation -- collective correlations
NASA Astrophysics Data System (ADS)
Li, Zhipan; Nikšić, Tamara; Vretenar, Dario; Yao, Jiangming
Semi-empirical relativistic energy density functionals (EDFs) or effective interactions implicitly comprise short-range correlations related to the repulsive core of the inter-nucleon interaction, and long-range correlations mediated by nuclear resonance modes. To model spectroscopic properties of finite nuclei, the self-consistent mean-field method must be extended to include collective correlations that arise from restoration of broken symmetries and fluctuations in collective coordinates. These correlations are sensitive to shell effects, vary with particle number, and cannot be included in a universal EDF. We review and compare recent advances in "beyond mean-field" methods based on relativistic EDFs: the angular-momentum and particle-number projected triaxial generator coordinate method, the five-dimensional quadrupole collective Hamiltonian and the axial quadrupole-octupole collective Hamiltonian models. Illustrative applications include low-energy collective excitation spectra and electromagnetic transition rates of nuclei characterised by quadrupole and/or octupole deformations: 24Mg, 76Kr, 240Pu and 224Ra, in comparison with available data.
NASA Astrophysics Data System (ADS)
Chavanis, Pierre-Henri
We discuss the dynamics and thermodynamics of the Brownian mean field (BMF) model which is a system of N Brownian particles moving on a circle and interacting via a cosine potential. It can be viewed as the canonical version of the Hamiltonian mean field (HMF) model. The BMF model displays a second order phase transition from a homogeneous phase to an inhomogeneous phase below a critical temperature T c = 1 / 2. We first complete the description of this model in the mean field approximation valid for N → +∞. In the strong friction limit, the evolution of the density towards the mean field Boltzmann distribution is governed by the mean field Smoluchowski equation. For T < T c , this equation describes a process of self-organization from a non-magnetized (homogeneous) phase to a magnetized (inhomogeneous) phase. We obtain an analytical expression for the temporal evolution of the magnetization close to T c . Then, we take fluctuations (finite N effects) into account. The evolution of the density is governed by the stochastic Smoluchowski equation. From this equation, we derive a stochastic equation for the magnetization and study its properties both in the homogenous and inhomogeneous phase. We show that the fluctuations diverge at the critical point so that the mean field approximation ceases to be valid. Actually, the limits N → +∞ and T → T c do not commute. The validity of the mean field approximation requires N( T - T c ) → +∞ so that N must be larger and larger as T approaches T c . We show that the direction of the magnetization changes rapidly close to T c while its amplitude takes a long time to relax. We also indicate that, for systems with long-range interactions, the lifetime of metastable states scales as e N except close to a critical point. The BMF model shares many analogies with other systems of Brownian particles with long-range interactions such as self-gravitating Brownian particles, the Keller-Segel model describing the chemotaxis
Relativistic mean field calculations in neutron-rich nuclei
Gangopadhyay, G.; Bhattacharya, Madhubrata; Roy, Subinit
Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.
Finite- to zero-range relativistic mean-field interactions
Niksic, T.; Vretenar, D.; Lalazissis, G. A.; Ring, P.
We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the {sigma}-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.
Symmetry energy of cold nucleonic matter within a relativistic mean field model encapsulating effects of high-momentum nucleons induced by short-range correlations
NASA Astrophysics Data System (ADS)
Cai, Bao-Jun; Li, Bao-An
It is well known that short-range nucleon-nucleon correlations (SRC) from the tensor components and/or the repulsive core of nuclear forces lead to a high- (low-)momentum tail (depletion) in the single-nucleon momentum distribution above (below) the nucleon Fermi surface in cold nucleonic matter. Significant progress was made recently in constraining the isospin-dependent parameters characterizing the SRC-modified single-nucleon momentum distribution in neutron-rich nucleonic matter using both experimental data and microscopic model calculations. Using the constrained single-nucleon momentum distribution in a nonlinear relativistic mean field (RMF) model, we study the equation of state (EOS) of asymmetric nucleonic matter (ANM), especially the density dependence of nuclear symmetry energy Esym(ρ ) . First, as a test of the model, the average nucleon kinetic energy extracted recently from electron-nucleus scattering experiments using a neutron-proton dominance model is well reproduced by the RMF model incorporating effects of the SRC-induced high-momentum nucleons, while it is significantly under predicted by the RMF model using a step function for the single-nucleon momentum distribution as in free Fermi gas (FFG) models. Second, consistent with earlier findings within nonrelativistic models, the kinetic symmetry energy of quasinucleons is found to be Esymkin(ρ0) =-16.94 ±13.66 MeV which is dramatically different from the prediction of Esymkin(ρ0) ≈12.5 MeV by FFG models at nuclear matter saturation density ρ0=0.16 fm-3 . Third, comparing the RMF calculations with and without the high-momentum nucleons using two sets of model parameters both reproducing identically all empirical constraints on the EOS of symmetric nuclear matter (SNM) and the symmetry energy of ANM at ρ0, the SRC-modified single-nucleon momentum distribution is found to make the Esym(ρ ) more concave around ρ0 by softening it significantly at both subsaturation and suprasaturation
Minimization method for relativistic electrons in a mean-field approximation of quantum electrodynamics
Hainzl, Christian; Lewin, Mathieu; Sere, Eric; Solovej, Jan Philip
We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles such as electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the photon field. All our results are nonperturbative and mathematically rigorous.
Hot and dense matter beyond relativistic mean field theory
NASA Astrophysics Data System (ADS)
Zhang, Xilin; Prakash, Madappa
Properties of hot and dense matter are calculated in the framework of quantum hadrodynamics by including contributions from two-loop (TL) diagrams arising from the exchange of isoscalar and isovector mesons between nucleons. Our extension of mean field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of isospin-symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in the study of core-collapse supernovae, young and old neutron stars, and mergers of compact binary stars. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for cold and β -equilibrated neutron-star matter is substantially softer than its MFT counterpart, it is able to support a 2 M⊙ neutron star required by recent precise determinations. In addition, radii of 1.4 M⊙ stars are smaller by ˜1 km than those obtained in MFT and lie in the range indicated by analysis of astronomical data. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as Γth=1 +(Pth/ɛth) , often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of Γth at supranuclear density found in MFT is, however, suppressed in
Nuclear matter properties in the relativistic mean-field theory at finite temperature with interaction between sigma-omega mesons
Costa, R. S.; Duarte, S. B.; Oliveira, J. C. T.; Chiapparini, M.
We study the nuclear matter properties in the regime of high temperatures using a relativistic mean-field theory. Contrasting with the usual linear Walecka model, we include the sigma-omega meson coupling in order to investigate the role of this interaction in the nucleon effective mass behavior. Some numerical results are presented and discussed.
K--nucleus relativistic mean field potentials consistent with kaonic atoms
NASA Astrophysics Data System (ADS)
Friedman, E.; Gal, A.; Mareš, J.; Cieplý, A.
K- atomic data are used to test several models of the K- nucleus interaction. The t(ρ)ρ optical potential, due to coupled channel models incorporating the Λ(1405) dynamics, fails to reproduce these data. A standard relativistic mean field (RMF) potential, disregarding the Λ(1405) dynamics at low densities, also fails. The only successful model is a hybrid of a theoretically motivated RMF approach in the nuclear interior and a completely phenomenological density dependent potential, which respects the low density theorem in the nuclear surface region. This best-fit K- optical potential is found to be strongly attractive, with a depth of 180+/-20 MeV at the nuclear interior, in agreement with previous phenomenological analyses.
Systematic nuclear structure studies using relativistic mean field theory in mass region A ˜ 130
NASA Astrophysics Data System (ADS)
Shukla, A.; Åberg, Sven; Bajpeyi, Awanish
Nuclear structure studies for even-even nuclei in the mass region \\backsim 130, have been performed, with a special focus around N or Z = 64. On the onset of deformation and lying between two closed shell, these nuclei have attracted attention in a number of studies. A revisit to these experimentally accessible nuclei has been made via the relativistic mean field. The role of pairing and density depletion in the interior has been specially investigated. Qualitative analysis between two versions of relativistic mean field suggests that there is no significant difference between the two approaches. Moreover, the role of the filling {{{s}}}1/2 orbital in density depletion towards the centre has been found to be consistent with our earlier work on the subject Shukla and Åberg (2014 Phys. Rev. C 89 014329).
Application of relativistic mean field and effective field theory densities to scattering observables for Ca isotopes
Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.
In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for {sup 40,42,44,48}Ca with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+{sup 40,42,44,48}Ca systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.
Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state
NASA Astrophysics Data System (ADS)
Kumar, Bharat; Biswal, S. K.; Patra, S. K.
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various Love numbers kl(l =2 ,3 ,4 ), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through an advanced LIGO detector from the final stages of an inspiraling binary neutron star merger.
Extended Chiral ({sigma},{pi},{omega}) Mean-Field Model with Vacuum Fluctuation Corrections
Uechi, Schun T.; Uechi, Hiroshi
Density-dependent relations among saturation properties of symmetric nuclear matter and properties of hadronic stars are discussed by applying the conserving chiral nonlinear ({sigma},{pi},{omega}) mean-field theory. The chiral nonlinear ({sigma},{pi},{omega}) mean-field theory is an extension of the conserving nonlinear (nonchiral){sigma}-{omega} mean-field theory, which is thermodynamically consistent, relativistic and Lorentz-covariant. In the extended chiral ({sigma},{pi},{omega}) mean-field model, all the masses of hadrons are produced by the spontaneous chiral symmetry breaking, which is different from conventional chiral partner models. By comparing both nonchiral and chiral mean-field approximations, the effects of the chiral symmetry breaking mechanism on the mass of {sigma}-meson, coefficients of nonlinear interactions and Fermi-liquid properties are investigated in nuclear matter and neutron stars.
Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides
NASA Astrophysics Data System (ADS)
Zhao, Jie; Lu, Bing-Nan; Vretenar, Dario; Zhao, En-Guang; Zhou, Shan-Gui
Background: Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier, the occurrence of a third barrier was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by a number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density functional theory (CDFT). Methods: Calculations are performed using the multidimensionally constrained relativistic mean field (MDC-RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES's of 226,228,230,232Th and 232,235,236,238U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and 238U . The third minima in 230 ,232Th are very shallow, whereas those in 226 ,228Th and 238U are quite prominent. With the functional PC-PK1 a third barrier is found only in 226 ,228 ,230Th . Single-nucleon levels around the Fermi surface are analyzed in 226Th, and it is found that the formation of the third minimum is mainly due to the Z =90 proton energy gap at β20≈1.5 and β30≈0.7 . Conclusions: The possible occurrence of a third barrier on the PES's of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases
Dynamical mean field solution of the Bose-Hubbard model.
Anders, Peter; Gull, Emanuel; Pollet, Lode; Troyer, Matthias; Werner, Philipp
We present the effective action and self-consistency equations for the bosonic dynamical mean field approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations, we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.
Mean-field fluid behavior of the gaussian core model
Louis; Bolhuis; Hansen
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated "mean-field fluid" over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.
The authors discuss and apply extensions needed to treat multiblock copolymers within the mean field theoretical framework for microphase separation in diblock copolymer metals, originally due to Leibler. The mean field calculations are complemented by lattice Monte Carlo realizations using the bond fluctuation model. They find that the microphase separation transition occurs at larger {sub {chi}}N as the number of blocks in increased beyond two (i.e., beyond diblock), and that the characteristic length scale of the emerging morphology decreases as the number of blocks increases. The latter prediction is in qualitative agreement with published experimental results due to Sontak and co-workers for model multiblock poly(styrene-isoprene) systems and recent results due to Hjelm and co-workers for a segmented poly(ester-urethane) relevant to Los Alamos interests. Additionally, the mean field predictions and bond fluctuation realizations yield consistent results.
Magnetic and antimagnetic rotation in 110Cd within tilted axis cranking relativistic mean-field theory
NASA Astrophysics Data System (ADS)
Peng, J.; Zhao, P. W.
The self-consistent tilted axis cranking relativistic mean-field (TAC-RMF) theory based on a point-coupling interaction is applied to investigate the observed magnetic and antimagnetic rotations in the nucleus 110Cd . The energy spectra, the relation between the spin and the rotational frequency, the deformation parameters, and the reduced M 1 and E 2 transition probabilities are studied with the various configurations. It is found that the configuration has to be changed to reproduce the energy spectra and the relations between the spin and the rotational frequency for both the magnetic and antimagnetic rotational bands. The shears mechanism for the magnetic rotation and the two-shears-like mechanism for the antimagnetic rotation are examined by investigating the orientation of the neutron and proton angular momenta. The calculated electromagnetic transitions B (M 1 ) and B (E 2 ) are in reasonable agreement with the data, and their tendencies are coincident with the typical characteristics of the magnetic and antimagnetic rotations.
Incorporating spatial correlations into multispecies mean-field models
NASA Astrophysics Data System (ADS)
Markham, Deborah C.; Simpson, Matthew J.; Maini, Philip K.; Gaffney, Eamonn A.; Baker, Ruth E.
In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modeling interactions between such species, we often make use of the mean-field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean-field approximation is only used in appropriate settings. In circumstances where the mean-field approximation is unsuitable, we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper, we provide a method that overcomes many of the failures of the mean-field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multispecies case and show results specific to a two-species problem. We compare averaged discrete results to both the mean-field approximation and our improved method, which incorporates spatial correlations. We note that the mean-field approximation fails dramatically in some cases, predicting very different behavior from that seen upon averaging multiple realizations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behavior in all cases, thus providing a more reliable modeling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.
Second relativistic mean field and virial equation of state for astrophysical simulations
Shen, G.; Horowitz, C. J.; O'Connor, E.
We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the virial expansion of a nonideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100 000 grid points in the temperature range T=0 to 80 MeV, the density range n{sub B}=10{sup -8} to 1.6 fm{sup -3}, and the proton fraction range Y{sub p}=0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3-based EOS, and previous EOSs by Lattimer-Swesty and H. Shen et al. for the thermodynamic properties, composition, and neutron star structure. The original FSUGold interaction produces an EOS, which we call FSU1.7, that has a maximum neutron star mass of 1.7 solar masses. A modification in the high-density EOS is introduced to increase the maximum neutron star mass to 2.1 solar masses and results in a slightly different EOS that we call FSU2.1. The EOS tables for FSU1.7 and FSU2.1 are available for download.
Asymptotics of Mean-Field O( N) Models
NASA Astrophysics Data System (ADS)
Kirkpatrick, Kay; Nawaz, Tayyab
We study mean-field classical N-vector models, for integers N≥2. We use the theory of large deviations and Stein's method to study the total spin and its typical behavior, specifically obtaining non-normal limit theorems at the critical temperatures and central limit theorems away from criticality. Important special cases of these models are the XY (N=2) model of superconductors, the Heisenberg (N=3) model [previously studied in Kirkpatrick and Meckes (J Stat Phys 152:54-92, 2013) but with a correction to the critical distribution here], and the Toy (N=4) model of the Higgs sector in particle physics.
Simulated Tempering and Swapping on Mean-Field Models
NASA Astrophysics Data System (ADS)
Bhatnagar, Nayantara; Randall, Dana
Simulated and parallel tempering are families of Markov Chain Monte Carlo algorithms where a temperature parameter is varied during the simulation to overcome bottlenecks to convergence due to multimodality. In this work we introduce and analyze the convergence for a set of new tempering distributions which we call entropy dampening. For asymmetric exponential distributions and the mean field Ising model with an external field simulated tempering is known to converge slowly. We show that tempering with entropy dampening distributions mixes in polynomial time for these models. Examining slow mixing times of tempering more closely, we show that for the mean-field 3-state ferromagnetic Potts model, tempering converges slowly regardless of the temperature schedule chosen. On the other hand, tempering with entropy dampening distributions converges in polynomial time to stationarity. Finally we show that the slow mixing can be very expensive practically. In particular, the mixing time of simulated tempering is an exponential factor longer than the mixing time at the fixed temperature.
A Monte Carlo investigation of the Hamiltonian mean field model
NASA Astrophysics Data System (ADS)
Pluchino, Alessandro; Andronico, Giuseppe; Rapisarda, Andrea
We present a Monte Carlo numerical investigation of the Hamiltonian mean field (HMF) model. We begin by discussing canonical Metropolis Monte Carlo calculations, in order to check the caloric curve of the HMF model and study finite size effects. In the second part of the paper, we present numerical simulations obtained by means of a modified Monte Carlo procedure with the aim to test the stability of those states at minimum temperature and zero magnetization (homogeneous Quasi stationary states), which exist in the condensed phase of the model just below the critical point. For energy densities smaller than the limiting value U∼0.68, we find that these states are unstable confirming a recent result on the Vlasov stability analysis applied to the HMF model.
Topological properties of the mean-field ϕ4 model
NASA Astrophysics Data System (ADS)
Andronico, A.; Angelani, L.; Ruocco, G.; Zamponi, F.
We study the thermodynamics and the properties of the stationary points (saddles and minima) of the potential energy for a ϕ4 mean-field model. We compare the critical energy vc [i.e., the potential energy v(T) evaluated at the phase transition temperature Tc ] with the energy vθ at which the saddle energy distribution show a discontinuity in its derivative. We find that, in this model, vc≫vθ , at variance to what has been found in different mean-field and short ranged systems, where the thermodynamic phase transitions take place at vc=vθ [Casetti, Pettini and Cohen, Phys. Rep. 337, 237 (2000)]. By direct calculation of the energy vs(T) of the "inherent saddles," i.e., the saddles visited by the equilibrated system at temperature T , we find that vs(Tc)˜vθ . Thus, we argue that the thermodynamic phase transition is related to a change in the properties of the inherent saddles rather than to a change of the topology of the potential energy surface at T=Tc . Finally, we discuss the approximation involved in our analysis and the generality of our method.
The Thermodynamic Limit in Mean Field Spin Glass Models
NASA Astrophysics Data System (ADS)
Guerra, Francesco; Toninelli, Fabio Lucio
We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N1 and N2 sites, respectively, with N1+N2=N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site.
Relativistic Energy Density Functionals: beyond mean-field description of exotic structures
Vretenar, D.; Niksic, T.; Ring, P.; Lalazissis, G. A.
The framework of relativistic energy density functionals is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. This approach enables a quantitative description of the evolution of shell-structure, deformation and shape coexistence phenomena in nuclei with soft potential energy surfaces, and singular properties of excitation spectra and transition rates at critical points of quantum shape phase transitions.
Mean-field vs. Stochastic Models for Transcriptional Regulation
NASA Astrophysics Data System (ADS)
Blossey, Ralf; Giuraniuc, Claudiu
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: the repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
Mean-field versus stochastic models for transcriptional regulation
NASA Astrophysics Data System (ADS)
Blossey, R.; Giuraniuc, C. V.
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ODE's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results that both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: The repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
Classical mutual information in mean-field spin glass models
NASA Astrophysics Data System (ADS)
Alba, Vincenzo; Inglis, Stephen; Pollet, Lode
We investigate the classical Rényi entropy Sn and the associated mutual information In in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and analytical tools we investigate the S-K model in the n -sheet booklet. This is achieved by gluing together n independent copies of the model, and it is the main ingredient for constructing the Rényi entanglement-related quantities. We find a glassy phase at low temperatures, whereas at high temperatures the model exhibits paramagnetic behavior, consistent with the regular S-K model. The temperature of the paramagnetic-glassy transition depends nontrivially on the geometry of the booklet. At high temperatures we provide the exact solution of the model by exploiting the replica symmetry. This is the permutation symmetry among the fictitious replicas that are used to perform disorder averages (via the replica trick). In the glassy phase the replica symmetry has to be broken. Using a generalization of the Parisi solution, we provide analytical results for Sn and In and for standard thermodynamic quantities. Both Sn and In exhibit a volume law in the whole phase diagram. We characterize the behavior of the corresponding densities, Sn/N and In/N , in the thermodynamic limit. Interestingly, at the critical point the mutual information does not exhibit any crossing for different system sizes, in contrast with local spin models.
First principles based mean field model for oxygen reduction reaction.
Jinnouchi, Ryosuke; Kodama, Kensaku; Hatanaka, Tatsuya; Morimoto, Yu
A first principles-based mean field model was developed for the oxygen reduction reaction (ORR) taking account of the coverage- and material-dependent reversible potentials of the elementary steps. This model was applied to the simulation of single crystal surfaces of Pt, Pt alloy and Pt core-shell catalysts under Ar and O(2) atmospheres. The results are consistent with those shown by past experimental and theoretical studies on surface coverages under Ar atmosphere, the shape of the current-voltage curve for the ORR on Pt(111) and the material-dependence of the ORR activity. This model suggests that the oxygen associative pathway including HO(2)(ads) formation is the main pathway on Pt(111), and that the rate determining step (RDS) is the removal step of O(ads) on Pt(111). This RDS is accelerated on several highly active Pt alloys and core-shell surfaces, and this acceleration decreases the reaction intermediate O(ads). The increase in the partial pressure of O(2)(g) increases the surface coverage with O(ads) and OH(ads), and this coverage increase reduces the apparent reaction order with respect to the partial pressure to less than unity. This model shows details on how the reaction pathway, RDS, surface coverages, Tafel slope, reaction order and material-dependent activity are interrelated.
Multiagent model and mean field theory of complex auction dynamics
NASA Astrophysics Data System (ADS)
Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng
Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner's attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.
Quark mean field model with pion and gluon corrections
NASA Astrophysics Data System (ADS)
Xing, Xueyong; Hu, Jinniu; Shen, Hong
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, mq, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around 2.3 M⊙ without hyperon degrees of freedom.
Relativistic mean-field study of the properties of Z=117 nuclei and the decay chains of the {sup 293,294}117 isotopes
Bhuyan, M.; Patra, S. K.; Gupta, Raj K.
We have calculated the binding energy, root-mean-square radius, and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean-field (RMF) model. The calculation is extended to various isotopes of the Z=117 element, starting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from a prolate to an oblate shape structure of the Z=117 nucleus in our mean-field approach. The most stable isotope (largest binding energy per nucleon) is found to be the {sup 288}117 nucleus. Also, the Q{sub {alpha}} values and the half-life T{sub 1/2}{sup {alpha}} for the {alpha}-decay chains of {sup 293}117 and {sup 294}117 are calculated, supporting the magic numbers at N=172 and/or 184.
Study of high-energy heavy-ion collisions in a relativistic BUU approach with momentum-dependent mean fields
NASA Astrophysics Data System (ADS)
Tomoyuki, Maruyama; Wolfgang, Cassing; Ulrich, Mosel; Stefan, Teis; Klaus, Weber
We introduce momentum-dependent scalar and vector fields into the Lorentz covariant relativistic BUU (RBUU) approach employing a polynomial ansatz for the relativistic nucleon-nucleon interaction. The momentum-dependent parametrizations are shown to be valid up to about 1 GeV/u for the empirical proton-nucleus optical potential. We perform numerical simulations for heavy-ion collisions within the RBUU approach adopting momentum-dependent and momentum-independent mean fields and calculate the transverse flow in and perpendicular to the reaction plane, the directivity distribution as well as subthreshold K +-production. By means of these observables we discuss the particular role of the momentum-dependent forces and their implications on the nuclear equation of state. We find that only a momentum-dependent parameter set can explain the experimental data on the transverse flow in the reaction plane from 150-1000 MeV/u and the differential K +-production cross sections at 1 GeV/u at the same time.
Neural Population Dynamics Modeled by Mean-Field Graphs
NASA Astrophysics Data System (ADS)
Kozma, Robert; Puljic, Marko
In this work we apply random graph theory approach to describe neural population dynamics. There are important advantages of using random graph theory approach in addition to ordinary and partial differential equations. The mathematical theory of large-scale random graphs provides an efficient tool to describe transitions between high- and low-dimensional spaces. Recent advances in studying neural correlates of higher cognition indicate the significance of sudden changes in space-time neurodynamics, which can be efficiently described as phase transitions in the neuropil medium. Phase transitions are rigorously defined mathematically on random graph sequences and they can be naturally generalized to a class of percolation processes called neuropercolation. In this work we employ mean-field graphs with given vertex degree distribution and edge strength distribution. We demonstrate the emergence of collective oscillations in the style of brains.
Deformed neutron stars due to strong magnetic field in terms of relativistic mean field theories
NASA Astrophysics Data System (ADS)
Yanase, Kota; Yoshinaga, Naotaka
Some observations suggest that magnetic field intensity of neutron stars that have particularly strong magnetic field, magnetars, reaches values up to 1014-15G. It is expected that there exists more strong magnetic field of several orders of magnitude in the interior of such stars. Neutron star matter is so affected by magnetic fields caused by intrinsic magnetic moments and electric charges of baryons that masses of neutron stars calculated by using Tolman-Oppenheimer-Volkoff equation is therefore modified. We calculate equation of state (EOS) in density-dependent magnetic field by using sigma-omega-rho model that can reproduce properties of stable nuclear matter in laboratory Furthermore we calculate modified masses of deformed neutron stars.
Density-Dependent Properties of Hadronic Matter in the self-consistent Chiral ({sigma},{pi},{omega}) Mean-Field Model
Uechi, Schun T.; Uechi, Hiroshi
Density-dependent relations among saturation properties of symmetric nuclear matter and properties of hadronic stars are discussed by applying the conserving chiral nonlinear ({sigma},{pi},{omega}) hadronic mean-field theory. The chiral nonlinear ({sigma},{pi},{omega}) mean-field theory is an extension of the conserving nonlinear (nonchiral) {sigma}-{omega} hadronic mean-field theory which is thermodynamically consistent, relativistic and is a Lorentz-covariant mean-field theory of hadrons. In the extended chiral ({sigma},{pi},{omega}) mean-field model, all the masses of hadrons are produced by the breaking of chiral symmetry, which is different from other conventional chiral partner models. By comparing both nonchiral and chiral mean-field approximations, the effects of the chiral symmetry breaking mechanism on the mass of {sigma}-meson, coefficients of nonlinear interactions and Fermi-liquid properties are investigated in nuclear matter and neutron stars.
Bound-state energy of double magic number plus one nucleon nuclei with relativistic mean-field approach
NASA Astrophysics Data System (ADS)
Mousavi, M.; Shojaei, M. R.
In this work, we have obtained energy levels and charge radius for the β-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magic number and a single nucleon energy level. Here we have taken 41Ca with a single neutron in the 40Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the core and the single nucleon. By using parametric Nikiforov-Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for 17O, 41Ca, 49Ca and 57Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.
Mean-Field Models of Structure and Dispersion of Polymer-nanoparticle Mixtures
bare polymer matrix by as much as an order of magnitude.2,3,12–14 Gas barrier properties of butyl rubber latexes was shown to be reduced by almost 2...research developments in coarse-grained modeling based on mean-field approaches of the equilibrium dispersion and structure of polymer nanoparticle...polymernanoparticle mixtures Report Title ABSTRACT We review some recent research developments in coarse-grained modeling based on mean-field approaches of the
We study the sign problem of the fermion determinant at nonzero baryon chemical potential. For this purpose we apply a simple model derived from Quantum Chromodynamics, in the limit of large chemical potential and mass. For SU(2) color, there is no sign problem and the mean-field approximation is similar to data from the lattice. For SU(3) color the sign problem is unavoidable, even in a mean-field approximation. We apply a phase-reweighting method, combined with the mean-field approximation, to estimate thermodynamic quantities. We also investigate the meanfield free energy using a saddle-point approximation [1].
a Mean-Field Version of the Ssb Model for X-Chromosome Inactivation
NASA Astrophysics Data System (ADS)
Gaeta, Giuseppe
Nicodemi and Prisco recently proposed a model for X-chromosome inactivation in mammals, explaining this phenomenon in terms of a spontaneous symmetry-breaking mechanism [{\\it Phys. Rev. Lett.} 99 (2007), 108104]. Here we provide a mean-field version of their model.
Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons.
Nicola, Wilten; Campbell, Sue Ann
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presence of heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons.
Magnetohydrodynamic Simulation-driven Kinematic Mean Field Model of the Solar Cycle
NASA Astrophysics Data System (ADS)
Simard, Corinne; Charbonneau, Paul; Bouchat, Amélie
We construct a series of kinematic axisymmetric mean-field dynamo models operating in the αΩ, α2Ω and α2 regimes, all using the full α-tensor extracted from a global magnetohydrodynamical simulation of solar convection producing large-scale magnetic fields undergoing solar-like cyclic polarity reversals. We also include an internal differential rotation profile produced in a purely hydrodynamical parent simulation of solar convection, and a simple meridional flow profile described by a single cell per meridional quadrant. An α2Ω mean-field model, presumably closest to the mode of dynamo action characterizing the MHD simulation, produces a spatiotemporal evolution of magnetic fields that share some striking similarities with the zonally-averaged toroidal component extracted from the simulation. Comparison with α2 and αΩ mean-field models operating in the same parameter regimes indicates that much of the complexity observed in the spatiotemporal evolution of the large-scale magnetic field in the simulation can be traced to the turbulent electromotive force. Oscillating α2 solutions are readily produced, and show some similarities with the observed solar cycle, including a deep-seated toroidal component concentrated at low latitudes and migrating equatorward in the course of the solar cycle. Various numerical experiments performed using the mean-field models reveal that turbulent pumping plays an important role in setting the global characteristics of the magnetic cycles.
Simard, Corinne; Charbonneau, Paul; Bouchat, Amelie E-mail: firstname.lastname@example.com
We construct a series of kinematic axisymmetric mean-field dynamo models operating in the {alpha}{Omega}, {alpha}{sup 2}{Omega} and {alpha}{sup 2} regimes, all using the full {alpha}-tensor extracted from a global magnetohydrodynamical simulation of solar convection producing large-scale magnetic fields undergoing solar-like cyclic polarity reversals. We also include an internal differential rotation profile produced in a purely hydrodynamical parent simulation of solar convection, and a simple meridional flow profile described by a single cell per meridional quadrant. An {alpha}{sup 2}{Omega} mean-field model, presumably closest to the mode of dynamo action characterizing the MHD simulation, produces a spatiotemporal evolution of magnetic fields that share some striking similarities with the zonally-averaged toroidal component extracted from the simulation. Comparison with {alpha}{sup 2} and {alpha}{Omega} mean-field models operating in the same parameter regimes indicates that much of the complexity observed in the spatiotemporal evolution of the large-scale magnetic field in the simulation can be traced to the turbulent electromotive force. Oscillating {alpha}{sup 2} solutions are readily produced, and show some similarities with the observed solar cycle, including a deep-seated toroidal component concentrated at low latitudes and migrating equatorward in the course of the solar cycle. Various numerical experiments performed using the mean-field models reveal that turbulent pumping plays an important role in setting the global characteristics of the magnetic cycles.
Model-independent mean-field theory as a local method for approximate propagation of information.
Haft, M; Hofmann, R; Tresp, V
We present a systematic approach to mean-field theory (MFT) in a general probabilistic setting without assuming a particular model. The mean-field equations derived here may serve as a local, and thus very simple, method for approximate inference in probabilistic models such as Boltzmann machines or Bayesian networks. Our approach is 'model-independent' in the sense that we do not assume a particular type of dependences; in a Bayesian network, for example, we allow arbitrary tables to specify conditional dependences. In general, there are multiple solutions to the mean-field equations. We show that improved estimates can be obtained by forming a weighted mixture of the multiple mean-field solutions. Simple approximate expressions for the mixture weights are given. The general formalism derived so far is evaluated for the special case of Bayesian networks. The benefits of taking into account multiple solutions are demonstrated by using MFT for inference in a small and in a very large Bayesian network. The results are compared with the exact results.
Going Beyond a Mean-field Model for the Learning Cortex: Second-Order Statistics
Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.
Mean-field models of the cortex have been used successfully to interpret the origin of features on the electroencephalogram under situations such as sleep, anesthesia, and seizures. In a mean-field scheme, dynamic changes in synaptic weights can be considered through fluctuation-based Hebbian learning rules. However, because such implementations deal with population-averaged properties, they are not well suited to memory and learning applications where individual synaptic weights can be important. We demonstrate that, through an extended system of equations, the mean-field models can be developed further to look at higher-order statistics, in particular, the distribution of synaptic weights within a cortical column. This allows us to make some general conclusions on memory through a mean-field scheme. Specifically, we expect large changes in the standard deviation of the distribution of synaptic weights when fluctuation in the mean soma potentials are large, such as during the transitions between the "up" and "down" states of slow-wave sleep. Moreover, a cortex that has low structure in its neuronal connections is most likely to decrease its standard deviation in the weights of excitatory to excitatory synapses, relative to the square of the mean, whereas a cortex with strongly patterned connections is most likely to increase this measure. This suggests that fluctuations are used to condense the coding of strong (presumably useful) memories into fewer, but dynamic, neuron connections, while at the same time removing weaker (less useful) memories. PMID:19669541
A self-consistent mean-field model for polyelectrolyte gels.
Rud, Oleg; Richter, Tobias; Borisov, Oleg; Holm, Christian; Košovan, Peter
We present a novel approach to modeling polyelectrolyte gels, exploiting the analogy between star-branched polymers and polymer networks as a computationally inexpensive yet reliable alternative to full-scale simulations. In the numerical mean-field model of a star-like polymer we modify the boundary conditions to represent an infinite network. We validate the predictions of our new model against a coarse-grained simulation model. We also validate it against a phenomenological analytical model which has been previously shown to agree with simulations in a limited range of parameters. The mean-field model explicitly considers local density gradients and agrees with the simulation results in a broad range of parameters, beyond that of the analytical model. Finally, we use the mean-field model for predictions of the swelling behaviour of weak polyelectrolyte gels under different pH conditions. We demonstrate that the local density gradients are important and that the ionization of the weak polyelectrolyte gel is significantly suppressed. Under the studied conditions the effective pKA is about one unit higher than that of the free monomer. This shift in the effective pKA stems from the different pH values inside and outside the gel.
Exact solution of the mean-field plus separable pairing model reexamined
NASA Astrophysics Data System (ADS)
Pan, Feng; Zhou, Dan; Dai, Lianrong; Draayer, J. P.
Exact solution of the nuclear mean-field plus separable pairing model is reexamined. New auxiliary constraints for solving the Bethe ansatz equations of the model are proposed. By using these auxiliary constraints, the Bethe ansatz form of eigenvectors of the mean-field plus separable pairing Hamiltonian with nondegenerate single-particle energies and nondegenerate separable pairing strengths purposed previously is verified. Since the solutions of the model with one- and two-orbit cases are known, verification of the solutions for these two special cases is made. To demonstrate structure and features of the solution, the model with three orbits in the d s shell is taken as a nontrivial example, of which two-pair results and the ground state of the three-pair case are provided explicitly. Since the number of equations involved increases with the number of orbits and pairs, to solve these equations for a large number of orbits and pairs seems still difficult.
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.
Szabó-Solticzky, András; Berthouze, Luc; Kiss, Istvan Z; Simon, Péter L
An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models.
Mean field theory of the linear sigma-model: Chiral solitons
NASA Astrophysics Data System (ADS)
Kahana, S.; Ripka, G.
The mean field theory of the chiral invariant sigma-model is outlined. Bound states (solitons) of valence quarks are obtained self-consistently using a hedgehog shape for the pion field. A schematic model for the coupled fermion-boson fields is presented. Renormalization is worked out for the fermion one-loop corrections and numerical results presented for the purely scalar-field case. The interpretation of the baryon number of the perturbed vacuum is considered.
Phase transition in a mean-field model for sympatric speciation
NASA Astrophysics Data System (ADS)
Schwämmle, V.; Luz-Burgoa, K.; Sá Martins, J. S.; de Oliveira, S. Moss
We introduce an analytical model for population dynamics with intra-specific competition, mutation and assortative mating as basic ingredients. The set of equations that describes the time evolution of population size in a mean-field approximation may be decoupled. We find a phase transition leading to sympatric speciation as a parameter that quantifies competition strength is varied. This transition, previously found in a computational model, occurs to be of first order.
Mean field theory of the linear sigma-model: chiral solitons
Kahana, S.; Ripka, G.
The mean field theory of the chiral invariant sigma-model is outlined. bound states (solitons) of valence quarks are obtained self-consistently using a hedgehog shape for the pion field. A schematic model for the coupled fermion-boson fields is presented. Renormalization is worked out for the fermion one-loop corrections and numerical results presented for the purely scalar-field case. The interpretation of the baryon number of the perturbed vacuum is considered.
Modeling of coherent ultrafast magneto-optical experiments: Light-induced molecular mean-field model
Hinschberger, Y.; Hervieux, P.-A.
We present calculations which aim to describe coherent ultrafast magneto-optical effects observed in time-resolved pump-probe experiments. Our approach is based on a nonlinear semi-classical Drude-Voigt model and is used to interpret experiments performed on nickel ferromagnetic thin film. Within this framework, a phenomenological light-induced coherent molecular mean-field depending on the polarizations of the pump and probe pulses is proposed whose microscopic origin is related to a spin-orbit coupling involving the electron spins of the material sample and the electric field of the laser pulses. Theoretical predictions are compared to available experimental data. The model successfully reproduces the observed experimental trends and gives meaningful insight into the understanding of magneto-optical rotation behavior in the ultrafast regime. Theoretical predictions for further experimental studies are also proposed.
A mean-field monomer-dimer model with attractive interaction: Exact solution and rigorous results
Alberici, D. Contucci, P. Mingione, E.
A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb method for the pure hard-core interacting case is used to compute upper and lower bounds for the pressure. The bounds are shown to coincide in the thermodynamic limit for a suitable choice of the monomer density m. The computation of the monomer density is achieved by solving a consistency equation in the phase space (h, J), where h tunes the monomer potential and J the attractive potential. The critical point and exponents are computed and show that the model is in the mean-field ferromagnetic universality class.
Mott transition in the dynamic Hubbard model within slave boson mean-field approach
NASA Astrophysics Data System (ADS)
Le, Duc-Anh
At zero temperature, the Kotliar-Ruckenstein slave boson mean-field approach is applied to the dynamic Hubbard model. In this paper, the influences of the dynamics of the auxiliary boson field on the Mott transition are investigated. At finite boson frequency, the Mott-type features of the Hubbard model is found to be enhanced by increasing the pseudospin coupling parameter g. For sufficiently large pseudospin coupling g, the Mott transition occurs even for modest values of the bare Hubbard interaction U. The lack of electron-hole symmetry is highlighted through the quasiparticle weight. Our results are in good agreement with the ones obtained by two-site dynamical mean-field theory and determinant quantum Monte Carlo simulation.
Application of mean-field model of polymer melt intercalation in organo-silicates for nanocomposites.
Meneghetti, Paulo; Qutubuddin, Syed
The mean-field, lattice-based model of polymer melt intercalation in organically-modified layered silicates (OLS) originally developed by Vaia and Giannelis was applied for different polymers such as poly(methyl methacrylate) (PMMA), polypropylene (PP), and poly(ethylene oxide) (PEO). The nature of each polymer controls significantly the intercalation of the system. The internal energy change caused by the interaction of polymer, surfactant and clay is the strongest factor in determining the equilibrium structure of the nanocomposite system.
Octupole degree of freedom for the critical-point candidate nucleus Sm152 in a reflection-asymmetric relativistic mean-field approach
NASA Astrophysics Data System (ADS)
Zhang, W.; Li, Z. P.; Zhang, S. Q.; Meng, J.
The potential energy surfaces of even-even Sm146-156 are investigated in the constrained reflection-asymmetric relativistic mean-field approach with parameter set PK1. It is shown that the critical-point candidate nucleus Sm152 marks the shape/phase transition not only from U(5) to SU(3) symmetry, but also from the octupole-deformed ground state in Sm150 to the quadrupole-deformed ground state in Sm154. By including the octupole degree of freedom, an energy gap near the Fermi surface for single-particle levels in Sm152 with β2=0.14~0.26 is found and the important role of the octupole deformation driving pair ν2f7/2 and ν1i13/2 is demonstrated.
Mean field study of a propagation-turnover lattice model for the dynamics of histone marking
NASA Astrophysics Data System (ADS)
Yao, Fan; Li, FangTing; Li, TieJun
We present a mean field study of a propagation-turnover lattice model, which was proposed by Hodges and Crabtree [Proc. Nat. Acad. Sci. 109, 13296 (2012)] for understanding how posttranslational histone marks modulate gene expression in mammalian cells. The kinetics of the lattice model consists of nucleation, propagation and turnover mechanisms, and exhibits second-order phase transition for the histone marking domain. We showed rigorously that the dynamics essentially depends on a non-dimensional parameter κ = k +/ k -, the ratio between the propagation and turnover rates, which has been observed in the simulations. We then studied the lowest order mean field approximation, and observed the phase transition with an analytically obtained critical parameter. The boundary layer analysis was utilized to investigate the structure of the decay profile of the mark density. We also studied the higher order mean field approximation to achieve sharper estimate of the critical transition parameter and more detailed features. The comparison between the simulation and theoretical results shows the validity of our theory.
Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model
NASA Astrophysics Data System (ADS)
Chen, Li; Göttlich, Simone; Yin, Qitao
In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation on the microscopic scale. For stochastic initial data, it is proved that the solution of the N-particle pedestrian flow system with properly chosen cut-off converges in the probability sense to the solution of the characteristics of the non-cut-off Vlasov equation. Furthermore, the result on propagation of chaos is also deduced in terms of bounded Lipschitz distance.
LETTER TO THE EDITOR: Car-oriented mean-field theory for traffic flow models
NASA Astrophysics Data System (ADS)
Schadschneider, Andreas; Schreckenberg, Michael
We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between consecutive cars. Therefore certain longer-ranged correlations are taken into account and even a mean-field approach yields non-trivial results. In fact for the model with 0305-4470/30/4/005/img5 the exact solution is reproduced. For 0305-4470/30/4/005/img6 the fundamental diagram shows a good agreement with results from simulations.
Mean field lattice model for adsorption isotherms in zeolite NaA
NASA Astrophysics Data System (ADS)
Ayappa, K. G.; Kamala, C. R.; Abinandanan, T. A.
Using a lattice model for adsorption in microporous materials, pure component adsorption isotherms are obtained within a mean field approximation for methane at 300 K and xenon at 300 and 360 K in zeolite NaA. It is argued that the increased repulsive adsorbate-adsorbate interactions at high coverages must play an important role in determining the adsorption behavior. Therefore, this feature is incorporated through a "coverage-dependent interaction" model, which introduces a free, adjustable parameter. Another important feature, the site volume reduction, has been treated in two ways: a van der Waal model and a 1D hard-rod theory [van Tassel et al., AIChE J. 40, 925 (1994)]; we have also generalized the latter to include all possible adsorbate overlap scenarios. In particular, the 1D hard-rod model, with our coverage-dependent interaction model, is shown to be in best quantitative agreement with the previous grand canonical Monte Carlo isotherms. The expressions for the isosteric heats of adsorption indicate that attractive and repulsive adsorbate-adsorbate interactions increase and decrease the heats of adsorption, respectively. It is concluded that within the mean field approximation, our simple model for repulsive interactions and the 1D hard-rod model for site volume reduction are able to capture most of the important features of adsorption in confined regions.
Elementary proof of convergence to the mean-field model for the SIR process.
Armbruster, Benjamin; Beck, Ekkehard
The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equation (ODE) based model which represents the mean-field approximation of the underlying stochastic SIR process on contact networks, only few rigorous approaches exist and these use complex semigroup and martingale techniques to prove that the expected fraction of the susceptible and infected nodes of the stochastic SIR process on a complete graph converges as the number of nodes increases to the solution of the mean-field ODE model. Extending the elementary proof of convergence for the SIS process introduced by Armbruster and Beck (IMA J Appl Math, doi: 10.1093/imamat/hxw010 , 2016) to the SIR process, we show convergence using only a system of three ODEs, simple probabilistic inequalities, and basic ODE theory. Our approach can also be generalized to many other types of compartmental models (e.g., susceptible-infected-recovered-susceptible (SIRS)) which are linear ODEs with the addition of quadratic terms for the number of new infections similar to the SI term in the SIR model.
Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model
Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.; ...
We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less
Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model
Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.; Calleja, R.
We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherent structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.
Slave-boson mean field versus quantum Monte Carlo results for the Hubbard model
NASA Astrophysics Data System (ADS)
Lilly, L.; Muramatsu, A.; Hanke, W.
The one-band Hubbard model is considered in the slave-boson formulation first introduced by Kotliar and Ruckenstein. It is shown that a mean-field approximation, where broken-symmetry states appropriate for a bipartite lattice are allowed, leads to a quantitative agreement with quantum Monte Carlo results for local observables over a wide range of interactions (0<=1). Thus, our saddle-point solutions constitute an excellent starting point for a systematic treatment of fluctuations.
Mean-field approximation for a limit order driven market model
NASA Astrophysics Data System (ADS)
Slanina, František
A mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that the evolution of the order book is governed by a matrix multiplicative process. The resulting stationary distribution of step-to-step price changes is calculated. It exhibits a power-law tail with exponent 2. We obtain also the price autocorrelation function, which agrees qualitatively with the experimentally observed negative autocorrelation for short times.
An exact solution of spherical mean-field plus a special separable pairing model
NASA Astrophysics Data System (ADS)
Dai, Lianrong; Pan, Feng; Draayer, J. P.
An exact solution of nuclear spherical mean-field plus a special orbit-dependent separable pairing model is studied, of which the separable pairing interaction parameters are obtained by a linear fitting in terms of the single-particle energies considered. The advantage of the model is that, similar to the standard pairing case, it can be solved easily by using the extended Heine-Stieltjes polynomial approach. With the analysis of the model in the ds- and pf-shell subspace, it is shown that this special separable pairing model indeed provides similar pair structures of the model with the original separable pairing interaction, and is obviously better than the standard pairing model in many aspects.
Mean-field thalamocortical modeling of longitudinal EEG acquired during intensive meditation training.
Saggar, Manish; Zanesco, Anthony P; King, Brandon G; Bridwell, David A; MacLean, Katherine A; Aichele, Stephen R; Jacobs, Tonya L; Wallace, B Alan; Saron, Clifford D; Miikkulainen, Risto
Meditation training has been shown to enhance attention and improve emotion regulation. However, the brain processes associated with such training are poorly understood and a computational modeling framework is lacking. Modeling approaches that can realistically simulate neurophysiological data while conforming to basic anatomical and physiological constraints can provide a unique opportunity to generate concrete and testable hypotheses about the mechanisms supporting complex cognitive tasks such as meditation. Here we applied the mean-field computational modeling approach using the scalp-recorded electroencephalogram (EEG) collected at three assessment points from meditating participants during two separate 3-month-long shamatha meditation retreats. We modeled cortical, corticothalamic, and intrathalamic interactions to generate a simulation of EEG signals recorded across the scalp. We also present two novel extensions to the mean-field approach that allow for: (a) non-parametric analysis of changes in model parameter values across all channels and assessments; and (b) examination of variation in modeled thalamic reticular nucleus (TRN) connectivity over the retreat period. After successfully fitting whole-brain EEG data across three assessment points within each retreat, two model parameters were found to replicably change across both meditation retreats. First, after training, we observed an increased temporal delay between modeled cortical and thalamic cells. This increase provides a putative neural mechanism for a previously observed reduction in individual alpha frequency in these same participants. Second, we found decreased inhibitory connection strength between the TRN and secondary relay nuclei (SRN) of the modeled thalamus after training. This reduction in inhibitory strength was found to be associated with increased dynamical stability of the model. Altogether, this paper presents the first computational approach, taking core aspects of physiology and
Free energy of mean-field spin-glass models: Evolution operator and perturbation expansion
NASA Astrophysics Data System (ADS)
Janiš, V.; Kauch, A.; Klíč, A.
The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. One of the authors recently proposed a representation of the free energy generating this solution via an evolution operator parametrized by attainable values of overlap of magnetizations between different states. Here, we introduce a perturbation expansion for the evolution operator that we use to derive all thermodynamic characteristics via the standard methods of statistical mechanics. We obtain a generic scheme for an approximate calculation of physical quantities of different mean-field spin-glass models at all temperatures. The small expansion parameter is a difference between the continuous order-parameter function and the corresponding order parameter from the solution with one level of replica-symmetry breaking. The first correction beyond the approximation with one level of replica-symmetry breaking is explicitly evaluated in the glassy phase of the Sherrington-Kirkpatrick model.
Mean-Field Theory of the Symmetry Breaking Model for X Chromosome Inactivation
NASA Astrophysics Data System (ADS)
Scialdone, A.; Barbieri, M.; Pallotti, D.; Nicodemi, M.
X Chromosome Inactivation (XCI) is the process in mammal femalecells whereby one of the X chromosomes is silenced to compensate dosage with respect to males. It is still mysterious how precisely one X chromosome is randomly chosen for inactivation. We discuss here a mean-field theory of the Symmetry Breaking (SB) model of XCI, a Statistical Mechanics model introduced to explain that process. The SB model poses that a single regulatory factor, an aggregate of molecules, is produced which acts to preserve from inactivation one of the X's. The model illustrates a physical mechanism, originating from a thermodynamic phase transition, for the self-assembling of such a single super-molecular aggregate which can spontaneously break the binding symmetry of equivalent targets. This results in a sharp, yet stochastic, regulatory mechanism of XCI. In particular, we focus here on how the model can predict the effects of genetic deletions.
Economic dynamics with financial fragility and mean-field interaction: A model
NASA Astrophysics Data System (ADS)
Di Guilmi, C.; Gallegati, M.; Landini, S.
Following Aoki's statistical mechanics methodology [Masanao Aoki, New Approaches to Macroeconomic Modeling, Cambridge University Press, 1996; Masanao Aoki, Modeling Aggregate Behaviour and Fluctuations in Economics, Cambridge University Press, 2002; Masanao Aoki, and Hiroshi Yoshikawa, Reconstructing Macroeconomics, Cambridge University Press, 2006], we provide some insights into the well-known works of [Bruce Greenwald, Joseph Stiglitz, Macroeconomic models with equity and credit rationing, in: R. Hubbard (Ed.), Information, Capital Markets and Investment, Chicago University Press, Chicago, 1990; Bruce Greenwald, Joseph Stiglitz, Financial markets imperfections and business cycles, Quarterly journal of Economics (1993)]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can be partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean-field interaction modeling and master equation techniques.
Bayesian Learning in Sparse Graphical Factor Models via Variational Mean-Field Annealing.
Yoshida, Ryo; West, Mike
We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate "artificial" posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data.
Anomalous mean-field behavior of the fully connected Ising model.
Colonna-Romano, Louis; Gould, Harvey; Klein, W
Although the fully connected Ising model does not have a length scale, we show that the critical exponents for thermodynamic quantities such as the mean magnetization and the susceptibility can be obtained using finite size scaling with the scaling variable equal to N, the number of spins. Surprisingly, the mean value and the most probable value of the magnetization are found to scale differently with N at the critical temperature of the infinite system, and the magnetization probability distribution is not a Gaussian, even for large N. Similar results inconsistent with the usual understanding of mean-field theory are found at the spinodal. We relate these results to the breakdown of hyperscaling and show that hyperscaling can be restored by increasing N while holding the Ginzburg parameter rather than the temperature fixed, or by doing finite size scaling at the pseudocritical temperature where the susceptibility is a maximum for a given value of N. We conclude that finite size scaling for the fully connected Ising model yields different results depending on how the mean-field limit is approached.
Mean-field approximation for the Sznajd model in complex networks
NASA Astrophysics Data System (ADS)
Araújo, Maycon S.; Vannucchi, Fabio S.; Timpanaro, André M.; Prado, Carmen P. C.
This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.
Modeling and computation of mean field equilibria in producers' game with emission permits trading
NASA Astrophysics Data System (ADS)
Zhang, Shuhua; Wang, Xinyu; Shanain, Aleksandr
In this paper, we present a mean field game to model the production behaviors of a very large number of producers, whose carbon emissions are regulated by government. Especially, an emission permits trading scheme is considered in our model, in which each enterprise can trade its own permits flexibly. By means of the mean field equilibrium, we obtain a Hamilton-Jacobi-Bellman (HJB) equation coupled with a Kolmogorov equation, which are satisfied by the adjoint state and the density of producers (agents), respectively. Then, we propose a so-called fitted finite volume method to solve the HJB equation and the Kolmogorov equation. The efficiency and the usefulness of this method are illustrated by the numerical experiments. Under different conditions, the equilibrium states as well as the effects of the emission permits price are examined, which demonstrates that the emission permits trading scheme influences the producers' behaviors, that is, more populations would like to choose a lower rather than a higher emission level when the emission permits are expensive.
Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
NASA Astrophysics Data System (ADS)
Guerra, Francesco
By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend this argument in order to compare the limiting free energy with the expression given by the Parisi Ansatz, and including full spontaneous replica symmetry breaking. Our main result is that the quenched average of the free energy is bounded from below by the value given in the Parisi Ansatz, uniformly in the size of the system. Moreover, the difference between the two expressions is given in the form of a sum rule, extending our previous work on the comparison between the true free energy and its replica symmetric Sherrington-Kirkpatrick approximation. We give also a variational bound for the infinite volume limit of the ground state energy per site.
Quantum correlated cluster mean-field theory applied to the transverse Ising model.
Zimmer, F M; Schmidt, M; Maziero, Jonas
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Effects of anisotropies in turbulent magnetic diffusion in mean-field solar dynamo models
Pipin, V. V.; Kosovichev, A. G.
We study how anisotropies of turbulent diffusion affect the evolution of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magnetohydrodynamics framework assuming that triple correlations provide relaxation to the turbulent electromotive force (so-called the 'minimal τ-approximation'). We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model and a distributed-dynamo model with a subsurface rotational shear layer. For both models, we investigate effects of the double- and triple-cell meridional circulation, recently suggested by helioseismology and numerical simulations. To characterize the anisotropy effects, we introduce a parameter of anisotropy as a ratio of the radial and horizontal intensities of turbulent mixing. It is found that the anisotropy affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the dynamo period approach to constant values for large values of the anisotropy parameter. The anisotropy reduces the overlap of toroidal magnetic fields generated in subsequent dynamo cycles, in the time-latitude 'butterfly' diagram. If we assume that sunspots are formed in the vicinity of the subsurface shear layer, then the distributed dynamo model with the anisotropic diffusivity satisfies the observational constraints from helioseismology and is consistent with the value of effective turbulent diffusion estimated from the dynamics of surface magnetic fields.
Mean-field dynamic criticality and geometric transition in the Gaussian core model
NASA Astrophysics Data System (ADS)
Coslovich, Daniele; Ikeda, Atsushi; Miyazaki, Kunimasa
We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.
Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones
NASA Astrophysics Data System (ADS)
Malpetti, Daniele; Roscilde, Tommaso
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
Extended dynamical mean-field study of the Hubbard model with long-range interactions
NASA Astrophysics Data System (ADS)
Huang, Li; Ayral, Thomas; Biermann, Silke; Werner, Philipp
Using extended dynamical mean-field theory and its combination with the G W approximation, we compute the phase diagrams and local spectral functions of the single-band extended Hubbard model on the square and simple cubic lattices, considering long-range interactions up to the third nearest neighbors. The longer-range interactions shift the boundaries between the metallic, charge-ordered insulating, and Mott insulating phases, and lead to characteristic changes in the screening modes and local spectral functions. Momentum-dependent self-energy contributions enhance the correlation effects and thus compete with the additional screening effect from longer-range Coulomb interactions. Our results suggest that the influence of longer-range intersite interactions is significant, and that these effects deserve attention in realistic studies of correlated materials.
Rhythmic behavior in a two-population mean-field Ising model.
Collet, Francesca; Formentin, Marco; Tovazzi, Daniele
Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.
Collisional relaxation in the inhomogeneous Hamiltonian mean-field model: Diffusion coefficients
NASA Astrophysics Data System (ADS)
Benetti, F. P. C.; Marcos, B.
Systems of particles with long-range interactions present two important processes: first, the formation of out-of-equilibrium quasistationary states (QSS) and, second, the collisional relaxation towards Maxwell-Boltzmann equilibrium in a much longer time scale. In this paper, we study the collisional relaxation in the Hamiltonian mean-field model using the appropriate kinetic equations for a system of N particles at order 1 /N : the Landau equation when collective effects are neglected and the Lenard-Balescu equation when they are taken into account. We derive explicit expressions for the diffusion coefficients using both equations for any magnetization, and we obtain analytic expressions for highly clustered configurations. An important conclusion is that in this system collective effects are crucial in order to describe the relaxation dynamics. We compare the diffusion calculated with the kinetic equations with simulations set up to simulate the system with or without collective effects, obtaining a very good agreement between theory and simulations.
Rhythmic behavior in a two-population mean-field Ising model
NASA Astrophysics Data System (ADS)
Collet, Francesca; Formentin, Marco; Tovazzi, Daniele
Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.
Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy*
NASA Astrophysics Data System (ADS)
Kechedzhi, Kostyantyn; Smelyanskiy, Vadim N.
Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p -spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.
Numerical evidence against both mean field and droplet scenarios of the Edwards-Anderson model
NASA Astrophysics Data System (ADS)
Fernandez, Julio F.; Alonso, Juan J.
From tempered Monte Carlo simulations, we have obtained accurate probability distributions p (q) of the spin-overlap parameter q for finite Edwards-Anderson (EA) and Sherrington-Kirkpatrick (SK) spin-glass systems at low temperatures. Our results for p (q) follow from averages over 105 disordered samples of linear sizes L = 4 - 8 and over 15 000 samples for L = 10 . In both the SK and EA models, at temperatures as low as 0 . 2Tsg , where Tsg is the transition temperature, p (q) varies insignificantly with L. This does not fit the trend that the droplet model predicts for large L. We have also calculated correlation functions, F (q1 ,q2) , from which rms deviations, δp , over different realizations of quenched disorder, as well as thermal fluctuations, w, of q values, follow. Our numerical results for δp and w scale as √{ L} and 1 / L , respectively, in the SK model. This fits in well with mean field predictions. On the other hand, our data for w and δp vary little, if at all, for the EA model.
Treatment of Fluctuation Effects in Mean-field Models of Chain Stretching
NASA Astrophysics Data System (ADS)
Douglas, Jack; Mansfield, Marc
Many recent studies of chain stretching in block copolymer materials, polymer brushes, and many-arm stars have been formulated in terms of mean- field models, leading generally to power-law potentials describing the chain stretching arising from interchain and intrachain excluded volume interactions. This type of model has been highly successful, but fluctuation effects associated with finite chain length are often neglected in model calculations. We investigate whether fluctuation effects can be accounted for by reintroducing these effective pseudo-potentials into a path-integral description to calculate the chain streching. Numerical treatment of chain swelling with repulsive power-law potentials leads to universal scaling curves which are similar to those found for chain swelling due to excluded volume in polymer solutions. Density profiles are also calculated and the parabolic potential led to a density profile having a "foot" for finite chain lengths, as in measurements on polymer "brushes". Analytic calculations indicate a general relation between the polymer size exponent nu and the power of the potential which also holds for Hamiltonian dynamical systems and thus the 2/3 power law describing the strong segregation scaling of block copolymer lamellae with chain mass corresponds to Kepler's third law of planetary motion relating the orbital scale to its period.
Nuclear mean field and double-folding model of the nucleus-nucleus optical potential
NASA Astrophysics Data System (ADS)
Khoa, Dao T.; Phuc, Nguyen Hoang; Loan, Doan Thi; Loc, Bui Minh
Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic 12C+12C and 16O+12C scattering at the refractive energies, where the Airy structure of the nuclear rainbow has been well established. The RT was found to affect significantly the real nucleus-nucleus optical potential at small internuclear distances, giving a potential strength close to that implied by the realistic optical model description of the Airy oscillation.
Mean-field message-passing equations in the Hopfield model and its generalizations
NASA Astrophysics Data System (ADS)
Mézard, Marc
Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations [belief-propagation and Thouless-Anderson Palmer (TAP) equations] in the best understood of such machines, namely the Hopfield model of neural networks, and we explicit how they can be used as iterative message-passing algorithms, providing a fast method to compute the local polarizations of neurons. In the "retrieval phase", where neurons polarize in the direction of one memorized pattern, we point out a major difference between the belief propagation and TAP equations: The set of belief propagation equations depends on the pattern which is retrieved, while one can use a unique set of TAP equations. This makes the latter method much better suited for applications in the learning process of restricted Boltzmann machines. In the case where the patterns memorized in the Hopfield model are not independent, but are correlated through a combinatorial structure, we show that the TAP equations have to be modified. This modification can be seen either as an alteration of the reaction term in TAP equations or, more interestingly, as the consequence of message passing on a graphical model with several hidden layers, where the number of hidden layers depends on the depth of the correlations in the memorized patterns. This layered structure is actually necessary when one deals with more general restricted Boltzmann machines.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B.; Nita, M.
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
Singular-potential random-matrix model arising in mean-field glassy systems.
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
Singular-potential random-matrix model arising in mean-field glassy systems
NASA Astrophysics Data System (ADS)
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
General model of phospholipid bilayers in fluid phase within the single chain mean field theory.
Guo, Yachong; Pogodin, Sergey; Baulin, Vladimir A
Coarse-grained model for saturated phospholipids: 1,2-didecanoyl-sn-glycero-3-phosphocholine (DCPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and unsaturated phospholipids: 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2- dioleoyl-sn-glycero-3-phosphocholine (DOPC) is introduced within the single chain mean field theory. A single set of parameters adjusted for DMPC bilayers gives an adequate description of equilibrium and mechanical properties of a range of saturated lipid molecules that differ only in length of their hydrophobic tails and unsaturated (POPC, DOPC) phospholipids which have double bonds in the tails. A double bond is modeled with a fixed angle of 120°, while the rest of the parameters are kept the same as saturated lipids. The thickness of the bilayer and its hydrophobic core, the compressibility, and the equilibrium area per lipid correspond to experimentally measured values for each lipid, changing linearly with the length of the tail. The model for unsaturated phospholipids also fetches main thermodynamical properties of the bilayers. This model is used for an accurate estimation of the free energies of the compressed or stretched bilayers in stacks or multilayers and gives reasonable estimates for free energies. The proposed model may further be used for studies of mixtures of lipids, small molecule inclusions, interactions of bilayers with embedded proteins.
Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
NASA Astrophysics Data System (ADS)
Hewson, A. C.
We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.
Correlation patterns of NIKKEI index constituents. Towards a mean-field model
NASA Astrophysics Data System (ADS)
Hayashi, Katsuhiko; Kaizoji, Taisei; Pichl, Lukáš
An analysis of minute-tick data from the Japanese stock index market is reported for a three-year period of 2000/7/4-2003/6/30. Correlation patterns and principal component distributions were determined for 180 constituents of the NIKKEI 225 index, excluding the effects of after-hours trading and constituent revisions. The first principal component describes about 30% of the total variance in constituent log returns (subject to slow decrease with the size of the correlation window), suggesting that a small number of physical parameters may describe the internal dynamics of the index, allowing for an adiabatic representation of index dynamics, and a self-consistent mean-field model of its constituents. Finally, it is shown that the introduction of a time gap into minute-tick data significantly improves the correlations of the price-weighed index with its constituents, even when such gap inserts are strictly penalized. This phenomenon corresponds to a heterogenous response time of index constituents to the adiabatic collective motion and also demonstrates the inhomogeneous nature of equidistant time ticks in financial trading.
Dynamic mean field theory for lattice gas models of fluid mixtures confined in mesoporous materials.
Edison, J R; Monson, P A
We present the extension of dynamic mean field theory (DMFT) for fluids in porous materials (Monson, P. A. J. Chem. Phys. 2008, 128, 084701) to the case of mixtures. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable equilibrium states for fluids in pores after a change in the bulk pressure or composition. It is especially useful for studying systems where there are capillary condensation or evaporation transitions. Nucleation processes associated with these transitions are emergent features of the theory and can be visualized via the time dependence of the density distribution and composition distribution in the system. For mixtures an important component of the dynamics is relaxation of the composition distribution in the system, especially in the neighborhood of vapor-liquid interfaces. We consider two different types of mixtures, modeling hydrocarbon adsorption in carbon-like slit pores. We first present results on bulk phase equilibria of the mixtures and then the equilibrium (stable/metastable) behavior of these mixtures in a finite slit pore and an inkbottle pore. We then use DMFT to describe the evolution of the density and composition in the pore in the approach to equilibrium after changing the state of the bulk fluid via composition or pressure changes.
Hamiltonian mean field model: Effect of network structure on synchronization dynamics
NASA Astrophysics Data System (ADS)
Virkar, Yogesh S.; Restrepo, Juan G.; Meiss, James D.
The Hamiltonian mean field model of coupled inertial Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony begins when the coupling constant K is inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors. When K is just beyond the transition to synchronization, we find that the degree of synchronization is highly dependent on the network's heterogeneity, but that for large K the degree of synchronization is robust to changes in the degree distribution. Our results are illustrated with numerical simulations on Erdös-Renyi networks and networks with power-law degree distributions.
Hamiltonian mean field model: Effect of network structure on synchronization dynamics.
Virkar, Yogesh S; Restrepo, Juan G; Meiss, James D
The Hamiltonian mean field model of coupled inertial Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by a network described by a weighted adjacency matrix. By studying the linear stability of the incoherent state, we find that the transition to synchrony begins when the coupling constant K is inversely proportional to the largest eigenvalue of the adjacency matrix. We derive a closed system of equations for a set of local order parameters to study the effect of network heterogeneity on the synchronization of the rotors. When K is just beyond the transition to synchronization, we find that the degree of synchronization is highly dependent on the network's heterogeneity, but that for large K the degree of synchronization is robust to changes in the degree distribution. Our results are illustrated with numerical simulations on Erdös-Renyi networks and networks with power-law degree distributions.
Clusters die hard: Time-correlated excitation in the Hamiltonian mean field model
NASA Astrophysics Data System (ADS)
Koyama, Hiroko; Konishi, Tetsuro; Ruffo, Stefano
The Hamiltonian mean field (HMF) model has a low-energy phase where N particles are trapped inside a cluster. Here, we investigate some properties of the trapping/untrapping mechanism of a single particle into/outside the cluster. Since the single particle dynamics of the HMF model resembles the one of a simple pendulum, each particle can be identified as a high-energy particle (HEP) or a low-energy particle (LEP), depending on whether its energy is above or below the separatrix energy. We then define the trapping ratio as the ratio of the number of LEP to the total number of particles and the "fully-clustered" and "excited" dynamical states as having either no HEP or at least one HEP. We analytically compute the phase-space average of the trapping ratio by using the Boltzmann-Gibbs stable stationary solution of the Vlasov equation associated with the N → ∞ limit of the HMF model. The same quantity, obtained numerically as a time average, is shown to be in very good agreement with the analytical calculation. Another important feature of the dynamical behavior of the system is that the dynamical state changes transitionally: the "fully-clustered" and "excited" states appear in turn. We find that the distribution of the lifetime of the "fully-clustered" state obeys a power law. This means that clusters die hard, and that the excitation of a particle from the cluster is not a Poisson process and might be controlled by some type of collective motion with long memory. Such behavior should not be specific of the HMF model and appear also in systems where itinerancy among different "quasi-stationary" states has been observed. It is also possible that it could mimick the behavior of transient motion in molecular clusters or some observed deterministic features of chemical reactions.
Nonequilibrium Dynamical Mean-Field Theory for the Charge-Density-Wave Phase of the Falicov-Kimball Model
Matveev, O. P.; Shvaika, A. M.; Devereaux, T. P.; Freericks, J. K.
Nonequilibrium dynamical mean-field theory (DMFT) is developed for the case of the charge-density-wave ordered phase. We consider the spinless Falicov-Kimball model which can be solved exactly. This strongly correlated system is then placed in an uniform external dc electric field. We present a complete derivation for nonequilibrium dynamical mean-field theory Green's functions defined on the Keldysh-Schwinger time contour. We also discuss numerical issues involved in solving the coupled equations.
Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches.
Moosavi, S Amin; Montakhab, Afshin
Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.
Out-of-equilibrium phase transitions in the Hamiltonian mean-field model: A closer look
NASA Astrophysics Data System (ADS)
Staniscia, F.; Chavanis, P. H.; de Ninno, G.
We provide a detailed discussion of out-of-equilibrium phase transitions in the Hamiltonian mean-field (HMF) model in the framework of Lynden-Bell's statistical theory of the Vlasov equation. For two-level initial conditions, the caloric curve β(E) only depends on the initial value f0 of the distribution function. We evidence different regions in the parameter space where the nature of the phase transitions between magnetized and nonmagnetized states changes: (i) For f0>0.10965, the system displays a second-order phase transition; (ii) for 0.109497
On the genesis of spike-wave oscillations in a mean-field model of human thalamic and corticothalamic dynamics
NASA Astrophysics Data System (ADS)
Rodrigues, Serafim; Terry, John R.; Breakspear, Michael
In this Letter, the genesis of spike-wave activity—a hallmark of many generalized epileptic seizures—is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the cortical signal, interplay to generate the spike-wave oscillation. The mechanism revealed provides an explanation of why approaches based on linear stability and Heaviside approximations to the activation function have failed to explain the phenomena of spike-wave behaviour in mean-field models. A mathematical understanding of this transition is a crucial step towards relating spiking network models and mean-field approaches to human brain modelling.
Brain activity modeling in general anesthesia: Enhancing local mean-field models using a slow adaptive firing rate
NASA Astrophysics Data System (ADS)
Molaee-Ardekani, B.; Senhadji, L.; Shamsollahi, M. B.; Vosoughi-Vahdat, B.; Wodey, E.
In this paper, an enhanced local mean-field model that is suitable for simulating the electroencephalogram (EEG) in different depths of anesthesia is presented. The main building elements of the model (e.g., excitatory and inhibitory populations) are taken from Steyn-Ross [M. L. Steyn-Ross , Phys. Rev. E 64, 011917 (2001), D. A. Steyn-Ross , Phys. Rev. E 64, 011918 (2001)] and Bojak and Liley [I. Bojak and D. T. Liley, Phys. Rev. E 71, 041902 (2005)] mean-field models and a new slow ionic mechanism is included in the main model. Generally, in mean-field models, some sigmoid-shape functions determine firing rates of neural populations according to their mean membrane potentials. In the enhanced model, the sigmoid function corresponding to excitatory population is redefined to be also a function of the slow ionic mechanism. This modification adapts the firing rate of neural populations to slow ionic activities of the brain. When an anesthetic drug is administered, the slow mechanism may induce neural cells to alternate between two levels of activity referred to as up and down states. Basically, the frequency of up-down switching is in the delta band (0-4Hz) and this is the main reason behind high amplitude, low frequency fluctuations of EEG signals in anesthesia. Our analyses show that the enhanced model may have different working states driven by anesthetic drug concentration. The model is settled in the up state in the waking period, it may switch to up and down states in moderate anesthesia while in deep anesthesia it remains in the down state.
Double Lynden-Bell structure of low-energy quasistationary distributions in the Hamiltonian mean-field model.
Konishi, Eiji; Sakagami, Masa-aki
In the Hamiltonian mean-field model, we study the core-halo structure of low-energy quasistationary states under unsteady water-bag type initial conditions. The core-halo structure results in the superposition of two independent Lynden-Bell distributions. We examine the completeness of the Lynden-Bell relaxation and the relaxation between these two Lynden-Bell distributions.
Statistical thermodynamics of lattice models in zeolites: Implications of local versus global mean field interactions
NASA Astrophysics Data System (ADS)
Ayappa, K. G.
The statistical thermodynamics of adsorption in caged zeolites is developed by treating the zeolite as an ensemble of M identical cages or subsystems. Within each cage adsorption is assumed to occur onto a lattice of n identical sites. Expressions for the average occupancy per cage are obtained by minimizing the Helmholtz free energy in the canonical ensemble subject to the constraints of constant M and constant number of adsorbates N. Adsorbate-adsorbate interactions in the Brag-Williams or mean field approximation are treated in two ways. The local mean field approximation (LMFA) is based on the local cage occupancy and the global mean field approximation (GMFA) is based on the average coverage of the ensemble. The GMFA is shown to be equivalent in formulation to treating the zeolite as a collection of interacting single site subsystems. In contrast, the treatment in the LMFA retains the description of the zeolite as an ensemble of identical cages, whose thermodynamic properties are conveniently derived in the grand canonical ensemble. For a z coordinated lattice within the zeolite cage, with ɛaa as the adsorbate-adsorbate interaction parameter, the comparisons for different values of ɛaa*=ɛaaz/2kT, and number of sites per cage, n, illustrate that for -1<ɛaa*<0 and n⩾10, the adsorption isotherms and heats of adsorption predicted with the two approaches are similar. In general, the deviation between the LMFA and GMFA is greater for smaller n and less sensitive to n for ɛaa*>0. We compare the isotherms predicted with the LMFA with previous GMFA predictions [K. G. Ayappa, C. R. Kamala, and T. A. Abinandanan, J. Chem. Phys. 110, 8714 (1999)] (which incorporates both the site volume reduction and a coverage-dependent ɛaa) for xenon and methane in zeolite NaA. In all cases the predicted isotherms are very similar, with the exception of a small steplike feature present in the LMFA for xenon at higher coverages.
Relativistic Continuum Shell Model
NASA Astrophysics Data System (ADS)
Grineviciute, Janina; Halderson, Dean
The R-matrix formalism of Lane and Thomas has been extended to the relativistic case so that the many-coupled channels problem may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The formalism was previously applied to the relativistic impulse approximation
Analytic models of regularly branched polymer brushes using the self-consistent mean field theory
NASA Astrophysics Data System (ADS)
LeSher, Daniel
Polymer brushes consist of multiple monomers connected together with one of the polymer chain's ends attached to a surface. Polymer brushes have shown great promise for a wide variety of applications including drug delivery dendrimer systems and as tunable brushes that can change their shape and physical properties in response to changes in their environment. Regularly branched polymer brushes which are structured as a function of their chemical indices are investigated here using the self-consistent mean field theory for electrically neutral polymers. The brushes were described using weighting functions, f(n), were n was the fewest number of monomers from a specified location to a free end. Brushes with weighting functions of the form f(n)=nb, f(n)=ebn, as well as f(n)=dan when d 2 and alpha > 2 were found to match the parabolic free chain end profile expected, while it was determined that polymer brushes described using f(n)=n b must be very small in order to remain in equilibrium. However, brushes described by f(n)=2G(N-n) N and f(n)2n were found to be unstable for real, positive values of the potential of the system.
MEAN-FIELD MODELING OF AN α{sup 2} DYNAMO COUPLED WITH DIRECT NUMERICAL SIMULATIONS OF RIGIDLY ROTATING CONVECTION
Masada, Youhei; Sano, Takayoshi E-mail: email@example.com
The mechanism of large-scale dynamos in rigidly rotating stratified convection is explored by direct numerical simulations (DNS) in Cartesian geometry. A mean-field dynamo model is also constructed using turbulent velocity profiles consistently extracted from the corresponding DNS results. By quantitative comparison between the DNS and our mean-field model, it is demonstrated that the oscillatory α{sup 2} dynamo wave, excited and sustained in the convection zone, is responsible for large-scale magnetic activities such as cyclic polarity reversal and spatiotemporal migration. The results provide strong evidence that a nonuniformity of the α-effect, which is a natural outcome of rotating stratified convection, can be an important prerequisite for large-scale stellar dynamos, even without the Ω-effect.
Threshold for chaos and thermalization in the one-dimensional mean-field bose-hubbard model.
Cassidy, Amy C; Mason, Douglas; Dunjko, Vanja; Olshanii, Maxim
We study the threshold for chaos and its relation to thermalization in the 1D mean-field Bose-Hubbard model, which, in particular, describes atoms in optical lattices. We identify the threshold for chaos, which is finite in the thermodynamic limit, and show that it is indeed a precursor of thermalization. Far above the threshold, the state of the system after relaxation is governed by the usual laws of statistical mechanics.
Chain architecture and micellization: A mean-field coarse-grained model for poly(ethylene oxide) alkyl ether surfactants
NASA Astrophysics Data System (ADS)
García Daza, Fabián A.; Colville, Alexander J.; Mackie, Allan D.
Microscopic modeling of surfactant systems is expected to be an important tool to describe, understand, and take full advantage of the micellization process for different molecular architectures. Here, we implement a single chain mean field theory to study the relevant equilibrium properties such as the critical micelle concentration (CMC) and aggregation number for three sets of surfactants with different geometries maintaining constant the number of hydrophobic and hydrophilic monomers. The results demonstrate the direct effect of the block organization for the surfactants under study by means of an analysis of the excess energy and entropy which can be accurately determined from the mean-field scheme. Our analysis reveals that the CMC values are sensitive to branching in the hydrophilic head part of the surfactant and can be observed in the entropy-enthalpy balance, while aggregation numbers are also affected by splitting the hydrophobic tail of the surfactant and are manifested by slight changes in the packing entropy.
Chain architecture and micellization: A mean-field coarse-grained model for poly(ethylene oxide) alkyl ether surfactants
García Daza, Fabián A.; Mackie, Allan D.; Colville, Alexander J.
Microscopic modeling of surfactant systems is expected to be an important tool to describe, understand, and take full advantage of the micellization process for different molecular architectures. Here, we implement a single chain mean field theory to study the relevant equilibrium properties such as the critical micelle concentration (CMC) and aggregation number for three sets of surfactants with different geometries maintaining constant the number of hydrophobic and hydrophilic monomers. The results demonstrate the direct effect of the block organization for the surfactants under study by means of an analysis of the excess energy and entropy which can be accurately determined from the mean-field scheme. Our analysis reveals that the CMC values are sensitive to branching in the hydrophilic head part of the surfactant and can be observed in the entropy-enthalpy balance, while aggregation numbers are also affected by splitting the hydrophobic tail of the surfactant and are manifested by slight changes in the packing entropy.
Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains
NASA Astrophysics Data System (ADS)
Angelini, A.; Amato, A.; Bianconi, G.; Bassetti, B.; Cosentino Lagomarsino, M.
We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear, or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese restaurant process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.
Study of bottleneck effect at an emergency evacuation exit using cellular automata model, mean field approximation analysis, and game theory
NASA Astrophysics Data System (ADS)
Tanimoto, Jun; Hagishima, Aya; Tanaka, Yasukaka
An improved cellular automaton model for pedestrian dynamics was established, where both static floor field and collision effect derived from game theory were considered. Several model parameters were carefully determined by previous studies. Results obtained through model-based simulation and analytical approach (derived from mean field approximation) proved that outflow rate from an evacuation exit, which is usually estimated using outflow coefficient in building codes in Japan, can be improved by placing an appropriate obstacle in front of the exit. This can reduce collision probability at the exit by increasing collisions around the obstacles ahead of the exit.
Multimode mean-field model for the quantum phase transition of a Bose-Einstein condensate in an optical resonator
NASA Astrophysics Data System (ADS)
Kónya, G.; Szirmai, G.; Domokos, P.
We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grand-canonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.
Light cone in the two-dimensional transverse-field Ising model in time-dependent mean-field theory
NASA Astrophysics Data System (ADS)
Hafner, J.; Blass, B.; Rieger, H.
We investigate the propagation of a local perturbation in the two-dimensional transverse-field Ising model with a time-dependent application of the mean-field theory based on the BBGKY hierarchy. We show that the perturbation propagates through the system with a finite velocity and that there is a transition from Manhattan to Euclidian metric, resulting in a light cone with an almost circular shape at sufficiently large distances. The propagation velocity of the perturbation defining the front of the light cone is discussed with respect to the parameters of the Hamiltonian and compared to exact results for the transverse-field Ising model in one dimension.
Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model
NASA Astrophysics Data System (ADS)
Yucesoy, B.; Katzgraber, Helmut G.; Machta, J.
The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states.
A mean field model for competition: from neutral ecology to the Red Queen.
O'Dwyer, James P; Chisholm, Ryan
Individual species are distributed inhomogeneously over space and time, yet, within large communities of species, aggregated patterns of biodiversity seem to display nearly universal behaviour. Neutral models assume that an individual's demographic prospects are independent of its species identity. They have successfully predicted certain static, time-independent patterns. But they have generally failed to predict temporal patterns, such as species ages or population dynamics. We construct a new, multispecies framework incorporating competitive differences between species, and assess the impact of this competition on static and dynamic patterns of biodiversity. We solve this model exactly for the special case of a Red Queen hypothesis, where fitter species are continually arising. The model predicts more realistic species ages than neutral models, without greatly changing predictions for static species abundance distributions. Our modelling approach may allow users to incorporate a broad range of ecological mechanisms.
About a solvable mean field model of a Gaussian spin glass
NASA Astrophysics Data System (ADS)
Barra, Adriano; Genovese, Giuseppe; Guerra, Francesco; Tantari, Daniele
In a series of papers, we have studied a modified Hopfield model of a neural network, with learned words characterized by a Gaussian distribution. The model can be represented as a bipartite spin glass, with one party described by dichotomic Ising spins, and the other party by continuous spin variables, with an a priori Gaussian distribution. By application of standard interpolation methods, we have found it useful to compare the neural network model (bipartite) from one side, with two spin glass models, each monopartite, from the other side. Of these, the first is the usual Sherrington-Kirkpatrick model, the second is a spin glass model, with continuous spins and inbuilt highly nonlinear smooth cut-off interactions. This model is an invaluable laboratory for testing all techniques which have been useful in the study of spin glasses. The purpose of this paper is to give a synthetic description of the most peculiar aspects, by stressing the necessary novelties in the treatment. In particular, it will be shown that the control of the infinite volume limit, according to the well-known Guerra-Toninelli strategy, requires in addition one to consider the involvement of the cut-off interaction in the interpolation procedure. Moreover, the control of the ergodic region, the annealed case, cannot be directly achieved through the standard application of the Borel-Cantelli lemma, but requires previous modification of the interaction. This remark could find useful application in other cases. The replica symmetric expression for the free energy can be easily reached through a suitable version of the doubly stochastic interpolation technique. However, this model shares the unique property that the fully broken replica symmetry ansatz can be explicitly calculated. A very simple sum rule connects the general expression of the fully broken free energy trial function with the replica symmetric one. The definite sign of the error term shows that the replica solution is optimal. Then
The hedgehog baryon as a variational mean field solution of the spherical linear chiral soliton model
NASA Astrophysics Data System (ADS)
Goeke, K.; Urbano, J. N.; Fiolhais, M.; Harvey, M.
We prove that the hedgehog baryon arises as a variational solution of the linear σ-model, if this is restricted to the chiral circle and if the boson Fock-states are described by coherent states and the valence quarks by a product of three identical wave functions each consisting of an orbital s-state multiplied with the most general one-quark spin-flavour configuration in the ud-sector. The opposite is shown to be not true, i.e., the assumption of a hedgehog state in the linear σ-model does not lead to fields which obey the requirements of the chiral circle.
Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy
states are coherent superposi- tion of states in the two wells, the so-called Schroedinger cat states. Formally, these states correspond to a coherent...of Schroedinger Cat States in an Infinite-Range Spin Model, Phys. Rev. E 90, 022104 (2014). [38] D. A. Garanin, X. Martínez Hidalgo, and E.M
Pipin, V. V.; Kosovichev, A. G.
This paper presents a study of kinematic axisymmetric mean-field dynamo models for the case of meridional circulation with a deep-seated stagnation point and a strong return flow at the bottom of the convection zone. This kind of circulation follows from mean-field models of the angular momentum balance in the solar convection zone. The dynamo models include turbulent sources of the large-scale poloidal magnetic field production due to kinetic helicity and a combined effect due to the Coriolis force and large-scale electric current. In these models the toroidal magnetic field, which is responsible for sunspot production, is concentrated at the bottom of the convection zone and is transported to low-latitude regions by a meridional flow. The meridional component of the poloidal field is also concentrated at the bottom of the convection zone, while the radial component is concentrated in near-polar regions. We show that it is possible for this type of meridional circulation to construct kinematic dynamo models that resemble in some aspects the sunspot magnetic activity cycle. However, in the near-equatorial regions the phase relation between the toroidal and poloidal components disagrees with observations. We also show that the period of the magnetic cycle may not always monotonically decrease with the increase of the meridional flow speed. Thus, for further progress it is important to determine the structure of the meridional circulation, which is one of the critical properties, from helioseismology observations.
Aperiodic sequences and magnetic models: non-universal critical behavior within mean-field approximation
NASA Astrophysics Data System (ADS)
Branco, Nilton; Faria, Maicon; Tragtenberg, Marcelo
We study the Ising model on a Bethe lattice, such that the exchange constant can assume two values, according to two-letter aperiodic sequences. Critical temperatures and exponents are calculated for three different sequences: Fibonacci, period-doubling and two-letter Rudin-Shapiro ones. These sequences are found to be irrelevant, marginal, and relevant, respectively, in the renormalization-group sense. The Fibonacci sequence presents the same critical behavior as for the uniform model and no log-periodic behavior is observed. For the marginal sequence, critical exponents depend on the ratio between the two possible exchange constants and a log-periodic behavior is clearly determined. Due to computational constraints, our results are not as precise for the Rudin-Shapiro sequence but we obtain evidence that the exponents are different from the classical ones and do not depend on the ratio between the exchange constants.
Dynamics and termination cost of spatially coupled mean-field models
NASA Astrophysics Data System (ADS)
Caltagirone, Francesco; Franz, Silvio; Morris, Richard G.; Zdeborová, Lenka
This work is motivated by recent progress in information theory and signal processing where the so-called spatially coupled design of systems leads to considerably better performance. We address relevant open questions about spatially coupled systems through the study of a simple Ising model. In particular, we consider a chain of Curie-Weiss models that are coupled by interactions up to a certain range. Indeed, it is well known that the pure (uncoupled) Curie-Weiss model undergoes a first-order phase transition driven by the magnetic field, and furthermore in the spinodal region such systems are unable to reach equilibrium in subexponential time if initialized in the metastable state. In contrast, the spatially coupled system is instead able to reach the equilibrium even when initialized to the metastable state. The equilibrium phase propagates along the chain in the form of a traveling wave. Here we study the speed of the wave front and the so-called termination cost—i.e., the conditions necessary for the propagation to occur. We reach several interesting conclusions about optimization of the speed and the cost.
Mean field analysis of a spatial stochastic model of a gene regulatory network.
Sturrock, M; Murray, P J; Matzavinos, A; Chaplain, M A J
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.
Mean-field and quantum-fluctuation dynamics in the driven dispersive Jaynes-Cummings model
NASA Astrophysics Data System (ADS)
Mavrogordatos, Th.; Szafulski, P.; Ginossar, E.; Szymańska, M. H.
In this work we investigate the regime of amplitude bistability in the driven dissipative Jaynes-Cummings (JC) model. We study the semiclassical equation dynamics in contrast to entangled cavity-photon and qubit quantum trajectories, discussing our results in the context of an out-of-equilibrium first order quantum dissipative phase transition for a single JC resonator. Finally, we compare the switching process between metastable states for the two system degrees of freedom by examining a single realization of the random qubit vector in the Bloch sphere next to the intracavity amplitude quasi distributions at given time instants.
Analytical approaches to modelling panspermia - beyond the mean-field paradigm
NASA Astrophysics Data System (ADS)
Lingam, Manasvi
We model the process of panspermia by adopting two different approaches. The first method conceives it as a self-replication process, endowed with non-local creation and extinction. We show that some features suggestive of universal behaviour emerge, such as exponential decay or growth, and a power spectral density that displays a power-law behaviour in a particular regime. We also present a special case wherein the number density of the planets seeded through panspermia approaches a finite asymptotic distribution. The power spectral density for the independent and spontaneous emergence of life is investigated in conjunction with its counterpart for panspermia. The former exhibits attributes characteristic of a noise spectrum, including the resemblance to white noise in a certain regime. These features are absent in panspermia, suggesting that the power spectral density could be utilized as a future tool for differentiating between the two processes. Our second approach adopts the machinery of Markov processes and diffusion, and we show that the power spectral density exhibits a power-law tail in some domains, as earlier, suggesting that this behaviour may be fairly robust. We comment on a generalization of the diffusive model, and also indicate how the methods and results developed herein could be used to analyse other phenomena.
Mott transitions in a three-component Falicov-Kimball model: A slave boson mean-field study
NASA Astrophysics Data System (ADS)
Le, Duc-Anh; Tran, Minh-Tien
Metal-insulator transitions in a three-component Falicov-Kimball model are investigated within the Kotliar-Ruckenstein slave boson mean-field approach. The model describes a mixture of two interacting fermion atom species loaded into an optical lattice at ultralow temperature. One species is two-component atoms, which can hop in the optical lattice, and the other is single-component atoms, which are localized. Different correlation-driven metal-insulator transitions are observed depending on the atom filling conditions and local interactions. These metal-insulator transitions are classified by the band renormalization factors and the double occupancies of the atom species. The filling conditions and the critical value of the local interactions for these metal-insulator transitions are also analytically established. The obtained results not only are in good agreement with the dynamical mean-field theory for the three-component Falicov-Kimball model but also clarify the nature and properties of the metal-insulator transitions in a simple physics picture.
Mean-field dispersion-induced spatial synchrony, oscillation and amplitude death, and temporal stability in an ecological model.
Banerjee, Tanmoy; Dutta, Partha Sharathi; Gupta, Anubhav
One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersal-induced stability interact. In the existing studies it is shown that dispersion among identical patches results in spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a proper interpretation of AD and OD in ecology, which may be important for the conservation and management of several communities in ecosystems.
A nonlinear relativistic nuclear model for protoneutronstars
NASA Astrophysics Data System (ADS)
Razeira, M.; Vasconcellos, C. A. Z.; Dillig, M.
In the last few decades, studies on the internal structure, composition, dynamics and evolution of protoneutron stars, neutron stars, pulsars, hybrid and strange stars became central topics for theoretical and experimental research. Since the observation of the first pulsar in 1967, whose characteristic observational features allowed its identification as a rotating neutron star, nuclear models have been widely employed in the description of the holly graal of modern physics, the equation of state of dense matter. As under the pull of gravity the energy density in the core of these compact stars is thought to approach or even exceed more than 6 times the density of ordinary nuclear matter, predictions on the structure of the stars depend sensitively on the equation of state provided by model calculations. Combined with the equations of the general relativity metric, predictions on the mass, radius, crust extent and moment of inertia of the stars are then susceptible to the comparison to observation. In this work, a theoretical modeling for protoneutron stars (nuclear matter at finite temperature) is studied in the framework of an effective many-body relativistic mean field theory and the Sommerfeld approximation which contains the fundamental baryon octet and leptonic degrees of freedom, sigma, omega, rho and delta mesons, chemical equilibrium and charge neutrality. Our predictions include the determination of the mass of protoneutron stars, the mass-radius relation, relative population, gravitational redshift among other properties.
Non-perturbative corrections to mean-field critical behavior: the spherical model on a spider-web graph
NASA Astrophysics Data System (ADS)
Balram, Ajit C.; Dhar, Deepak
We consider the spherical model on a spider-web graph. This graph is effectively infinite dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of δ-functions, and all the modes are localized. The fractional number of modes with frequency less than ω varies as exp ( - C/ω) for ω tending to zero, where C is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time t varies as exp ( - C‧t1/3), for large t, where C‧ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free energy per site at temperature T, near and above the critical temperature Tc, also has an essential singularity of the type exp [ - K(T - Tc)-1/2].
Self-consistent mean-field model based on molecular dynamics: Application to lipid-cholesterol bilayers
NASA Astrophysics Data System (ADS)
Khelashvili, George A.; Pandit, Sagar A.; Scott, H. L.
We have developed a dynamic self-consistent mean-field model, based on molecular-dynamics simulations, to study lipid-cholesterol bilayers. In this model the lipid bilayer is represented as a two-dimensional lattice field in the lipid chain order parameters, while cholesterol molecules are represented by hard rods. The motion of rods in the system is continuous and is not confined to lattice cells. The statistical mechanics of chain ordering is described by a mean field derived from an extension of a model due to Marčelja. The time evolution of the system is governed by stochastic equations. The ensemble of chain configurations required in partition sums, and the energies of interaction, are taken from atomistic level molecular-dynamics simulations of lipid bilayers. The model allows us to simulate systems 500nm in lateral size for 20μs time scales, or greater. We have applied the model to dipalmitoyl-phosphatidylcholine-cholesterol (Chol) bilayers at 50°C for Chol concentrations between 2% and 33%. At low concentrations of Chol (2%-4%), the model predicts the formation of isolated clusters of Chol surrounded by relatively ordered lipid chains, randomly dispersed in the disordered bilayer. With increasing Chol composition, regions of Chol-induced order begin to overlap. Starting from about 11% Chol this ordering effect becomes system wide and regions unaffected by Chol are no longer detectable. From the analysis of properties of the model we conclude that the change in lipid chain order with increasing Chol concentration is continuous over the 20-μs scale of the simulations. We also conclude that at 50°C no large-scale Chol-rich and Chol-depleted coexisting phase-separated regions form at any concentration. At no point in any of the simulations do we observe a higher degree of lateral organization, such as Chol-based superlattice structures.
Approximate analytical solution for nuclear matter in a mean-field Walecka model and Coester line behavior
Delfino, A.; Silva, J.B.; Malheiro, M.
We study nuclear matter, at the mean-field approximation, by considering as equal the values of the scalar and the vector density in the Walecka model, which is a very reasonable approximation up to the nuclear matter saturation density. It turns out that the model has an analytical solution for the scalar and vector couplings as functions only of the nuclear matter density and binding energy. The nuclear matter properties are very close to the original version of the model. This solution allows us to show that the correlation between the binding energy and the saturation density is Coester line like. The liquid-gas phase transition is also studied and the critical and flash temperatures are again very similar to the original ones.
Modeling MHD accretion-ejection: episodic ejections of jets triggered by a mean-field disk dynamo
Stepanovs, Deniss; Fendt, Christian; Sheikhnezami, Somayeh E-mail: firstname.lastname@example.com
We present MHD simulations exploring the launching, acceleration, and collimation of jets and disk winds. The evolution of the disk structure is consistently taken into account. Extending our earlier studies, we now consider the self-generation of the magnetic field by an α{sup 2}Ω mean-field dynamo. The disk magnetization remains on a rather low level, which helps to evolve the simulations for T > 10, 000 dynamical time steps on a domain extending 1500 inner disk radii. We find the magnetic field of the inner disk to be similar to the commonly found open field structure, favoring magneto-centrifugal launching. The outer disk field is highly inclined and predominantly radial. Here, differential rotation induces a strong toroidal component, which plays a key role in outflow launching. These outflows from the outer disk are slower, denser, and less collimated. If the dynamo action is not quenched, magnetic flux is continuously generated, diffuses outward through the disk, and fills the entire disk. We have invented a toy model triggering a time-dependent mean-field dynamo. The duty cycles of this dynamo lead to episodic ejections on similar timescales. When the dynamo is suppressed as the magnetization falls below a critical value, the generation of the outflows and also accretion is inhibited. The general result is that we can steer episodic ejection and large-scale jet knots by a disk-intrinsic dynamo that is time-dependent and regenerates the jet-launching magnetic field.
Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model
NASA Astrophysics Data System (ADS)
Yucesoy, Burcu; Katzgraber, Helmut G.; Machta, Jonathan
The three and four-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states. J. M. and B. Y. are supported in part by the NSF (Grant No. DMR-0907235 and DMR-1208046).
Fractional Spin Fluctuations as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model.
Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi
Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.
Irreversible mean-field model of the critical behavior of charge-density waves below the threshold for sliding
NASA Astrophysics Data System (ADS)
Sornette, Didier
A mean-field (MF) model of the critical behavior of charge-density waves below the threshold for sliding is proposed, which replaces the combined effect of the pinning force and of the forces exerted by the neighbors on a given particle n by an effective force threshold Xn. It allows one to rationalize the numerical results of Middleton and Fisher [Phys. Rev. Lett. 66 (1991) 92] on the divergence of the polarization and of the largest correlation length and of Pla and Nori [Phys. Rev. Lett. 67 (1991) 919] on the distribution D( d) of sliding bursts of size d, measured in narrow intervals of driving fields E at a finite distance below the threshold Ec.
Fractional Spin Fluctuations as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
NASA Astrophysics Data System (ADS)
Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi
Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.
Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling
NASA Astrophysics Data System (ADS)
Koehl, Patrice; Orland, Henri; Delarue, Marc
We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ1 for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.
Adapting Poisson-Boltzmann to the self-consistent mean field theory: application to protein side-chain modeling.
Koehl, Patrice; Orland, Henri; Delarue, Marc
We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ(1) for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.
Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling
Koehl, Patrice; Orland, Henri; Delarue, Marc
We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ1 for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains. PMID:21823735
Kinetic phase transitions in a surface-reaction model with diffusion: Computer simulations and mean-field theory
NASA Astrophysics Data System (ADS)
Jensen, Iwan; Fogedby, Hans C.
A simple surface-reaction model based upon the oxidation of carbon monoxide on a catalytic surface, introduced by Ziff, Gulari, and Barshad (ZGB) [Phys. Rev. Lett. 56, 2553 (1986)], has been extended in order to include diffusion of the adsorbed particles (both O and CO). The ZGB model is a nonequilibrium model exhibiting both a first- and a second-order phase transition. The effects of diffusion on the behavior of the model has been explored by means of computer simulations. The main effect of diffusion is to change the positions of the phase transitions and increase the rate of CO2 formation. Fast diffusion causes the second-order transition to disappear from the system. Simple explanations of these changes are given. The extended version of the ZGB model has furthermore been studied by mean-field theory in the pair approximation. This approach gives qualitatively correct predictions about the effects of diffusion and yields quantitative predictions in good agreement with simulation results in the vicinity of the first-order transition.
Large pseudocounts and L2-norm penalties are necessary for the mean-field inference of Ising and Potts models
NASA Astrophysics Data System (ADS)
Barton, J. P.; Cocco, S.; De Leonardis, E.; Monasson, R.
The mean-field (MF) approximation offers a simple, fast way to infer direct interactions between elements in a network of correlated variables, a common, computationally challenging problem with practical applications in fields ranging from physics and biology to the social sciences. However, MF methods achieve their best performance with strong regularization, well beyond Bayesian expectations, an empirical fact that is poorly understood. In this work, we study the influence of pseudocount and L2-norm regularization schemes on the quality of inferred Ising or Potts interaction networks from correlation data within the MF approximation. We argue, based on the analysis of small systems, that the optimal value of the regularization strength remains finite even if the sampling noise tends to zero, in order to correct for systematic biases introduced by the MF approximation. Our claim is corroborated by extensive numerical studies of diverse model systems and by the analytical study of the m-component spin model for large but finite m. Additionally, we find that pseudocount regularization is robust against sampling noise and often outperforms L2-norm regularization, particularly when the underlying network of interactions is strongly heterogeneous. Much better performances are generally obtained for the Ising model than for the Potts model, for which only couplings incoming onto medium-frequency symbols are reliably inferred.
Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model.
Oliveira, T P; Branco, N S
We employ a mean-field approximation to study the Ising model with aperiodic modulation of its interactions in one spatial direction. Two different values for the exchange constant, J(A) and J(B), are present, according to the Fibonacci sequence. We calculate the pseudocritical temperatures for finite systems and extrapolate them to the thermodynamic limit. We explicitly obtain the exponents β, δ, and γ and, from the usual scaling relations for anisotropic models at the upper critical dimension (assumed to be 4 for the model we treat), we calculate α, ν, ν(∥), η, and η(∥). Within the framework of a renormalization-group approach, the Fibonacci sequence is a marginal one and we obtain exponents that depend on the ratio r≡J(B)/J(A), as expected; however, the scaling relation γ=β(δ-1) is obeyed for all values of r we studied. We characterize some thermodynamic functions as log-periodic functions of their arguments, as expected for aperiodic-modulated models, and obtain precise values for the exponents from this characterization.
Growth-induced polarity formation in solid solutions of organic molecules: Markov mean-field model and Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Wüst, Thomas; Hulliger, Jürg
A layer-by-layer growth model is presented for the theoretical investigation of growth-induced polarity formation in solid solutions H1-XGX of polar (H) and nonpolar (G) molecules (X: molar fraction of G molecules in the solid, 0
Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models
NASA Astrophysics Data System (ADS)
Steenbakkers, Rudi J. A.; Tzoumanekas, Christos; Li, Ying; Liu, Wing Kam; Kröger, Martin; Schieber, Jay D.
We present a method to map the full equilibrium distribution of the primitive-path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field 'target' model. Most previous works used the Doi-Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which includes fluctuations in all these variables as well as in the spatial positions of the entanglements. This turns out to be essential to obtain qualitative and quantitative agreement with the equilibrium PP-length distribution obtained from multi-chain simulations. By fitting this distribution, we are able to determine two of the three parameters of the model, which govern its equilibrium properties. This mapping is executed for four different linear polymers and for different molecular weights. The two parameters are found to depend on chemistry, but not on molecular weight. The model predicts a constant plateau modulus minus a correction inversely proportional to molecular weight. The value for well-entangled chains, with the parameters determined ab initio, lies in the range of experimental data for the materials investigated.
Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes
NASA Astrophysics Data System (ADS)
Sampaio Filho, C. I. N.; dos Santos, T. B.; Moreira, A. A.; Moreira, F. G. B.; Andrade, J. S.
We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability Pi j˜r-α , where ri j is the Manhattan distance between nodes i and j , and the exponent α is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000), 10.1038/35022643]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent α . Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For α ≤3 the critical behavior is described by mean-field exponents, while for α ≥4 it belongs to the Ising universality class. Finally, in the region where the crossover occurs, 3 <α <4 , the critical exponents are dependent on α .
Fine structure of the spectra of the Kondo lattice model: Two-site cellular dynamical mean-field theory study
NASA Astrophysics Data System (ADS)
Osolin, Žiga; Žitko, Rok
We study the antiferromagnetic and paramagnetic Kondo insulator phases of the Kondo lattice model on the cubic lattice at half filling using the cellular dynamical mean-field theory (CDMFT) with the numerical renormalization group (NRG) as the impurity solver, focusing on the fine details of the spectral function and self-energy. We find that the nonlocal correlations increase the gap in both the antiferromagnetic and Kondo insulator phases and shrink the extent of the antiferromagnetic phase in the phase diagram but do not alter any properties qualitatively. The agreement between the numerical CDMFT results and those within a simple hybridization picture, which adequately describes the overall band structure of the system but neglects all effects on the inelastic-scattering processes, is similar to that of the single-site DMFT results; there are deviations that are responsible for the additional fine structure, in particular for the asymmetric spectral resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic quantum phase transition. These features appear broader in the CDMFT mostly due to numerical artifacts linked to more aggressive state truncation required in the NRG.
Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes.
Sampaio Filho, C I N; Dos Santos, T B; Moreira, A A; Moreira, F G B; Andrade, J S
We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability P_{ij}∼r^{-α}, where r_{ij} is the Manhattan distance between nodes i and j, and the exponent α is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000)NATUAS0028-083610.1038/35022643]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent α. Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For α≤3 the critical behavior is described by mean-field exponents, while for α≥4 it belongs to the Ising universality class. Finally, in the region where the crossover occurs, 3<α<4, the critical exponents are dependent on α.
Static quadrupolar susceptibility for a Blume-Emery-Griffiths model based on the mean-field approximation
NASA Astrophysics Data System (ADS)
Pawlak, A.; Gülpınar, G.; Erdem, R.; Ağartıoğlu, M.
The expressions for the dipolar and quadrupolar susceptibilities are obtained within the mean-field approximation in the Blume-Emery-Griffiths model. Temperature as well as crystal field dependences of the susceptibilities are investigated for two different phase diagram topologies which take place for K/J=3 and K/J=5.0.Their behavior near the second and first order transition points as well as multi-critical points such as tricritical, triple and critical endpoint is presented. It is found that in addition to the jumps connected with the phase transitions there are broad peaks in the quadrupolar susceptibility. It is indicated that these broad peaks lie on a prolongation of the first-order line from a triple point to a critical point ending the line of first-order transitions between two distinct paramagnetic phases. It is argued that the broad peaks are a reminiscence of very strong quadrupolar fluctuations at the critical point. The results reveal the fact that near ferromagnetic-paramagnetic phase transitions the quadrupolar susceptibility generally shows a jump whereas near the phase transition between two distinct paramagnetic phases it is an edge-like.
The relativistic Black-Scholes model
NASA Astrophysics Data System (ADS)
Trzetrzelewski, Maciej
The Black-Scholes equation, after a certain coordinate transformation, is equivalent to the heat equation. On the other hand the relativistic extension of the latter, the telegraphers equation, can be derived from the Euclidean version of the Dirac equation. Therefore, the relativistic extension of the Black-Scholes model follows from relativistic quantum mechanics quite naturally. We investigate this particular model for the case of European vanilla options. Due to the notion of locality incorporated in this way, one finds that the volatility frown-like effect appears when comparing to the original Black-Scholes model.
Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.
Cruz, Roberto de la; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance
Analytic models of relativistic accretion disks
NASA Astrophysics Data System (ADS)
Zhuravlev, V. V.
We present not a literature review but a description, as detailed and consistent as possible, of two analytic models of disk accretion onto a rotating black hole: a standard relativistic disk and a twisted relativistic disk. Although one of these models is older than the other, both are of topical interest for black hole studies. The treatment is such that the reader with only a limited knowledge of general relativity and relativistic hydrodynamics, with little or no use of additional sources, can gain insight into many technical details lacking in the original papers.
Slave-boson mean-field theory versus variational-wave-function approach for the periodic Anderson model
NASA Astrophysics Data System (ADS)
Yang, Min-Fong; Sun, Shih-Jye; Hong, Tzay-Ming
We show that a special kind of slave-boson mean-field approximation, which allows for the symmetry-broken states appropriate for a bipartite lattice, can give essentially the same results as those by the variational-wave-function approach proposed by Gula´csi, Strack, and Vollhardt [Phys. Rev. B 47, 8594 (1993)]. The advantages of our approach are briefly discussed.
Continuous Time Finite State Mean Field Games
Gomes, Diogo A.; Mohr, Joana Souza, Rafael Rigao
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.
Exact quantisation of the relativistic Hopfield model
NASA Astrophysics Data System (ADS)
Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M.
We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.
Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model.
Coen, Stéphane; Randle, Hamish G; Sylvestre, Thibaut; Erkintalo, Miro
A generalized Lugiato-Lefever equation is numerically solved with a Newton-Raphson method to model Kerr frequency combs. We obtain excellent agreement with past experiments, even for an octave-spanning comb. Simulations are much faster than with any other technique despite including more modes than ever before. Our study reveals that Kerr combs are associated with temporal cavity solitons and dispersive waves, and opens up new avenues for the understanding of Kerr-comb formation.
Modeling of Entangled Network Chains and Linear Solvent Chains in a Single-Chain-Mean-Field Slip-Link Model
J. L. Influence of Solvent Size on the Mechanical Properties and Rheology of Polydimethylsiloxane-based Polymeric Gels. Polymer 2011, 52, 3422–3430...2. Schieber, J. Fluctuations in Entanglements of Polymer Liquids. Journal of Chemical Physics 2003, 18 (11), 5162–5166. 3. Schieber, J.; Neergaard, J...Gupta, S. A Full-chain, Temporary Network Model with Sliplinks, Chain-length Fluctuations, Chain Connectivity and Chain Stretching. Journal of
Advanced relativistic VLBI model for geodesy
NASA Astrophysics Data System (ADS)
Soffel, Michael; Kopeikin, Sergei; Han, Wen-Biao
Our present relativistic part of the geodetic VLBI model for Earthbound antennas is a consensus model which is considered as a standard for processing high-precision VLBI observations. It was created as a compromise between a variety of relativistic VLBI models proposed by different authors as documented in the IERS Conventions 2010. The accuracy of the consensus model is in the picosecond range for the group delay but this is not sufficient for current geodetic purposes. This paper provides a fully documented derivation of a new relativistic model having an accuracy substantially higher than one picosecond and based upon a well accepted formalism of relativistic celestial mechanics, astrometry and geodesy. Our new model fully confirms the consensus model at the picosecond level and in several respects goes to a great extent beyond it. More specifically, terms related to the acceleration of the geocenter are considered and kept in the model, the gravitational time-delay due to a massive body (planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived taking into account the motion of the body, and a new formalism for the time-delay problem of radio sources located at finite distance from VLBI stations is presented. Thus, the paper presents a substantially elaborated theoretical justification of the consensus model and its significant extension that allows researchers to make concrete estimates of the magnitude of residual terms of this model for any conceivable configuration of the source of light, massive bodies, and VLBI stations. The largest terms in the relativistic time delay which can affect the current VLBI observations are from the quadrupole and the angular momentum of the gravitating bodies that are known from the literature. These terms should be included in the new geodetic VLBI model for improving its consistency.
Periodic mean-field solutions and the spectra of discrete bosonic fields: Trace formula for Bose-Hubbard models.
Engl, Thomas; Urbina, Juan Diego; Richter, Klaus
We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number N. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, nonperturbative solutions of the, typically nonlinear, wave equation of the classical (mean-field) limit. To this end, we construct the semiclassical approximation for both the smooth and oscillatory parts of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects such as vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommensurable frequencies, our formulas are generically valid also in the free-field case of noninteracting bosons.
Screening parameters for the relativistic hydrogenic model
NASA Astrophysics Data System (ADS)
Lanzini, Fernando; Di Rocco, Héctor O.
We present a Relativistic Screened Hydrogenic Model (RSHM) where the screening parameters depend on the variables (n , l , j) and the parameters (Z , N) . These screening parameters were derived theoretically in a neat form with no use of experimental values nor numerical values from self-consistent codes. The results of the model compare favorably with those obtained by using more sophisticated approaches. For the interested reader, a copy of our code can be requested from the corresponding author.
Interface-roughening phase diagram of the three-dimensional Ising model for all interaction anisotropies from hard-spin mean-field theory.
Cağlar, Tolga; Berker, A Nihat
The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d=2 Ising model for the full range of anisotropy, yielding no roughening transition.
Modeling relativistic plasmas with PIC using VORPAL
NASA Astrophysics Data System (ADS)
Nieter, Chet; Cary, John R.
VORPAL, a fully object-oriented, dimension-free plasma simulation code, now has a fully developed PIC model. This PIC model has been applied to studies of Laser Wake Field Acceleration, including the nonlinear structure of the wake field generated in the colliding pulse injection scheme and in the development of a new injection scheme that reduces timing requirements. (See Giacone et al. and Cary et al. at this conference). Since the PIC model was developed using VORPAL's object oriented architecture, it works in any dimension and with both serial and parallel runs. Several different update methods are available, including both relativistic and non-relativistic Boris push and an electrostatic update as well.
Information geometry of mean-field approximation.
Tanaka, T
I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.
Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics.
Marten, Frank; Rodrigues, Serafim; Suffczynski, Piotr; Richardson, Mark P; Terry, John R
In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations. We demonstrate that transitions to epileptic dynamics via changes in system parameters are qualitatively the same as in the original model with delay, as well as demonstrating that the onset of epileptic activity may arise due to regions of bistability. Hence, the model presents in one unique framework, two competing theories for the genesis of epileptiform activity. Similarities between model transitions and clinical data are presented and we argue that statistics obtained from, and a parameter estimation of this model may be a potential means of classifying and predicting the onset and offset of seizure activity.
Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach
NASA Astrophysics Data System (ADS)
Haldar, P.; Laad, M. S.; Hassan, S. R.
It is long known that the best single-site coherent potential approximation falls short of describing Anderson localization. Here, we study a binary alloy disorder [or equivalently, a spinless Falicov-Kimball (FK)] model and construct a dominantly analytic cluster extension that treats intracluster (1 /d ,d = spatial dimension) correlations exactly. We find that, in general, the irreducible two-particle vertex exhibits clear nonanalyticities before the band splitting transition of the Hubbard type occurs, signaling onset of an unusual type of localization at strong coupling. Using time-dependent response to a sudden local quench as a diagnostic, we find that the long-time wave-function overlap changes from a power-law to an anomalous form at strong coupling, lending additional support to this idea. Our results also imply such "strong" localization in the equivalent FK model, the simplest interacting fermion system.
Construction of traveling clusters in the Hamiltonian mean-field model by nonequilibrium statistical mechanics and Bernstein-Greene-Kruskal waves.
Yamaguchi, Yoshiyuki Y
Traveling clusters are ubiquitously observed in the Hamiltonian mean-field model for a wide class of initial states, which are not predicted to become spatially inhomogeneous states by nonequilibrium statistical mechanics and by nonlinear Landau damping. To predict such a cluster state from a given initial state, we combine nonequilibrium statistical mechanics and a construction method of Bernstein-Greene-Kruskal (BGK) waves with the aid of phenomenological assumptions. The phenomenological theory is partially successful, and the theoretically constructed cluster states are in good agreement with N-body simulations. Robustness of the theory is also discussed for unsuccessful initial states.
A mean-field model of the alkane-saturated lipid bilayer above its phase transition. I. Development of the model.
Gruen, D W
A statistical mechanical model of a bilayer of dipalmitoyl-3-sn-phosphatidylcholine molecules in equilibrium with an aqueous phase saturated with an n-alkane is presented. A mean-field approach developed in previous work on a solventless bilayer (Gruen, Biochim. Biophys. Acta. 595:161--183, 1980) is extended to allow alkane chains to exist in the hydrophobic core of the membrane. As the alkane chains are chemically similar to the lipid chains, much of the analysis follows directly from the solventless model. Novel features of the present model are the inclusion of (a) a term which models the free energy cost of creating space for alkane conformations, (b) a term which constrains the chains to pack evenly in the hydrophobic region of the membrane, and (c) a term which estimates the free energy of mixing of the lipid and alkane molecules in the plane of the bilayer. On uptake of alkane, the dimensions of the bilayer increase. Allowance is made for an increase in thickness and/or an increase in area per lipid. A thermodynamic framework is established which allows evaluation of the free energy of a bilayer of arbitrary dimensions with a view to predicting the equilibrium structure. PMID:6894396
Application of the Stoner-Wohlfarth model with interaction for the determination of the saturation magnetisation, anisotropy field, and mean field interaction in bulk amorphous ferromagnets
NASA Astrophysics Data System (ADS)
Collocott, S. J.
Magnetic hysteresis curves of bulk amorphous ferromagnet alloys of composition Nd 60Fe 30Al 10, Nd 60Fe 20Co 10Al 10 and Pr 58Fe 24Al 18 have been measured in applied magnetic fields up to 9 T at temperatures in the range 10-350 K. The behaviour of the demagnetisation curve in the first quadrant is interpreted using a mean field interaction model as proposed by Callen et al. [Phys. Rev. B 16 (1977) 263], which extends the Stoner-Wohlfarth model [Philos. Trans. Roy. Soc. A 240 (1948) 599] for a random distribution of non-interacting uniaxial grains. Application of the mean field interaction model enables the determination of the saturation magnetisation Ms, anisotropy field Ha, and interaction parameter d, and from these other magnetic parameters, such as the anisotropy constant, K, are deduced. For the three alloys, the temperature dependent behaviour of Ms, Ha, d and K over the range 20-350 K are found to be qualitatively similar, though there are quantitative differences. In all cases Ms increases with decreasing temperature, both Ha and K increase with decreasing temperature, reaching a peak in the range 75-120 K, and then decreasing, and d decreases approximately linearly as the temperature decreases. The physical mechanisms responsible for coercivity in these materials are discussed in the context of random anisotropy and a strong pinning model of domain walls.
Effect of platykurtic and leptokurtic distributions in the random-field Ising model: mean-field approach.
Duarte Queirós, Sílvio M; Crokidakis, Nuno; Soares-Pinto, Diogo O
The influence of the tail features of the local magnetic field probability density function (PDF) on the ferromagnetic Ising model is studied in the limit of infinite range interactions. Specifically, we assign a quenched random field whose value is in accordance with a generic distribution that bears platykurtic and leptokurtic distributions depending on a single parameter tau<3 to each site. For tau<5/3, such distributions, which are basically Student-t and r distribution extended for all plausible real degrees of freedom, present a finite standard deviation, if not the distribution has got the same asymptotic power-law behavior as a alpha-stable Lévy distribution with alpha=(3-tau)/(tau-1). For every value of tau, at specific temperature and width of the distribution, the system undergoes a continuous phase transition. Strikingly, we impart the emergence of an inflexion point in the temperature-PDF width phase diagrams for distributions broader than the Cauchy-Lorentz (tau=2) which is accompanied with a divergent free energy per spin (at zero temperature).
Finite nuclei in relativistic models with a light chiral scalar meson
Serot, B.D.; Furnstahl, R.J.
Relativistic chiral models with a light scalar, meson appear to provide an economical marriage of successful relativistic mean-field theories and chiral symmetry. In these models, the scalar meson serves as both the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon (NN) attraction. However, while some of these models can reproduce the empirical nuclear matter saturation point, they fail to reproduce observed properties of finite nuclei, such as spin-orbit splittings, shell structure, charge densities, and surface energetics. There deficiencies imply that this realization of chiral symmetry is incorrect. An alternative scenario for chiral hadronic models, which features a heavy chiral scalar and dynamical generation of the NN attraction, is discussed.
Anomalous diffusion in the evolution of soccer championship scores: Real data, mean-field analysis, and an agent-based model
NASA Astrophysics Data System (ADS)
da Silva, Roberto; Vainstein, Mendeli H.; Gonçalves, Sebastián; Paula, Felipe S. F.
Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva , Comput. Phys. Commun.CPHCBZ0010-465510.1016/j.cpc.2012.10.030 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.
Finite nuclei in relativistic models with a light chiral scalar meson
Furnstahl, R.J. ); Serot, B.D. )
Relativistic chiral models with a light scalar meson appear to provide an economical marriage of successful relativistic mean-field theories and chiral symmetry. The scalar meson serves as both the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon ([ital NN]) attraction. However, while some of these models can reproduce the empirical nuclear matter saturation point, they fail to reproduce observed properties of finite nuclei, such as spin-orbit splittings, shell structure, charge densities, and surface energetics. These deficiencies imply that this realization of chiral symmetry is incorrect. An alternative scenario, which features a heavy chiral scalar and dynamical generation of the [ital NN] attraction, is discussed.
A Generalization of Mean Field Theory in a Cluster with Many Sites on the Ising Model from the Bogoliubov Inequality: Hexagonal Nanowire and Nanotube
NASA Astrophysics Data System (ADS)
Santos, Jander P.
A generalization of mean field theory in a cluster with many sites was obtained for the spin-1/2 Ising model from the Gibbs-Bogoliubov inequality. The expressions for the free energy and the magnetization were obtained. The generalization was applied in a structure of the nanowire and nanotube hexagonal lattices, for clusters of seven sites and six sites, respectively. The results for the magnetization, the free energy, the internal energy, the entropy, the specific heat, and the critical frontiers were obtained. The critical temperature and the compensation temperature in a cylindrical Ising nanowire are investigated, in order to clarify the distinction between the ferromagnetic and ferrimagnetic behaviors when the core-shell exchange coupling takes a different sign. The results were compared with other works.
A Generalization of Mean Field Theory in a Cluster with Many Sites on the Ising Model from the Bogoliubov Inequality: Hexagonal Nanowire and Nanotube
NASA Astrophysics Data System (ADS)
Santos, Jander P.
A generalization of mean field theory in a cluster with many sites was obtained for the spin-1/2 Ising model from the Gibbs-Bogoliubov inequality. The expressions for the free energy and the magnetization were obtained. The generalization was applied in a structure of the nanowire and nanotube hexagonal lattices, for clusters of seven sites and six sites, respectively. The results for the magnetization, the free energy, the internal energy, the entropy, the specific heat, and the critical frontiers were obtained. The critical temperature and the compensation temperature in a cylindrical Ising nanowire are investigated, in order to clarify the distinction between the ferromagnetic and ferrimagnetic behaviors when the core-shell exchange coupling takes a different sign. The results were compared with other works.
Relativistic constituent quark model with infrared confinement
Branz, Tanja; Faessler, Amand; Gutsche, Thomas; Lyubovitskij, Valery E.; Ivanov, Mikhail A.; Koerner, Juergen G.
We refine the relativistic constituent quark model developed in our previous papers to include the confinement of quarks. It is done, first, by introducing the scale integration in the space of {alpha} parameters, and, second, by cutting this scale integration on the upper limit which corresponds to an infrared cutoff. In this manner one removes all possible thresholds present in the initial quark diagram. The cutoff parameter is taken to be the same for all physical processes. We adjust other model parameters by fitting the calculated quantities of the basic physical processes to available experimental data. As an application, we calculate the electromagnetic form factors of the pion and the transition form factors of the {omega} and {eta} Dalitz decays.
Fornace, Mark E; Lee, Joonho; Miyamoto, Kaito; Manby, Frederick R; Miller, Thomas F
We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.
Accurate mean-field modeling of the Barkhausen noise power in ferromagnetic materials, using a positive-feedback theory of ferromagnetism
NASA Astrophysics Data System (ADS)
Harrison, R. G.
A mean-field positive-feedback (PFB) theory of ferromagnetism is used to explain the origin of Barkhausen noise (BN) and to show why it is most pronounced in the irreversible regions of the hysteresis loop. By incorporating the ABBM-Sablik model of BN into the PFB theory, we obtain analytical solutions that simultaneously describe both the major hysteresis loop and, by calculating separate expressions for the differential susceptibility in the irreversible and reversible regions, the BN power response at all points of the loop. The PFB theory depends on summing components of the applied field, in particular, the non-monotonic field-magnetization relationship characterizing hysteresis, associated with physical processes occurring in the material. The resulting physical model is then validated by detailed comparisons with measured single-peak BN data in three different steels. It also agrees with the well-known influence of a demagnetizing field on the position and shape of these peaks. The results could form the basis of a physics-based method for modeling and understanding the significance of the observed single-peak (and in multi-constituent materials, multi-peak) BN envelope responses seen in contemporary applications of BN, such as quality control in manufacturing, non-destructive testing, and monitoring the microstructural state of ferromagnetic materials.
Designing a planar vector field to investigate the role of a slow variable in an enhanced mean-field model during general anesthesia
Molaee-Ardekani, Behnam; Shamsollahi, Mohammad-Bagher; Senhadji, Lotfi; Vosoughi-Vahdat, Bijan; Wodey, Eric
Local mean-field models (MFMs) describe regional brain activities by some connected differential equations. In an overall view, constituting variables of these differential equations can be divided to very fast, fast and slow variables. In this article we propose a method that can be used to determine role of a slow variable in behavior of MFMs. Very fast variables can be adiabatically removed from the equations. Isoclines of fast and slow variables and their corresponding vector field can provide valuable information about model behavior and role of the slow variable in it. The vector field of our interested MFM that is an enhanced MFM designed specially for general anesthesia, is a 3D field (one slow and two fast variables) and it is not so convenient for visually inspecting the role of the slow variable in this model. To afford this problem we design a 2D (planar) vector filed that only considers the slow variable and one of the fast variables. PMID:17946364
Mean-field coarse-grained model for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer systems.
García Daza, Fabián A; Colville, Alexander J; Mackie, Allan D
The microscopic modeling of surfactant systems is of the utmost importance in understanding the mechanisms related to the micellization process because it allows for prediction and comparison with experimental data of diverse equilibrium system properties. In this work, we present a coarse-grained model for Pluronics, a trademarked type of triblock copolymer, from simulations based on a single-chain mean-field theory (SCMF). This microscopic model is used to quantify the micellization process of these nonionic surfactants at 37 °C and has been shown to be able to quantitatively reproduce experimental data of the critical micelle concentration (CMC) along with other equilibrium properties. In particular, these results correctly capture the experimental behavior with respect to the lengths of the hydrophobic and hydrophilic moieties of the surfactants for low and medium hydrophobicities. However, for the more highly hydrophobic systems with low CMCs, a deviation is found which has been previously attributed to nonequilibrium effects in the experimental data (Garcı́a Daza, F. A.; Mackie, A. D. Low Critical Micelle Concentration Discrepancy between Theory and Experiment. J. Phys. Chem. Lett. 2014, 5, 2027-2032).
"Phase diagram" of a mean field game
NASA Astrophysics Data System (ADS)
Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis
Mean field games were introduced by J-M. Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the "seminar problem" introduced by O. Guéant, J-M. Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agents are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space. For this reason, the "seminar problem" appears to be an interesting toy model on which both intuition and technical approaches can be tested as a preliminary study toward more complex mean field game models.
Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases
NASA Astrophysics Data System (ADS)
PÈ©kalski, J.; Ciach, A.; Almarza, N. G.
The short-range attraction and long-range repulsion between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces, or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion. At the ground state of the model (T = 0) the lattice is empty for small values of the chemical potential μ, and fully occupied for large μ. For intermediate values of μ periodically distributed clusters, bubbles, or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For T > 0 we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.
Dynamic mean field theory for lattice gas models of fluids confined in porous materials: higher order theory based on the Bethe-Peierls and path probability method approximations.
Edison, John R; Monson, Peter A
Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.
Dynamic mean field theory for lattice gas models of fluids confined in porous materials: Higher order theory based on the Bethe-Peierls and path probability method approximations
Edison, John R.; Monson, Peter A.
Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.
Predictive beyond-mean-field rate equations for multisite lattice–gas models of catalytic surface reactions: CO oxidation on Pd(100)
Liu, Da -Jiang; Zahariev, Federico; Gordon, Mark S.; ...
Tailored multisite lattice–gas (msLG) models are developed for CO oxidation on Pd(100) at low-pressures. These models include multiple adsorption site types and superlattice adlayer ordering due to short-range exclusion for highly mobile reactant adspecies. However, they are simplified to neglect longer-range weaker adspecies interactions, so that the key energetic parameters are the CO desorption barrier and the reaction barrier. We discuss existing density functional theory results for these energies and present additional analysis for CO adsorption. After also including an appropriate nontrivial specification of the dynamics of adsorption onto mixed reactant adlayers, we develop rate equations for the reaction kinetics.more » Our formulation goes beyond traditional mean-field (MF) Langmuirian treatments by accounting for multiple adsorption sites and for the strong spatial correlations associated with superlattice ordering. Specifically, we utilize factorization approximations based on appropriate site motifs, and also Padé resummation of exact low-coverage expansions for sticking coefficients. Our beyond-MF rate equations are successful in accurately predicting key aspects of reactive steady-state behavior, and thus expand the utility of rate equation formulations in surface chemistry. This is confirmed by comparison with precise kinetic Monte Carlo simulation results. Furthermore, we not only assess bistability and criticality observed for CO oxidation but also find more complex multistability associated with symmetry-breaking transitions in high-coverage CO adlayers.« less
Predictive beyond-mean-field rate equations for multisite lattice–gas models of catalytic surface reactions: CO oxidation on Pd(100)
Liu, Da -Jiang; Zahariev, Federico; Gordon, Mark S.; Evans, James W.
Tailored multisite lattice–gas (msLG) models are developed for CO oxidation on Pd(100) at low-pressures. These models include multiple adsorption site types and superlattice adlayer ordering due to short-range exclusion for highly mobile reactant adspecies. However, they are simplified to neglect longer-range weaker adspecies interactions, so that the key energetic parameters are the CO desorption barrier and the reaction barrier. We discuss existing density functional theory results for these energies and present additional analysis for CO adsorption. After also including an appropriate nontrivial specification of the dynamics of adsorption onto mixed reactant adlayers, we develop rate equations for the reaction kinetics. Our formulation goes beyond traditional mean-field (MF) Langmuirian treatments by accounting for multiple adsorption sites and for the strong spatial correlations associated with superlattice ordering. Specifically, we utilize factorization approximations based on appropriate site motifs, and also Padé resummation of exact low-coverage expansions for sticking coefficients. Our beyond-MF rate equations are successful in accurately predicting key aspects of reactive steady-state behavior, and thus expand the utility of rate equation formulations in surface chemistry. This is confirmed by comparison with precise kinetic Monte Carlo simulation results. Furthermore, we not only assess bistability and criticality observed for CO oxidation but also find more complex multistability associated with symmetry-breaking transitions in high-coverage CO adlayers.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Mohseni, F.; Mendoza, M.; Succi, S.; Herrmann, H. J.
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1 / 2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation
NASA Astrophysics Data System (ADS)
Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.
Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from "wake" to "coma." In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the
Mean-field kinetic nucleation theory
NASA Astrophysics Data System (ADS)
Kalikmanov, V. I.
A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.
NASA Astrophysics Data System (ADS)
Karkheck, John; Stell, George
A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several
Mean field and collisions in hot nuclei
K /umlt o/hler, H.S.
Collisions between heavy nuclei produce nuclear matter of high density and excitation. Brueckner methods are used to calculate the momentum and temperature dependent mean field for nucleons propagating through nuclear matter during these collisions. The mean field is complex and the imaginary part is related to the ''two-body'' collision, while the real part relates to ''one-body'' collisions. A potential model for the N-N interactions is avoided by calculating the Reaction matrix directly from the T-matrix (i.e., N-N phase shifts) using a version of Brueckner theory previously published by the author. Results are presented for nuclear matter at normal and twice normal density and for temperatures up to 50 MeV. 23 refs., 7 figs.
Beyond-mean-field study of the hyperon impurity effect in hypernuclei with shape coexistence
NASA Astrophysics Data System (ADS)
Wu, X. Y.; Mei, H.; Yao, J. M.; Zhou, Xian-Rong
Background: The hyperon impurity effect in nuclei has been extensively studied in different mean-field models. Recently, there is a controversy about whether the Λ hyperon is more tightly bound in the normal deformed (ND) states than that in the superdeformed (SD) states. Purpose: This article is aimed to provide a beyond-mean-field study of the low-lying states of hypernuclei with shape coexistence and to shed some light on the controversy. Method: The models of relativistic mean field and beyond based on a relativistic point-coupling energy functional are adopted to study the low-lying states of both Ar37Lambda; and 36Ar. The wave functions of low-lying states are constructed as a superposition of a set of relativistic mean-field states with different values of quadrupole deformation parameter. The projections onto both particle number and angular momentum are considered. Results: The Λ binding energies in both ND and SD states of Ar37Lambda; are studied in the case of the Λ hyperon occupying the s ,p , or d state in the spherical limit, respectively. For comparison, four sets of nucleon-hyperon point-coupling interactions are used, respectively. Moreover, the spectra of low-lying states in 36Ar and
Relativistic Landau models and generation of fuzzy spheres
NASA Astrophysics Data System (ADS)
Hasebe, Kazuki
Noncommutative geometry naturally emerges in low energy physics of Landau models as a consequence of level projection. In this work, we proactively utilize the level projection as an effective tool to generate fuzzy geometry. The level projection is specifically applied to the relativistic Landau models. In the first half of the paper, a detail analysis of the relativistic Landau problems on a sphere is presented, where a concise expression of the Dirac-Landau operator eigenstates is obtained based on algebraic methods. We establish SU(2) "gauge" transformation between the relativistic Landau model and the Pauli-Schrödinger nonrelativistic quantum mechanics. After the SU(2) transformation, the Dirac operator and the angular momentum operators are found to satisfy the SO(3, 1) algebra. In the second half, the fuzzy geometries generated from the relativistic Landau levels are elucidated, where unique properties of the relativistic fuzzy geometries are clarified. We consider mass deformation of the relativistic Landau models and demonstrate its geometrical effects to fuzzy geometry. Super fuzzy geometry is also constructed from a supersymmetric quantum mechanics as the square of the Dirac-Landau operator. Finally, we apply the level projection method to real graphene system to generate valley fuzzy spheres.
Mean-field approaches for Ξ- hypernuclei and current experimental data
NASA Astrophysics Data System (ADS)
Sun, T. T.; Hiyama, E.; Sagawa, H.; Schulze, H.-J.; Meng, J.
Motivated by the recently observed hypernucleus (Kiso event) C15Ξ (14N+Ξ- ), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The Ξ N interactions are constructed to reproduce the two possibly observed Ξ- removal energies, 4.38 ±0.25 MeV or 1.11 ±0.25 MeV. The present result is preferable to be 14N(g .s .) +Ξ-(1 p ) , corresponding to the latter value.
Hot and dense hadronic matter in an effective mean-field approach
Lavagno, A.
We investigate the equation of state of hadronic matter at finite values of baryon density and temperature reachable in high-energy heavy-ion collisions. The analysis is performed by requiring the Gibbs conditions on the global conservation of baryon number, electric charge fraction, and zero net strangeness. We consider an effective relativistic mean-field model with the inclusion of DELTA isobars, hyperons, and the lightest pseudoscalar and vector meson degrees of freedom. In this context, we study the influence of the DELTA-isobar degrees of freedom in the hadronic equation of state and, in connection, the behavior of different particle-antiparticle ratios and strangeness production.
Nonrelativistic approaches derived from point-coupling relativistic models
Lourenco, O.; Dutra, M.; Delfino, A.; Sa Martins, J. S.
We construct nonrelativistic versions of relativistic nonlinear hadronic point-coupling models, based on new normalized spinor wave functions after small component reduction. These expansions give us energy density functionals that can be compared to their relativistic counterparts. We show that the agreement between the nonrelativistic limit approach and the Skyrme parametrizations becomes strongly dependent on the incompressibility of each model. We also show that the particular case A=B=0 (Walecka model) leads to the same energy density functional of the Skyrme parametrizations SV and ZR2, while the truncation scheme, up to order {rho}{sup 3}, leads to parametrizations for which {sigma}=1.
Dynamics of capillary condensation in lattice gas models of confined fluids: a comparison of dynamic mean field theory with dynamic Monte Carlo simulations.
Edison, John R; Monson, Peter A
This article addresses the accuracy of a dynamic mean field theory (DMFT) for fluids in porous materials [P. A. Monson, J. Chem. Phys. 128, 084701 (2008)]. The theory is used to study the relaxation processes of fluids in pores driven by step changes made to a bulk reservoir in contact with the pore. We compare the results of the DMFT to those obtained by averaging over large numbers of dynamic Monte Carlo (DMC) simulation trajectories. The problem chosen for comparison is capillary condensation in slit pores, driven by step changes in the chemical potential in the bulk reservoir and involving a nucleation process via the formation of a liquid bridge. The principal difference between the DMFT results and DMC is the replacement of a distribution of nucleation times and location along the pore for the formation of liquid bridges by a single time and location. DMFT is seen to yield an otherwise qualitatively accurate description of the dynamic behavior.
Modeling the magnetic isotherms of (La0.56Ce0.14)Sr0.30MnO3 by a mean-field scaling method and estimation of magnetic entropy change
NASA Astrophysics Data System (ADS)
Yahyaoui, S.; Khalfaoui, M.; Kallel, S.; Kallel, N.; Amaral, J. S.; Ben Lamine, A.
We report a study on the magnetic properties of the (La0.56Ce0.14)Sr0.30MnO3 perovskite, by a mean-field method. By scaling of the experimental magnetization data, the mean-field exchange parameter λ and the BS function of the equation of state BS [ (H +Hexch) / T ] are directly determined, as well as the order of the phase transition. The spin quantum number of the manganite has been also determined. The mean-field scaling has been used to estimate magnetic entropy change (- ΔSM) within the thermodynamics of the model and without using the usual numerical integration of a Maxwell relation. The maxima of the positive absolute value of (- ΔSM) upon variation of the applied magnetic field at 1 and 5 T are about 1.68 and 5.04 J kg-1 K-1, respectively. Satisfactory agreement between the mean-field model and experimental behavior has been found.
The relativistic feedback discharge model of terrestrial gamma ray flashes
NASA Astrophysics Data System (ADS)
Dwyer, Joseph R.
As thunderclouds charge, the large-scale fields may approach the relativistic feedback threshold, above which the production of relativistic runaway electron avalanches becomes self-sustaining through the generation of backward propagating runaway positrons and backscattered X-rays. Positive intracloud (IC) lightning may force the large-scale electric fields inside thunderclouds above the relativistic feedback threshold, causing the number of runaway electrons, and the resulting X-ray and gamma ray emission, to grow exponentially, producing very large fluxes of energetic radiation. As the flux of runaway electrons increases, ionization eventually causes the electric field to discharge, bringing the field below the relativistic feedback threshold again and reducing the flux of runaway electrons. These processes are investigated with a new model that includes the production, propagation, diffusion, and avalanche multiplication of runaway electrons; the production and propagation of X-rays and gamma rays; and the production, propagation, and annihilation of runaway positrons. In this model, referred to as the relativistic feedback discharge model, the large-scale electric fields are calculated self-consistently from the charge motion of the drifting low-energy electrons and ions, produced from the ionization of air by the runaway electrons, including two- and three-body attachment and recombination. Simulation results show that when relativistic feedback is considered, bright gamma ray flashes are a natural consequence of upward +IC lightning propagating in large-scale thundercloud fields. Furthermore, these flashes have the same time structures, including both single and multiple pulses, intensities, angular distributions, current moments, and energy spectra as terrestrial gamma ray flashes, and produce large current moments that should be observable in radio waves.
Properties of Doubly Heavy Baryons in the Relativistic Quark Model
Ebert, D.; Faustov, R.N.; Galkin, V.O.; Martynenko, A.P.
Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit.
Relativistic reflection: Review and recent developments in modeling
NASA Astrophysics Data System (ADS)
Dauser, T.; García, J.; Wilms, J.
Measuring relativistic reflection is an important tool to study the innermost regions of the an accreting black hole system. In the following we present a brief review on the different aspects contributing to the relativistic reflection. The combined approach is for the first time incorporated in the new ``relxill'' model. The advantages of this more self-consistent approach are briefly summarized. A special focus is put on the new definition of the intrinsic reflection fraction in the lamp post geometry, which allows to draw conclusions about the primary source of radiation in these system. Additionally the influence of the high energy cutoff of the primary source on the reflection spectrum is motivated, revealing the remarkable capabilities of constraining E_cut by measuring relativistic reflection spectra from NuSTAR, preferably with lower energy coverage.
A relativistic toy model for Unruh black holes
NASA Astrophysics Data System (ADS)
Carbonaro, P.
We consider the wave propagation in terms of acoustic geometry in a quantum relativistic system. This reduces, in the hydrodynamic limit, to the equations which govern the motion of a relativistic Fermi-degenerate gas in one space dimension. The derivation of an acoustic metric for one-dimensional (1D) systems is in general plagued with the impossibility of defining a conformal factor. Here we show that, although the system is intrinsically one-dimensional, the Unruh procedure continues to work because of the particular structure symmetry of the model. By analyzing the dispersion relation, attention is also paid to the quantum effects on the wave propagation.
Machine Learning for Dynamical Mean Field Theory
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy
Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.
Dynamics of capillary condensation in lattice gas models of confined fluids: A comparison of dynamic mean field theory with dynamic Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Edison, John R.; Monson, Peter A.
This article addresses the accuracy of a dynamic mean field theory (DMFT) for fluids in porous materials [P. A. Monson, J. Chem. Phys. 128, 084701 (2008)], 10.1063/1.2837287. The theory is used to study the relaxation processes of fluids in pores driven by step changes made to a bulk reservoir in contact with the pore. We compare the results of the DMFT to those obtained by averaging over large numbers of dynamic Monte Carlo (DMC) simulation trajectories. The problem chosen for comparison is capillary condensation in slit pores, driven by step changes in the chemical potential in the bulk reservoir and involving a nucleation process via the formation of a liquid bridge. The principal difference between the DMFT results and DMC is the replacement of a distribution of nucleation times and location along the pore for the formation of liquid bridges by a single time and location. DMFT is seen to yield an otherwise qualitatively accurate description of the dynamic behavior.
Modeling terrestrial gamma ray flashes produced by relativistic feedback discharges
NASA Astrophysics Data System (ADS)
Liu, Ningyu; Dwyer, Joseph R.
This paper reports a modeling study of terrestrial gamma ray flashes (TGFs) produced by relativistic feedback discharges. Terrestrial gamma ray flashes are intense energetic radiation originating from the Earth's atmosphere that has been observed by spacecraft. They are produced by bremsstrahlung interactions of energetic electrons, known as runaway electrons, with air atoms. An efficient physical mechanism for producing large fluxes of the runaway electrons to make the TGFs is the relativistic feedback discharge, where seed runaway electrons are generated by positrons and X-rays, products of the discharge itself. Once the relativistic feedback discharge becomes self-sustaining, an exponentially increasing number of relativistic electron avalanches propagate through the same high-field region inside the thundercloud until the electric field is partially discharged by the ionization created by the discharge. The modeling results indicate that the durations of the TGF pulses produced by the relativistic feedback discharge vary from tens of microseconds to several milliseconds, encompassing all durations of the TGFs observed so far. In addition, when a sufficiently large potential difference is available in thunderclouds, a self-propagating discharge known as the relativistic feedback streamer can be formed, which propagates like a conventional positive streamer. For the relativistic feedback streamer, the positive feedback mechanism of runaway electron production by the positrons and X-rays plays a similar role as the photoionization for the conventional positive streamer. The simulation results of the relativistic feedback streamer show that a sequence of TGF pulses with varying durations can be produced by the streamer. The relativistic streamer may initially propagate with a pulsed manner and turn into a continuous propagation mode at a later stage. Milliseconds long TGF pulses can be produced by the feedback streamer during its continuous propagation. However
Isomeric state in {sup 53}Co: A mean field analysis
Patra, S. K.; Bhat, F. H.; Panda, R. N.; Arumugam, P.; Gupta, Raj K.
We study the ground and the first excited intrinsic states of {sup 53}Co and its mirror nucleus {sup 53}Fe, within the frameworks of the relativistic and nonrelativistic mean field formalisms. The analysis of the single-particle energy spectra of these nuclei show a competition of spins 1/2{sup -} and 3/2{sup -} in a low-lying excited state, which agrees well with the recent experimental observation [D. Rudolph et al., Eur. Phys. J. A 36, 131 (2008)] of spin and parity J{sup {pi}}=3/2{sup -} for the isomeric configuration in {sup 53}Co.
Relativistic HD and MHD modelling for AGN jets
NASA Astrophysics Data System (ADS)
Keppens, R.; Porth, O.; Monceau-Baroux, R.; Walg, S.
Relativistic hydro and magnetohydrodynamics (MHD) provide a continuum fluid description for plasma dynamics characterized by shock-dominated flows approaching the speed of light. Significant progress in its numerical modelling emerged in the last two decades; we highlight selected examples of modern grid-adaptive, massively parallel simulations realized by our open-source software MPI-AMRVAC (Keppens et al 2012 J. Comput. Phys. 231 718). Hydrodynamical models quantify how energy transfer from active galactic nuclei (AGN) jets to their surrounding interstellar/intergalactic medium (ISM/IGM) gets mediated through shocks and various fluid instability mechanisms (Monceau-Baroux et al 2012 Astron. Astrophys. 545 A62). With jet parameters representative for Fanaroff-Riley type-II jets with finite opening angles, we can quantify the ISM volumes affected by jet injection and distinguish the roles of mixing versus shock-heating in cocoon regions. This provides insight in energy feedback by AGN jets, usually incorporated parametrically in cosmological evolution scenarios. We discuss recent axisymmetric studies up to full 3D simulations for precessing relativistic jets, where synthetic radio maps can confront observations. While relativistic hydrodynamic models allow one to better constrain dynamical parameters like the Lorentz factor and density contrast between jets and their surroundings, the role of magnetic fields in AGN jet dynamics and propagation characteristics needs full relativistic MHD treatments. Then, we can demonstrate the collimating properties of an overal helical magnetic field backbone and study differences between poloidal versus toroidal field dominated scenarios (Keppens et al 2008 Astron. Astrophys. 486 663). Full 3D simulations allow one to consider the fate of non-axisymmetric perturbations on relativistic jet propagation from rotating magnetospheres (Porth 2013 Mon. Not. R. Astron. Soc. 429 2482). Self-stabilization mechanisms related to the detailed
An Extended Magnetohydrodynamics Model for Relativistic Weakly Collisional Plasmas
NASA Astrophysics Data System (ADS)
Chandra, Mani; Gammie, Charles F.; Foucart, Francois; Quataert, Eliot
Black holes that accrete far below the Eddington limit are believed to accrete through a geometrically thick, optically thin, rotationally supported plasma that we will refer to as a radiatively inefficient accretion flow (RIAF). RIAFs are typically collisionless in the sense that the Coulomb mean free path is large compared to {GM}/{c}2, and relativistically hot near the event horizon. In this paper we develop a phenomenological model for the plasma in RIAFs, motivated by the application to sources such as Sgr A* and M87. The model is derived using Israel-Stewart theory, which considers deviations up to second order from thermal equilibrium, but modified for a magnetized plasma. This leads to thermal conduction along magnetic field lines and a difference in pressure, parallel and perpendicular to the field lines (which is equivalent to anisotropic viscosity). In the non-relativistic limit, our model reduces to the widely used Braginskii theory of magnetized, weakly collisional plasmas. We compare our model to the existing literature on dissipative relativistic fluids, describe the linear theory of the plasma, and elucidate the physical meaning of the free parameters in the model. We also describe limits of the model when the conduction is saturated and when the viscosity implies a large pressure anisotropy. In future work, the formalism developed in this paper will be used in numerical models of RIAFs to assess the importance of non-ideal processes for the dynamics and radiative properties of slowly accreting black holes.
Kinematic arguments against single relativistic shell models for GRBs
NASA Technical Reports Server (NTRS)
Fenimore, Edward E.; Ramirez, E.; Sumner, M. C.
Two main types of models have been suggested to explain the long durations and multiple peaks of Gamma Ray Bursts (GRBs). In one, there is a very quick release of energy at a central site resulting in a single relativistic shell that produces peaks in the time history through its interactions with the ambient material. In the other, the central site sporadically releases energy over hundreds of seconds forming a peak with each burst of energy. The authors show that the average envelope of emission and the presence of gaps in GRBs are inconsistent with a single relativistic shell. They estimate that the maximum fraction of a single shell that can produce gamma-rays in a GRB with multiple peaks is 10(exp (minus)3), implying that single relativistic shells require 10(exp 3) times more energy than previously thought. They conclude that either the central site of a GRB must produce (approx)10(exp 51) erg/s(exp (minus)1) for hundreds of seconds, or the relativistic shell must have structure on a scales the order of (radical)(epsilon)(Gamma)(exp (minus)1), where (Gamma) is the bulk Lorentz factor ((approximately)10(exp 2) to 10(exp 3)) and (epsilon) is the efficiency.
Models of Dilute Relativistic Plasmas Around Black Holes
NASA Astrophysics Data System (ADS)
Quataert, Eliot
In some regimes, mass flowing onto a central black hole can become sufficiently hot and low density that the collisional mean free path is appreciable compared to the size of the system. I describe new analytical and numerical models of these relativistically hot low collisionality plasmas around black holes. I also describe the application of these models to interpreting observations of the accreting black holes being observed by the Event Horizon Telescope.
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Mean-field descriptions of collective migration with strong adhesion.
Johnston, Stuart T; Simpson, Matthew J; Baker, Ruth E
Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean-field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.
Electroexcitation of the Roper resonance in the relativistic quark models
Inna Aznauryan
The amplitudes of the transition gamma* N -> P11(1440) are calculated within light-front relativistic quark model assuming that the P11(1440) is the first radial excitation of the 3q nucleon state. The results are compared with those obtained in close approaches by other authors and with standard nonrelativistic results. One of the reasons for this study was to present all these results within unified definition of helicity amplitudes consistent with the definition used in the extraction of the helicity amplitudes from experimental data in one-pion electroproduction. The results of relativistic quark models are qualitatively in good agreement with each other and differ strongly from nonrelativistic calculations. At small Q2 , these results for the transverse amplitude A12 are consistent, but fail to reproduce experimental data. The most probable explanation of this discrepancy is the absence of pion cloud contribution in the approaches under consideration.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d < 2κ. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. Lastly, this is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d
Back-reaction beyond the mean field approximation
Kluger, Y.
A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large N{sub f} expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/N{sub f} is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e{sup +}e{sup {minus}} plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the N{sub f} expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation.
Heavy-light mesons in a relativistic model
NASA Astrophysics Data System (ADS)
Liu, Jing-Bin; Yang, Mao-Zhi
We study the heavy-light mesons in a relativistic model, which is derived from the Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation to the heavy quark. The kernel we choose is based on scalar confinement and vector Coulomb potentials. The transverse interaction of the gluon exchange is also taken into account in this model. The spectra and wave functions of D, Ds, B, Bs meson states are obtained. The spectra are calculated up to the order of 1/m Q, and wave functions are treated to leading order. Supported by National Natural Science Foundation of China (11375088, 10975077, 10735080, 11125525)
Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
NASA Astrophysics Data System (ADS)
Gravejat, Philippe; Lewin, Mathieu; Séré, Éric
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant α. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an L 1 function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to α by the formula αphys ≃ α(1 + 2α/(3π) log Λ)-1, where Λ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge Z. In the nonrelativistic limit, we obtain that this number is ≤ 2 Z, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Séré and Solovej on the mean-field approximation of no-photon QED.
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N.
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
Relativistic Modeling Capabilities in PERSEUS Extended MHD Simulation Code for HED Plasmas
NASA Astrophysics Data System (ADS)
Hamlin, Nathaniel; Seyler, Charles
We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as hybrid X-pinches and laser-plasma interactions. A major challenge of a relativistic fluid implementation is the recovery of primitive variables (density, velocity, pressure) from conserved quantities at each time step of a simulation. This recovery, which reduces to straightforward algebra in non-relativistic simulations, becomes more complicated when the equations are made relativistic, and has thus far been a major impediment to two-fluid simulations of relativistic HED plasmas. By suitable formulation of the relativistic generalized Ohm's law as an evolution equation, we have reduced the central part of the primitive variable recovery problem to a straightforward algebraic computation, which enables efficient and accurate relativistic two-fluid simulations. Our code recovers expected non-relativistic results and reveals new physics in the relativistic regime. Work supported by the National Nuclear Security Administration stewardship sciences academic program under Department of Energy cooperative Agreement DE-NA0001836.
Instabilities in the Mean Field Limit
NASA Astrophysics Data System (ADS)
Han-Kwan, Daniel; Nguyen, Toan T.
Consider a system of N particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a {C}^2 smooth potential in any dimension. We prove that in the mean field limit N → + ∞, the N particles system displays instabilities in times of order log N, for some configurations approximately distributed according to unstable homogeneous equilibria.
A relativistic two-fluid model of compact stars
NASA Astrophysics Data System (ADS)
Chakraborty, Koushik; Rahaman, Farook; Mallick, Arkopriya
We propose a relativistic model of compact star admitting conformal symmetry. Quark matter and baryonic matter which are considered as two different fluids, constitute the star. We define interaction equations between the normal baryonic matter and the quark matter and study the physical situations for repulsive, attractive and zero interaction between the constituent matters. The measured value of the Bag constant is used to explore the spacetime geometry inside the star. From the observed values of the masses of some compact objects, we have obtained theoretical values of the radii. Theoretical values of the radii match well with the previous predictions for such compact objects.
A two-fluid model for relativistic heat conduction
López-Monsalvo, César S.
Three years ago it was presented in these proceedings the relativistic dynamics of a multi-fluid system together with various applications to a set of topical problems [1]. In this talk, I will start from such dynamics and present a covariant formulation of relativistic thermodynamics which provides us with a causal constitutive equation for the propagation of heat in a relativistic setting.
Mean Field Theories of Icosahedral Quasicrystals.
NASA Astrophysics Data System (ADS)
Troian, Sandra Marina
studied. We also rederive and generalize a model free energy presented by Kalugin et al. to show that their original conclusion of a metastable quasicrystal is invalidated by the inclusion of a local quartic term in the free energy. Lastly, we review three other mean field theories recently proposed to explain the existence of quasicrystals.
Socio-economic applications of finite state mean field games.
Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
A "Boosted Fireball" Model for Structured Relativistic Jets
NASA Astrophysics Data System (ADS)
Duffell, Paul C.; MacFadyen, Andrew I.
We present a model for relativistic jets which generates a particular angular distribution of Lorentz factor and energy per solid angle. We consider a fireball with specific internal energy E/M launched with bulk Lorentz factor γ B . In its center-of-momentum frame the fireball expands isotropically, converting its internal energy into radially expanding flow with asymptotic Lorentz factor η0 ~ E/M. In the lab frame the flow is beamed, expanding with Lorentz factor Γ = 2η0γ B in the direction of its initial bulk motion and with characteristic opening angle θ0 ~ 1/γ B . The flow is jet-like with Γθ0 ~ 2η0 such that jets with Γ > 1/θ0 are naturally produced. The choice η0 ~ γ B ~ 10 yields a jet with Γ ~ 200 on-axis and angular structure characterized by opening angle θ0 ~ 0.1 of relevance for cosmological gamma-ray bursts (GRBs), while γ B >~ 1 may be relevant for low-luminosity GRBs. The model produces a family of outflows, of relevance for different relativistic phenomena with structures completely determined by η0 and γ B . We calculate the energy per unit solid angle for the model and use it to compute light curves for comparison with the widely used top-hat model. The jet break in the boosted fireball light curve is greatly subdued when compared to the top-hat model because the edge of the jet is smoother than for a top-hat. This may explain missing jet breaks in afterglow light curves.
Reaction cross sections of intermediate energy {alpha} particles within a relativistic optical model
Ait-Tahar, S.; Nedjadi, Y.
The suggestion made recently by H. Abele {ital et} {ital al}. that relativistic effects in the interaction of alpha particles with various nuclei at intermediate energies may remove the existing discrepancy between the theoretical predictions and the experimental data for the reaction cross section is investigated. We use a relativistic model based on the Kemmer-Duffin-Petiau equation and find that relativistic effects do not lead to a reduction in the reaction cross section within the present approach. Alternative explanations are discussed.
Mean-field behavior of cluster dynamics
NASA Astrophysics Data System (ADS)
Persky, N.; Ben-Av, R.; Kanter, I.; Domany, E.
The dynamic behavior of cluster algorithms is analyzed in the classical mean-field limit. Rigorous analytical results below Tc establish that the dynamic exponent has the value zSW=1 for the Swendsen-Wang algorithm and zW=0 for the Wolff algorithm. An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below Tc demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data.
Radiative leptonic Bc decay in the relativistic independent quark model
NASA Astrophysics Data System (ADS)
Barik, N.; Naimuddin, Sk.; Dash, P. C.; Kar, Susmita
The radiative leptonic decay Bc-→μ-ν¯μγ is analyzed in its leading order in a relativistic independent quark model based on a confining potential in an equally mixed scalar-vector harmonic form. The branching ratio for this decay in the vanishing lepton mass limit is obtained as Br(Bc→μνμγ)=6.83×10-5, which includes the contributions of the internal bremsstrahlung and structure-dependent diagrams at the level of the quark constituents. The contributions of the bremsstrahlung and the structure-dependent diagrams, as well as their additive interference parts, are compared and found to be of the same order of magnitude. Finally, the predicted photon energy spectrum is observed here to be almost symmetrical about the peak value of the photon energy at Ẽγ≃(MBc)/(4), which may be quite accessible experimentally at LHC in near future.
Numerical accuracy of mean-field calculations in coordinate space
NASA Astrophysics Data System (ADS)
Ryssens, W.; Heenen, P.-H.; Bender, M.
Background: Mean-field methods based on an energy density functional (EDF) are powerful tools used to describe many properties of nuclei in the entirety of the nuclear chart. The accuracy required of energies for nuclear physics and astrophysics applications is of the order of 500 keV and much effort is undertaken to build EDFs that meet this requirement. Purpose: Mean-field calculations have to be accurate enough to preserve the accuracy of the EDF. We study this numerical accuracy in detail for a specific numerical choice of representation for mean-field equations that can accommodate any kind of symmetry breaking. Method: The method that we use is a particular implementation of three-dimensional mesh calculations. Its numerical accuracy is governed by three main factors: the size of the box in which the nucleus is confined, the way numerical derivatives are calculated, and the distance between the points on the mesh. Results: We examine the dependence of the results on these three factors for spherical doubly magic nuclei, neutron-rich 34Ne , the fission barrier of 240Pu , and isotopic chains around Z =50 . Conclusions: Mesh calculations offer the user extensive control over the numerical accuracy of the solution scheme. When appropriate choices for the numerical scheme are made the achievable accuracy is well below the model uncertainties of mean-field methods.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Acceleration of Relativistic Electrons: A Comparison of Two Models
NASA Astrophysics Data System (ADS)
Green, J. C.; Kivelson, M. G.
Observations of relativistic electron fluxes show order of magnitude increases during some geomagnetic storms. Many electron acceleration models have been proposed to explain the flux enhancements but attempts to validate these models have yielded ambiguous results. Here we examine two models of electron acceleration, radial diffusion via enhanced ULF wave activity [Elkington et al.,1999] and acceleration by resonant interaction with whistler waves[Summers,1998; Roth et al.,1999]. Two methods are used to compare observations with features predicted by the models. First, the evolution of phase space density as a function of L during flux enhancement events is evaluated. The phase space density (PSD) is calculated at constant first, second and third adiabatic invariants using data obtained by the CEPPAD-HIST instrument and the MFE instrument onboard the Polar spacecraft. Liouville's theorem states that PSD calculated at constant adiabatic invariants does not change with time unless some mechanism violates one of the invariants. The radial diffusion model predicts that only the flux invariant will be violated during the acceleration process while acceleration by whistler waves violates the first invariant. Therefore, the two models predict a different evolution of the PSD as a function of time and L. Previous examinations of the evolution of PSD have yielded ambiguous results because PSD calculations are highly dependent on the global accuracy of magnetic field models. We examine the PSD versus L profiles for a series of geomagnetic storms and in addition determine how errors in the Tsyganenko 96 field model affect the results by comparing the measured magnetic field to the model magnetic field used in the calculations. Second, the evolution of the relativistic electron pitch angle distributions is evaluated. Previous studies of pitch angle distributions were limited because few spacecraft have the necessary instrumentation and global coverage. The CEPPAD
A model distribution function for relativistic bi-Maxwellian with drift
Naito, O.
A model distribution function for relativistic bi-Maxwellian with drift is proposed, based on the maximum entropy principle and the relativistic canonical transformation. Since the obtained expression is compatible with the existing distribution functions and has a relatively simple form as well as smoothness, it might serve as a useful tool in the research fields of space or high temperature fusion plasmas.
Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models, and stimulated Raman adiabatic passage
Graefe, E. M.; Korsch, H. J.; Witthaut, D.
We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning.
Mean-field avalanches in jammed spheres
NASA Astrophysics Data System (ADS)
Franz, S.; Spigler, S.
Disordered systems are characterized by the existence of many sample-dependent local-energy minima that cause a step-wise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three-dimensional systems of soft spheres, either at jamming or at slightly higher densities.
Mean-field avalanches in jammed spheres.
Franz, S; Spigler, S
Disordered systems are characterized by the existence of many sample-dependent local-energy minima that cause a step-wise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three-dimensional systems of soft spheres, either at jamming or at slightly higher densities.
Simulations and analytic models of relativistic magnetized jets
NASA Astrophysics Data System (ADS)
Tchekhovskoi, Alexandre Dmitrievich
Astrophysical jets are tightly collimated streams that are often observed to move at velocities close to the speed of light. While many such systems are known, understanding and explaining how jets collimate and accelerate has been a long-standing challenge and is currently an area of active research. Finding analytic solutions for jets is extremely hard because the equations that describe the jets are highly nonlinear and difficult to solve analytically. Only in the last few years has it become possible to simulate ultrarelativistic jets computationally, which has led to unprecedented insights into their structure. We now think that many relativistic jets are produced by magnetic fields twisted by the rotation of a central compact object, which can be a black hole or a neutron star. In this thesis I present numerical and analytical studies of relativistic jets. In Chapter 2, I start with a discussion of a simple, idealized model that has the bare minimum of ingredients needed for the production of jets: regular magnetic field, spinning central compact object, and externally imposed collimation. The model assumes that magnetic field in the jet is so strong that plasma inertia is negligible and can be ignored. The simplicity of this model allows for a fully analytic description and an intuitive understanding of the results. Despite being simple, this model possesses non-trivial properties and has important applications to various astrophysical systems --- compact object binaries, gamma-ray bursts, and active galactic nuclei. Chapters 3 -- 7 add an extra level of realism (and sophistication) into jet models: they account for mass inertia of the jet fluid and study its effects on the jet structure. Chapter 4 discusses the effect of jet confinement on the acceleration of the jet. Chapter 5 shows that deconfinement can also have a dramatic effect on the jet. Chapter 6 studies how the structure of the jet changes if the central object driving the jet is a black hole
Schrödinger Approach to Mean Field Games.
Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis
Mean field games (MFG) provide a theoretical frame to model socioeconomic systems. In this Letter, we study a particular class of MFG that shows strong analogies with the nonlinear Schrödinger and Gross-Pitaevskii equations introduced in physics to describe a variety of physical phenomena. Using this bridge, many results and techniques developed along the years in the latter context can be transferred to the former, which provides both a new domain of application for the nonlinear Schrödinger equation and a new and fruitful approach in the study of mean field games. Utilizing this approach, we analyze in detail a population dynamics model in which the "players" are under a strong incentive to coordinate themselves.
Quasi-exactly solvable relativistic soft-core Coulomb models
Agboola, Davids Zhang, Yao-Zhong
By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials V{sub q}(r)=-Z/(r{sup q}+{beta}{sup q}){sup 1/q}, Z>0, {beta}>0, q{>=}1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations. - Highlights: Black-Right-Pointing-Pointer The relativistic bound-state solutions of the soft-core Coulomb models. Black-Right-Pointing-Pointer Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer The hidden Lie algebraic structure discussed for the models. Black-Right-Pointing-Pointer Results useful in describing mesonic atoms and interaction of intense laser fields with atom.
The Thomas–Fermi quark model: Non-relativistic aspects
Liu, Quan Wilcox, Walter
The first numerical investigation of non-relativistic aspects of the Thomas–Fermi (TF) statistical multi-quark model is given. We begin with a review of the traditional TF model without an explicit spin interaction and find that the spin splittings are too small in this approach. An explicit spin interaction is then introduced which entails the definition of a generalized spin "flavor". We investigate baryonic states in this approach which can be described with two inequivalent wave functions; such states can however apply to multiple degenerate flavors. We find that the model requires a spatial separation of quark flavors, even if completely degenerate. Although the TF model is designed to investigate the possibility of many-quark states, we find surprisingly that it may be used to fit the low energy spectrum of almost all ground state octet and decuplet baryons. The charge radii of such states are determined and compared with lattice calculations and other models. The low energy fit obtained allows us to extrapolate to the six-quark doubly strange H-dibaryon state, flavor symmetric strange states of higher quark content and possible six quark nucleon–nucleon resonances. The emphasis here is on the systematics revealed in this approach. We view our model as a versatile and convenient tool for quickly assessing the characteristics of new, possibly bound, particle states of higher quark number content. -- Highlights: • First application of the statistical Thomas–Fermi quark model to baryonic systems. • Novel aspects: spin as generalized flavor; spatial separation of quark flavor phases. • The model is statistical, but the low energy baryonic spectrum is successfully fit. • Numerical applications include the H-dibaryon, strange states and nucleon resonances. • The statistical point of view does not encourage the idea of bound many-quark baryons.
Resummed mean-field inference for strongly coupled data
NASA Astrophysics Data System (ADS)
Jacquin, Hugo; Rançon, A.
We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion of the log-likelihood, the method outperforms standard mean-field inference methods, even when they are regularized. The inference is stable with respect to sampling noise, contrarily to previous works based either on the small correlation expansion, on the Bethe free energy, or on the mean-field and Gaussian models. Because it is mostly analytic, its complexity is still very low, requiring an iterative algorithm to solve for N auxiliary variables, that resorts only to matrix inversions and multiplications. We test our algorithm on the Sherrington-Kirkpatrick model submitted to a random external field and large random couplings, and demonstrate that even without regularization, the inference is stable across the whole phase diagram. In addition, the calculation leads to a consistent estimation of the entropy of the data and allows us to sample form the inferred distribution to obtain artificial data that are consistent with the empirical distribution.
Mean-field theory of echo state networks
NASA Astrophysics Data System (ADS)
Massar, Marc; Massar, Serge
Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study "echo state networks," networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.
HBT Pion Interferometry with Phenomenological Mean Field Interaction
NASA Astrophysics Data System (ADS)
Hattori, K.
To extract information on hadron production dynamics in the ultrarelativistic heavy ion collision, the space-time structure of the hadron source has been measured using Hanbury Brown and Twiss interferometry. We study the distortion of the source images due to the effect of a final state interaction. We describe the interaction, taking place during penetrating through a cloud formed by evaporating particles, in terms of a one-body mean field potential localized in the vicinity of the source region. By adopting the semiclassical method, the modification of the propagation of an emitted particle is examined. In analogy to the optical model applied to nuclear reactions, our phenomenological model has an imaginary part of the potential, which describes the absorption in the cloud. In this work, we focus on the pion interferometry and mean field interaction obtained using a phenomenological pipi forward scattering amplitude in the elastic channels. The p-wave scattering wit h rho meson resonance leads to an attractive mean field interaction, and the presence of the absorptive part is mainly attributed to the formation of this resonance. We also incorporate a simple time dependence of the potential reflecting the dynamics of the evaporating source. Using the obtained potential, we examine how and to what extent the so-called HBT Gaussian radius is varied by the modification of the propagation.
Dynamical mean-field theory for flat-band ferromagnetism
NASA Astrophysics Data System (ADS)
Nguyen, Hong-Son; Tran, Minh-Tien
The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.
Nonlocal relativistic diffusion (NoRD) model of cosmic ray propagation
NASA Astrophysics Data System (ADS)
Uchaikin, V. V.; Sibatov, R. T.
The problem of physical interpretation of the nonlocal relativistic diffusion (NoRD model) for cosmic ray transport in the Galaxy is discussed. The model accounts for the turbulent character of the interstellar medium and the relativistic principle of the speed limitation. Involving fractional calculus and non-Gaussian Lévy statistics yields numerical results compatible with observation data. A special attention is paid to the knee problem. The relativistic speed limit requirement steepens theoretical background spectrum at certain energies, and the position of the break, its sharpness and slopes of asymptotes depend on Dα (E) and α.
Relativistic feedback models of terrestrial gamma-ray flashes and gamma-ray glows
NASA Astrophysics Data System (ADS)
Dwyer, J. R.
Relativistic feedback discharges, also known as dark lightning, are capable of explaining many of the observed properties of terrestrial gamma-ray flashes (TGFs) and gamma-ray glows, both created within thunderstorms. During relativistic feedback discharges, the generation of energetic electrons is self-sustained via the production of backward propagating positrons and back-scattered x-rays, resulting in very larges fluxes of energetic radiation. In addition, ionization produces large electric currents that generate LF/VLF radio emissions and eventually discharge the electric field, terminating the gamma-ray production. In this presentation, new relativistic feedback model results will be presented and compared to recent observations.
A hydrodynamical model for relativistic spin quantum plasmas
Asenjo, Felipe A.; Munoz, Victor; Valdivia, J. Alejandro; Mahajan, Swadesh M.
Based on the one-body particle-antiparticle Dirac theory of electrons, a set of relativistic quantum fluid equations for a spin half plasma is derived. The particle-antiparticle nature of the relativistic particles is explicit in this fluid theory, which also includes quantum effects such as spin. The nonrelativistic limit is shown to be in agreement with previous attempts to develop a spin plasma theory derived from the Pauli Hamiltonian. Harnessing the formalism to the study of electromagnetic mode propagation, conceptually new phenomena are revealed; the particle-antiparticle effects increase the fluid opacity to these waves, while the spin effects tend to make the fluid more transparent.
Nonlinear Walecka models and point-coupling relativistic models
Lourenco, O.; Amaral, R. L. P. G.; Dutra, M.; Delfino, A.
We study hadronic nonlinear point-coupling (NLPC) models which reproduce numerically the binding energy, the incompressibility, and the nucleon effective mass at the nuclear matter saturation obtained by different nonlinear Walecka (NLW) models. We have investigated their behaviors as functions of the nuclear matter density to observe how they deviate from known NLW models. In our study we present a meson-exchange modified nonlinear Walecka model (MNLW) which exactly underlies a nonlinear point-coupling model (NLPC) presenting third- and fourth-order scalar density self-couplings. A discussion about naive dimensional analysis (NDA) and naturalness is also provided for a large class of NLW and NLPC models. At finite temperature, critical and flash parameters of both approaches are presented.
A picosecond accuracy relativistic VLBI model via Fermi normal coordinates
NASA Technical Reports Server (NTRS)
Shahid-Saless, Bahman; Hellings, Ronald W.; Ashby, Neil
Fermi normal coordinates are used to construct transformations relating solar system barycentric coordinates to local inertial geocentric coordinates. Relativistic corrections to terrestrial VLBI measurements are calculated, and this formalism is developed to include corrections needed for picosecond accuracy. A calculation of photon time delay which includes effects arising from the motion of gravitational sources is given.
Mean field theory studies of surface reactions on disordered substrates
NASA Astrophysics Data System (ADS)
Cortés, Joaquín.; Narváez, Ana; Puschmann, Heinrich; Valencia, Eliana
A mean field theory (MFT) in the site and pair approximations of a surface reaction system on a disordered substrate showing geometric heterogeneity is proposed, characterizing the substrate completely through the set { qi} of probabilities that a surface site has i neighbours that belong to the substrate in the model. The MFT results allow the interpretation of the Monte Carlo (MC) simulations carried out for the ZGB algorithm at instantaneous and finite rates over a series heterogeneous substrates corresponding to percolation clusters. The change in the character of the irreversible phase transitions (IPT) with the degree of disorder or branching of the substrate and its theoretical interpretation are analyzed.
Small-world network spectra in mean-field theory.
Grabow, Carsten; Grosskinsky, Stefan; Timme, Marc
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean-field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering, and social science.
Non relativistic limit of integrable QFT and Lieb-Liniger models
NASA Astrophysics Data System (ADS)
Bastianello, Alvise; De Luca, Andrea; Mussardo, Giuseppe
In this paper we study a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda field theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.
Kinetic and mean field description of Gibrat's law
NASA Astrophysics Data System (ADS)
Toscani, Giuseppe
I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.
The effectiveness of mean-field theory for avalanche distributions
NASA Astrophysics Data System (ADS)
Lee, Edward; Raju, Archishman; Sethna, James
We explore the mean-field theory of the pseudogap found in avalanche systems with long-range anisotropic interactions using analytical and numerical tools. The pseudogap in the density of low-stability states emerges from the competition between stabilizing interactions between spins in an avalanche and the destabilizing random movement towards the threshold caused by anisotropic couplings. Pazmandi et al. have shown that for the Sherrington-Kirkpatrick model, the pseudogap scales linearly and produces a distribution of avalanche sizes with exponent t=1 in contrast with that predicted from RFIM t=3/2. Lin et al. have argued that the scaling exponent ? of the pseudogap depends on the tail of the distribution of couplings and on non-universal values like the strain rate and the magnitude of the coupling strength. Yet others have argued that the relationship between the pseudogap scaling and the distribution of avalanche sizes is dependent on dynamical details. Despite the theoretical arguments, the class of RFIM mean-field models is surprisingly good at predicting the distribution of avalanche sizes in a variety of different magnetic systems. We investigate these differences with a combination of theory and simulation.
Tensor interaction and short range correlations in relativistic nuclear models
Panda, Prafulla K.; Providencia, C.; Providencia, J. da
Short range correlations are introduced using a Jastrow factor in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. The pion exchange, including the tensor contribution, is taken into account. It is shown that both the tensor contribution of pion exchange and short range correlations soften the equation of state. Neutron matter with correlations presents no minimum at low densities.
a Nonlinear Model for Relativistic Electrons at Positive Temperature
NASA Astrophysics Data System (ADS)
Hainzl, Christian; Lewin, Mathieu; Seiringer, Robert
We study the relativistic electron-positron field at positive temperature in the Hartree-Fock approximation. We consider both the case with and without exchange terms, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, Séré and Solovej where the case of zero temperature was considered.
Variation after projection with a triaxially deformed nuclear mean field
NASA Astrophysics Data System (ADS)
Gao, Zao-Chun; Horoi, Mihai; Chen, Y. S.
We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin (J ), isospin (T ), and mass number (A ). Systematic VAP calculations with JTA projection have been performed for the even-even s d -shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin projection is crucial in achieving good approximation of the full shell model calculation; (2) the intrinsic shapes of the VAP wave functions with spin projection are always triaxial, while the Hartree-Fock-Bogoliubov methods likely provide axial intrinsic shapes. Finally, our analysis suggests that one may not be possible to associate an intrinsic shape to an exact shell model wave function.
Mean-field theory of assortative networks of phase oscillators
NASA Astrophysics Data System (ADS)
Restrepo, Juan G.; Ott, Edward
Employing the Kuramoto model as an illustrative example, we show how the use of the mean-field approximation can be applied to large networks of phase oscillators with assortativity. We then use the ansatz of Ott and Antonsen (Chaos, 19 (2008) 037113) to reduce the mean-field kinetic equations to a system of ordinary differential equations. The resulting formulation is illustrated by application to a network Kuramoto problem with degree assortativity and correlation between the node degrees and the natural oscillation frequencies. Good agreement is found between the solutions of the reduced set of ordinary differential equations obtained from our theory and full simulations of the system. These results highlight the ability of our method to capture all the phase transitions (bifurcations) and system attractors. One interesting result is that degree assortativity can induce transitions from a steady macroscopic state to a temporally oscillating macroscopic state through both (presumed) Hopf and SNIPER (saddle-node, infinite period) bifurcations. Possible use of these techniques to a broad class of phase oscillator network problems is discussed.
Mean-field analysis for parallel asymmetric exclusion process with anticipation effect.
Hao, Qing-Yi; Jiang, Rui; Hu, Mao-Bin; Wu, Qing-Song
This paper studies an extended parallel asymmetric exclusion process, in which the anticipation effect is taken into account. The fundamental diagram of the model has been investigated via cluster mean field analysis. Different from previous mean field analysis, in which the n -cluster probabilities P(σ{i},…,σ{i+n-1}) involve the (n+2) -cluster probabilities P(τ{i-1},…,τ{i+n}) , our mean-field analysis is asymmetric because the three-cluster probabilities P(σ{i},σ{i+1},σ{i+2}) involve the six-cluster probabilities P(τ{i-1},…,τ{i+4}) . We find an excellent agreement between Monte Carlo simulations and cluster mean field analysis, which indicates that the mean field analysis might give the exact expression.
A Study of the Mean Field Approach to Knapsack Problems.
Pi, Hong; Ohlsson, Mattias
The mean field theory approach to knapsack problems is extended to multiple knapsacks and generalized assignment problems with Potts mean field equations governing the dynamics. Numerical tests against "state of the art" conventional algorithms shows good performance for the mean field approach. The inherently parallelism of the mean field equations makes them suitable for direct implementations in microchips. It is demonstrated numerically that the performance is essentially not affected when only a limited number of bits is used in the mean field equations. Also, a hybrid algorithm with linear programming and mean field components is showed to further improve the performance for the difficult homogeneous N x M knapsack problem. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.
Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation.
Dunkel, Jörn; Hänggi, Peter
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still delta correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
Nuclear equation of state in a relativistic independent quark model with chiral symmetry and dependence on quark masses
NASA Astrophysics Data System (ADS)
Barik, N.; Mishra, R. N.; Mohanty, D. K.; Panda, P. K.; Frederico, T.
We have calculated the properties of nuclear matter in a self-consistent manner with a quark-meson coupling mechanism incorporating the structure of nucleons in vacuum through a relativistic potential model; where the dominant confining interaction for the free independent quarks inside a nucleon is represented by a phenomenologically average potential in equally mixed scalar-vector harmonic form. Corrections due to spurious center of mass motion as well as those due to other residual interactions, such as the one gluon exchange at short distances and quark-pion coupling arising out of chiral symmetry restoration, have been considered in a perturbative manner to obtain the nucleon mass in vacuum. The nucleon-nucleon interaction in nuclear matter is then realized by introducing additional quark couplings to σ and ω mesons through mean field approximations. The relevant parameters of the interaction are obtained self-consistently while realizing the saturation properties such as the binding energy, pressure, and compressibility of the nuclear matter. We also discuss some implications of chiral symmetry in nuclear matter along with the nucleon and nuclear σ term and the sensitivity of nuclear matter binding energy with variations in the light quark mass.
Triaxially deformed relativistic point-coupling model for Λ hypernuclei: A quantitative analysis of the hyperon impurity effect on nuclear collective properties
NASA Astrophysics Data System (ADS)
Xue, W. X.; Yao, J. M.; Hagino, K.; Li, Z. P.; Mei, H.; Tanimura, Y.
Background: The impurity effect of hyperons on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of E 2 transition strength in low-lying states of the hypernucleus Λ7Li . Many more data on low-lying states of Λ hypernuclei will be measured soon for s d -shell nuclei, providing good opportunities to study the Λ impurity effect on nuclear low-energy excitations. Purpose: We carry out a quantitative analysis of the Λ hyperon impurity effect on the low-lying states of s d -shell nuclei at the beyond-mean-field level based on a relativistic point-coupling energy density functional (EDF), considering that the Λ hyperon is injected into the lowest positive-parity (Λs) and negative-parity (Λp) states. Method: We adopt a triaxially deformed relativistic mean-field (RMF) approach for hypernuclei and calculate the Λ binding energies of hypernuclei as well as the potential-energy surfaces (PESs) in the (β ,γ ) deformation plane. We also calculate the PESs for the Λ hypernuclei with good quantum numbers by using a microscopic particle rotor model (PRM) with the same relativistic EDF. The triaxially deformed RMF approach is further applied in order to determine the parameters of a five-dimensional collective Hamiltonian (5DCH) for the collective excitations of triaxially deformed core nuclei. Taking 25,27Mg Λ and Si31Λ as examples, we analyze the impurity effects of Λs and Λp on the low-lying states of the core nuclei. Results: We show that Λs increases the excitation energy of the 21+ state and decreases the E 2 transition strength from this state to the ground state by 12 %to17 % . On the other hand, Λp tends to develop pronounced energy minima with larger deformation, although it modifies the collective parameters in such a way that the collectivity of the core nucleus can be either increased or decreased. Conclusions: The quadrupole deformation significantly affects the �
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Modeling the detector of charge states of relativistic multicharged ions
NASA Astrophysics Data System (ADS)
Malyshevsky, V. S.; Fomin, G. V.; Ivanova, I. A.
A way to identify charge distributions of relativistic multicharged ions by recording the angular distribution of the Cherenkov radiation of ions is analyzed; preliminarily, ions with different charges are separated by ion velocities in an external target with a large charge number. As a result, when an ion beam enters the Cherenkov radiator, different charges radiate at different angles to the direction of the ion motion and the radiation intensity is proportional to the fraction of ions with a given charge in the beam.
A finite Zitterbewegung model for relativistic quantum mechanics
Noyes, H.P.
Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.
Relativistic compact anisotropic charged stellar models with Chaplygin equation of state
NASA Astrophysics Data System (ADS)
Bhar, Piyali; Murad, Mohammad Hassan
This paper presents a new model of static spherically symmetric relativistic charged stellar objects with locally anisotropic matter distribution together with the Chaplygin equation of state. The interior spacetime has been matched continuously to the exterior Reissner-Nordström geometry. Different physical properties of the stellar model have been investigated, analyzed, and presented graphically.
Numerical calculations in the new framework of the RMF theory with π mean field
NASA Astrophysics Data System (ADS)
Sugimoto, S.; Toki, H.; Ikeda, K.
Usually, π meson field is not included in the Relativistic Mean Field(RMF) Theory. Because π meson has pseudo scalar nature, it is not exchanged by single particle orbits under the mean field approximation as far as the parity and charge symmetries hold. It is, however, desirable to revise the RMF theory to include the π meson field because it plays a essentially important role in producing many aspects of nuclear structures. As mentioned before, π meson field dose not contribute to the mean field under the mean field approximation. To make π meson free from this restriction it is necessary to break the parity and charge symmetries of single particle orbits. It means that single particle orbits have not good parity quantum numbers and good charge quantum numbers. They are mixed states of parities and charge states. In this way we incorporate π meson field into the RMF theory on the same footing as other mesons which are usually used in the RMF calculations, for example σ, ω etc. Present study in this new framework is performed for N=Z nuclei in medium heavy region, for example, ^40Ca, ^56Ni, ^80Zr, and ^100Sn. We found that the π meson field has finite expectation value. It contributes to the total energies of those nuclei in the non-negligible way. In this talk we report the formulation and the results. We also mention our plan for the parity and charge projection.
Mean field theory for U(n) dynamical groups
NASA Astrophysics Data System (ADS)
Rosensteel, G.
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick {\\mathfrak s}{\\mathfrak u} (2) model and the Elliott {\\mathfrak s}{\\mathfrak u} (3) model. When the energy in the {\\mathfrak s}{\\mathfrak u} (3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
A comparison of a GCM simulation of the seasonal cycle of the atmosphere with observation. I - Mean fields and the annual harmonic. II - Stationary waves and transient fluctuations. [general circulation model
NASA Technical Reports Server (NTRS)
Straus, David M.; Shukla, J.
The seasonal cycle of a GCM is analyzed in terms of the behavior of the monthly and seasonal mean fields and the structure of the annual harmonic. The GCM is found to be successful in simulating the Northern Hemisphere sea-level pressure and 200-mb heights over eastern continents and oceans and in the entire Southern Hemisphere. Problems in the simulation include an anomalously deep Aleutian low and low values of the height over Europe in winter. The GCM fails to show the observed amplitude of the annual harmonic in 200-mb temperature over Antarctica. In the second section, the seasonal dependence of the stationary and transient eddies of the GCM are presented for a two-year annual cycle. The accuracy of the wave and eddy simulations is analyzed.
Nuclear mean field on and near the drip lines
NASA Astrophysics Data System (ADS)
Otsuka, Takaharu; Fukunishi, Nobuhisa
We discuss two subjects related to the structure of nuclei near the drip lines. The first is the vanishing of N = 20 magic structure in Z ≪ N = 20 nuclei. Large-scale state-of-the-art shell-model calculations with 2sld and lower 2plf shells are shown to present a unified description of N = 20 isotones with Z = 10-20, covering both stable and unstable nuclei. The calculations demonstrate that, although the N = 20 closed-shell structure remains for Z ≥ 14, the N = 20 closed-shell structure vanishes naturally towards nuclei with Z ≤ 12, giving rise to various anomalous features including those in 32Mg and 31Na. It is suggested that, in these nuclei, the deformed mean field overcomes the shell gap created by the spherical mean potential. Furthermore, the almost perfect agreement with a recent experiment is presented for the B(E2; 0 1+ → 2 1+) value of 32Mg. The second part is devoted to the mean field for loosely bound neutrons. The variational shell model (VSM) is explained with an application to the anomalous ground state of 11Be. The VSM has been proposed recently to describe the structure of neutron-rich unstable nuclei. Contrary to the failure of spherical Hartree-Fock, the anomalous {1}/{2}+ ground state and its neutron halo are reproduced with Skyrme SIII interaction. This state is bound due to dynamical coupling between the core and the loosely bound neutron which oscillates between 2 s{1}/{2} and l d{5}/{2} orbits. The direct neutron capture is discussed briefly in its relation to the neutron halo.
Covariant Newtonian and relativistic dynamics of (magneto)-elastic solid model for neutron star crust
NASA Astrophysics Data System (ADS)
Carter, B.; Chachoua, E.; Chamel, N.
This work develops the dynamics of a perfectly elastic solid model for application to the outer crust of a magnetised neutron star. Particular attention is given to the Noether identities responsible for energy-momentum conservation, using a formulation that is fully covariant, not only (as is usual) in a fully relativistic treatment but also (sacrificing accuracy and elegance for economy of degrees of gravitational freedom) in the technically more complicated case of the Newtonian limit. The results are used to obtain explicit (relativistic and Newtonian) formulae for the propagation speeds of generalised (Alfven type) magneto-elastic perturbation modes.
Stochastic two-fluid model for relativistic heavy-ion collisions
Ayik, S. |; Ivanov, Y.B.; Russkikh, V.N.; Noerenberg, W.
A reduction of the relativistic Boltzmann-Langevin Equation (BLE), to a stochastic two-fluid model is presented, and transport coefficients associated with fluid dynamical variables are extracted. The approach is applied to investigate equilibration in a counter-streaming nuclear system.
Stochastic two-fluid model for relativistic heavy-ion collisions. [Boltzmann[endash]Langevin Equation
Ayik, S. Joint Inst. for Heavy Ion Research, Oak Ridge, TN ); Ivanov, Y.B.; Russkikh, V.N.; Noerenberg, W. )
A reduction of the relativistic Boltzmann-Langevin Equation (BLE), to a stochastic two-fluid model is presented, and transport coefficients associated with fluid dynamical variables are extracted. The approach is applied to investigate equilibration in a counter-streaming nuclear system.
Longitudinal and Transverse Parton Momentum Distributions for Hadrons within Relativistic Constituent Quark Models
Frederico, T.; Pace, E.; Pasquini, B.; Salme, G.
Longitudinal and transverse parton distributions for pion and nucleon are calculated from hadron vertexes obtained by a study of form factors within relativistic quark models. The relevance of the one-gluon-exchange dominance at short range for the behavior of the form factors at large momentum transfer and of the parton distributions at the end points is stressed.
On the Methods for Constructing Meson-Baryon Reaction Models within Relativistic Quantum Field Theory
B. Julia-Diaz, H. Kamano, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki
Within the relativistic quantum field theory, we analyze the differences between the $\\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
Pipin, V. V.; Sokoloff, D. D.; Zhang, H.; Kuzanyan, K. M.
It is believed that magnetic helicity conservation is an important constraint on large-scale astrophysical dynamos. In this paper, we study a mean-field solar dynamo model that employs two different formulations of the magnetic helicity conservation. In the first approach, the evolution of the averaged small-scale magnetic helicity is largely determined by the local induction effects due to the large-scale magnetic field, turbulent motions, and the turbulent diffusive loss of helicity. In this case, the dynamo model shows that the typical strength of the large-scale magnetic field generated by the dynamo is much smaller than the equipartition value for the magnetic Reynolds number 10{sup 6}. This is the so-called catastrophic quenching (CQ) phenomenon. In the literature, this is considered to be typical for various kinds of solar dynamo models, including the distributed-type and the Babcock-Leighton-type dynamos. The problem can be resolved by the second formulation, which is derived from the integral conservation of the total magnetic helicity. In this case, the dynamo model shows that magnetic helicity propagates with the dynamo wave from the bottom of the convection zone to the surface. This prevents CQ because of the local balance between the large-scale and small-scale magnetic helicities. Thus, the solar dynamo can operate in a wide range of magnetic Reynolds numbers up to 10{sup 6}.
Relativistic jet models for the BL Lacertae object Mrk 421 during three epochs of observation
NASA Technical Reports Server (NTRS)
Mufson, S. L.; Hutter, D. J.; Kondo, Y.; Wisniewski, W. Z.
Coordinated observation of the nearby BL Lacertae object Mrk 421 obtained during May 1980, January 1984, and March 1984 are described. These observations give a time-frozen picture of the continuous spectrum of Mrk 421 at X-ray, ultraviolet, optical, and radio wavelengths. The observed spectra have been fitted to an inhomogeneous relativistic jet model. In general, the models reproduce the data well. Many of the observed differences during the three epochs can be attributed to variations in the opening angle of the jet and in the angle that the jet makes to the line of sight. The jet models obtained here are compared with the homogeneous, spherically symmetric, synchrotron self-Compton models for this source. The models are also compared with the relativistic jet models obtained for other active galactic nuclei.
Axisymmetric toroidal modes of general relativistic magnetized neutron star models
Asai, Hidetaka; Lee, Umin E-mail: email@example.com
We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength B{sub S} ∼ 10{sup 16} G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to B{sub S} and is well represented by a linear function of R/M for a given B{sub S}, where M and R are the mass and radius of the star. The toroidal mode frequencies for B{sub S} ∼ 10{sup 15} G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.
Comparisons of cross-section predictions for relativistic iron and argon beams with semiempirical fragmentation models
NASA Technical Reports Server (NTRS)
Townsend, Lawrence W.; Tripathi, Ram K.; Khan, Ferdous
Cross-section predictions with semi-empirical nuclear fragmentation models from the Langley Research Center and the Naval Research Laboratory are compared with experimental data for the breakup of relativistic iron and argon projectile nuclei in various targets. Both these models are commonly used to provide fragmentation cross-section inputs into galactic cosmic ray transport codes for shielding and exposure analyses. Overall, the Langley model appears to yield better agreement with the experimental data.
Particle spectra and efficiency in nonlinear relativistic shock acceleration - survey of scattering models
NASA Astrophysics Data System (ADS)
Ellison, Donald C.; Warren, Donald C.; Bykov, Andrei M.
We include a general form for the scattering mean free path, λmfp(p), in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, self-generated magnetic turbulence that leads to a scattering mean free path with a stronger momentum dependence than the λmfp ∝ p dependence for Bohm diffusion. In unmagnetized shocks, this turbulence is strong enough to dominate the background magnetic field so the shock can be treated as parallel regardless of the initial magnetic field orientation, making application to γ-ray bursts, pulsar winds, type Ibc supernovae, and extragalactic radio sources more straightforward and realistic. In addition to changing the scale of the shock precursor, we show that, when nonlinear effects from efficient Fermi acceleration are taken into account, the momentum dependence of λmfp(p) has an important influence on the efficiency of cosmic ray production as well as the accelerated particle spectral shape. These effects are absent in non-relativistic shocks and do not appear in relativistic shock models unless nonlinear effects are self-consistently described. We show, for limited examples, how the changes in Fermi acceleration translate to changes in the intensity and spectral shape of γ-ray emission from proton-proton interactions and pion-decay radiation.
Mean field limit for bosons and propagation of Wigner measures
NASA Astrophysics Data System (ADS)
Ammari, Z.; Nier, F.
We consider the N-body Schrödinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [Ammari, Z. and Nier, F., "Mean field limit for bosons and infinite dimensional phase-space analysis," Ann. Henri Poincare 9, 1503 (2008)], the mean field limit is translated into a semiclassical problem with a small parameter ɛ →0, after introducing an ɛ-dependent bosonic quantization. The limits of quantum correlation functions are expressed as a push forward by a nonlinear flow (e.g., Hartree) of the associated Wigner measures. These object and their basic properties were introduced by Ammari and Nier in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for a rather general class of quantum states in their mean field limit.
Mean field limit for bosons and propagation of Wigner measures
Ammari, Z.; Nier, F.
We consider the N-body Schroedinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [Ammari, Z. and Nier, F., 'Mean field limit for bosons and infinite dimensional phase-space analysis', Ann. Henri Poincare 9, 1503 (2008)], the mean field limit is translated into a semiclassical problem with a small parameter {epsilon}{yields}0, after introducing an {epsilon}-dependent bosonic quantization. The limits of quantum correlation functions are expressed as a push forward by a nonlinear flow (e.g., Hartree) of the associated Wigner measures. These object and their basic properties were introduced by Ammari and Nier in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for a rather general class of quantum states in their mean field limit.
Spherical relativistic vacuum core models in a Λ-dominated era
NASA Astrophysics Data System (ADS)
Yousaf, Z.
This paper is devoted to analyzing the effects of the cosmological constant in the evolution of exact analytical collapsing vacuum core celestial models. For this purpose, relativistic spherical geometry coupled with null expansion locally anisotropic matter distributions is considered. We have first developed a relation between tidal forces and structural variables. We then explored some viable spherical cosmological models by taking the expansion-free condition. Our first class of spherical models is obtained after constraining system matter content, while the second class is obtained by considering barotropic equation of state. We propose that our calculated solutions could be regarded as a relativistic toy model for those astronomical compact populations where vacuum core is expected to appear, like cosmological voids.
Mean-field theory of meta-learning
NASA Astrophysics Data System (ADS)
Plewczynski, Dariusz
We discuss here the mean-field theory for a cellular automata model of meta-learning. Meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of interacting, learning agents that acquire and process incoming information using various types, or different versions, of machine learning algorithms. The abstract learning space, where all agents are located, is constructed here using a fully connected model that couples all agents with random strength values. The cellular automata network simulates the higher level integration of information acquired from the independent learning trials. The final classification of incoming input data is therefore defined as the stationary state of the meta-learning system using simple majority rule, yet the minority clusters that share the opposite classification outcome can be observed in the system. Therefore, the probability of selecting a proper class for a given input data, can be estimated even without the prior knowledge of its affiliation. The fuzzy logic can be easily introduced into the system, even if learning agents are built from simple binary classification machine learning algorithms by calculating the percentage of agreeing agents.
Optical model description of momentum transfer in relativistic heavy ion collisions
NASA Technical Reports Server (NTRS)
Khan, F.; Khandelwal, G. S.; Townsend, L. W.; Wilson, J. W.; Norbury, J. W.
An optical model description of momentum transfer in relativistic heavy ion collisions, based upon composite particle multiple scattering theory, is presented. The imaginary component of the complex momentum transfer, which comes from the absorptive part of the optical potential, is identified as the longitudinal momentum downshift of the projectile. Predictions of fragment momentum distribution observables are made and compared with experimental data. Use of the model as a tool for estimating collision impact parameters is discussed.
Project: Modeling Relativistic Electrons from Nuclear Explosions in the Magnetosphere
Cowee, Misa; Gary, S. Peter; Winske, Dan; Liu, Kaijun
We present a summary of the FY12 activities for DTRA-funded project 'Modeling Relativistic Electrons from Nuclear Explosions in the Magnetosphere'. We briefly review the outstanding scientific questions and discuss the work done in the last year to try to answer these questions. We then discuss the agenda for this Technical Meeting with the DTRA sponsors. In the last year, we have continued our efforts to understand artificial radiation belts from several different perspectives: (1) Continued development of Electron Source Model (ESM) and comparison to HANE test data; (2) Continued studies of relativistic electron scattering by waves in the natural radiation belts; (3) Began study of self-generated waves from the HANE electrons; and (4) Began modeling for the UCLA laser experiment.
General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks
NASA Astrophysics Data System (ADS)
Donmez, Orhan
We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.
Structure of relativistic shocks in pulsar winds: A model of the wisps in the Crab Nebula
NASA Technical Reports Server (NTRS)
Gallant, Yves A.; Arons, Jonathan
We propose a model of a optical 'wisps' of the Crab Nebula, features observed in the nebular synchrotron surface brightness near the central pulsar, as manifestations of the internal structure of the shock terminating the pulsar wind. We assume that this wind is composed of ions and a much denser plasma of electrons and positrons, frozen together to a toroidal magnetic field and flowing relativistically. We construct a form of solitary wave model of the shock structure in which we self-consistently solve for the ion orbits and the dynamics of the relativistically hot, magnetized e(+/-) background flow. We ignore dispersion in the ion energies, and we treat the pairs as an adiabatic fluid. The synchrotron emission enhancements, observed as the wisps, are then explained as the regions where reflection of the ions in the self-consistent magnetic field causes compressions of the e(+/-).
Relativistic model for the nonmesonic weak decay of single-lambda hypernuclei
NASA Astrophysics Data System (ADS)
Fontoura, C. E.; Krmpotić, F.; Galeão, A. P.; De Conti, C.; Krein, G.
Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay (NMWD) of single-Λ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the (π ,K) one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of {}{{Λ }}12{{C}} are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the only noteworthy difference is that the ratio {{{Γ }}}n/{{{Γ }}}p is appreciably higher and closer to the experimental value in the relativistic calculation. The ability of describing existing data, including the most recent ones, on NMWD of Λ-hypernuclei, warrants application of the formalism to evaluate similar decay processes in charmed nuclei.
Semileptonic decays of Λ _c baryons in the relativistic quark model
NASA Astrophysics Data System (ADS)
Faustov, R. N.; Galkin, V. O.
Motivated by recent experimental progress in studying weak decays of the Λ _c baryon we investigate its semileptonic decays in the framework of the relativistic quark model based on the quasipotential approach with the QCD-motivated potential. The form factors of the Λ _c→ Λ lν _l and Λ _c→ nlν _l decays are calculated in the whole accessible kinematical region without extrapolations and additional model assumptions. Relativistic effects are systematically taken into account including transformations of baryon wave functions from the rest to moving reference frame and contributions of the intermediate negative-energy states. Baryon wave functions found in the previous mass spectrum calculations are used for the numerical evaluation. Comprehensive predictions for decay rates, asymmetries and polarization parameters are given. They agree well with available experimental data.
Ultra-relativistic heavy ion collisions in a multi-string model
Werner, K.
We present a model for ultra-relativistic heavy ion collisions based on color string formation and subsequent independent string fragmentation. Strings are formed due to color exchange between quarks at each individual nucleon nucleon collision. The fragmentation is treated as in e/sup +/e/sup -/ or lepton nucleon scattering. Calculation for pp, pA, and AA were carried out using the Monte Carlo code VENUS for Very Energetic Nuclear Scattering (version 1.0). 20 refs., 6 figs.
Breit and Quantum Electrodynamics Energy Contributions in Multielectron Atoms from the Relativistic Screened Hydrogenic Model
NASA Astrophysics Data System (ADS)
Di Rocco, Héctor O.; Lanzini, Fernando
The correction to the Coulomb repulsion between two electrons due to the exchange of a transverse photon, referred to as the Breit interaction, as well as the main quantum electrodynamics contributions to the atomic energies (self-energy and vacuum polarization), are calculated using the recently formulated relativistic screened hydrogenic model. Comparison with the results of multiconfiguration Dirac-Hartree-Fock calculations and experimental X- ray energies is made.
A Maximum Principle for SDEs of Mean-Field Type
Andersson, Daniel Djehiche, Boualem
We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
Mean-field Ohm's law and coaxial helicity injection in force-free plasmas
Weening, R. H.
A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity {eta} and hyper-resistivity {Lambda} terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.
Mean-field theory of atomic self-organization in optical cavities
NASA Astrophysics Data System (ADS)
Jäger, Simon B.; Schütz, Stefan; Morigi, Giovanna
Photons mediate long-range optomechanical forces between atoms in high-finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second-order phase transition that separates a uniform spatial density from a Bragg grating maximizing scattering into the cavity and is controlled by the laser intensity. Starting from a Fokker-Planck equation describing the semiclassical dynamics of the N -atom distribution function, we systematically develop a mean-field model and analyze its predictions for the equilibrium and out-of-equilibrium dynamics. The validity of the mean-field model is tested by comparison with the numerical simulations of the N -body Fokker-Planck equation and by means of a Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. The mean-field theory predictions well reproduce several results of the N -body Fokker-Planck equation for sufficiently short times and are in good agreement with existing theoretical approaches based on field-theoretical models. The mean field, on the other hand, predicts thermalization time scales which are at least one order of magnitude shorter than the ones predicted by the N -body dynamics. We attribute this discrepancy to the fact that the mean-field ansatz discards the effects of the long-range incoherent forces due to cavity losses.
Simplified method for including spatial correlations in mean-field approximations
NASA Astrophysics Data System (ADS)
Markham, Deborah C.; Simpson, Matthew J.; Baker, Ruth E.
Biological systems involving proliferation, migration, and death are observed across all scales. For example, they govern cellular processes such as wound healing, as well as the population dynamics of groups of organisms. In this paper, we provide a simplified method for correcting mean-field approximations of volume-excluding birth-death-movement processes on a regular lattice. An initially uniform distribution of agents on the lattice may give rise to spatial heterogeneity, depending on the relative rates of proliferation, migration, and death. Many frameworks chosen to model these systems neglect spatial correlations, which can lead to inaccurate predictions of their behavior. For example, the logistic model is frequently chosen, which is the mean-field approximation in this case. This mean-field description can be corrected by including a system of ordinary differential equations for pairwise correlations between lattice site occupancies at various lattice distances. In this work we discuss difficulties with this method and provide a simplification in the form of a partial differential equation description for the evolution of pairwise spatial correlations over time. We test our simplified model against the more complex corrected mean-field model, finding excellent agreement. We show how our model successfully predicts system behavior in regions where the mean-field approximation shows large discrepancies. Additionally, we investigate regions of parameter space where migration is reduced relative to proliferation, which has not been examined in detail before and find our method is successful at correcting the deviations observed in the mean-field model in these parameter regimes.
Weakly nonlinear ion-acoustic excitations in a relativistic model for dense quantum plasma.
Behery, E E; Haas, F; Kourakis, I
The dynamics of linear and nonlinear ionic-scale electrostatic excitations propagating in a magnetized relativistic quantum plasma is studied. A quantum-hydrodynamic model is adopted and degenerate statistics for the electrons is taken into account. The dispersion properties of linear ion acoustic waves are examined in detail. A modified characteristic charge screening length and "sound speed" are introduced, for relativistic quantum plasmas. By employing the reductive perturbation technique, a Zakharov-Kuznetzov-type equation is derived. Using the small-k expansion method, the stability profile of weakly nonlinear slightly supersonic electrostatic pulses is also discussed. The effect of electron degeneracy on the basic characteristics of electrostatic excitations is investigated. The entire analysis is valid in a three-dimensional as well as in two-dimensional geometry. A brief discussion of possible applications in laboratory and space plasmas is included.
Breaking of relativistically intense longitudinal space charge waves: A description using Dawson sheet model
Sengupta, Sudip
Spatio-temporal evolution of relativistically intense longitudinal space charge waves in a cold homogeneous plasma is studied analytically as well as numerically, as an initial value problem, using Dawson sheet model. It is found that, except for very special initial conditions which generates the well known longitudinal Akhiezer-Polovin mode, for all other initial conditions, the waves break through a novel mechanism called phase mixing at an amplitude well below the Akhiezer-Polovin limit. An immediate consequence of this is, that Akhiezer-Polovin waves break when subjected to arbitrarily small longitudinal perturbations. We demonstrate this by performing extensive numerical simulations. This result may be of direct relevance to ultrashort, ultraintense laser/beam pulse-plasma interaction experiments where relativistically intense waves are routinely excited.
Breaking of relativistically intense longitudinal space charge waves: A description using Dawson sheet model
NASA Astrophysics Data System (ADS)
Sengupta, Sudip
Spatio-temporal evolution of relativistically intense longitudinal space charge waves in a cold homogeneous plasma is studied analytically as well as numerically, as an initial value problem, using Dawson sheet model. It is found that, except for very special initial conditions which generates the well known longitudinal Akhiezer-Polovin mode, for all other initial conditions, the waves break through a novel mechanism called phase mixing at an amplitude well below the Akhiezer-Polovin limit. An immediate consequence of this is, that Akhiezer-Polovin waves break when subjected to arbitrarily small longitudinal perturbations. We demonstrate this by performing extensive numerical simulations. This result may be of direct relevance to ultrashort, ultraintense laser/beam pulse-plasma interaction experiments where relativistically intense waves are routinely excited.
Dynamical systems approach to relativistic spherically symmetric static perfect fluid models
NASA Astrophysics Data System (ADS)
Heinzle, J. Mark; Röhr, Niklas; Uggla, Claes
We investigate relativistic spherically symmetric static perfect fluid models with barotropic equations of state that are asymptotically polytropic and linear at low and high pressures, respectively. We generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. This is accomplished by introducing dimensionless variables that are asymptotically homology invariant in the low pressure regime, which yields a reformulation of the field equations into a regular dynamical system on a three-dimensional compact state space. A global picture of the solution space is thus obtained which makes it possible to derive qualitative features and to prove theorems about mass radius properties. Moreover, the framework is also suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.
Multi Module Modeling of Ultra-Relativistic Heavy Ion Collisions.
Magas, V. K.; Csernai, L. P.; Keranen, A.; Manninen, J.; Strottman, D. D.
Multi Module Model is required for the realistic and detailed description of an ultrarelativistic heavy ion reaction. We are working in the framework of such a model: initial stages are described by Effective String Rope Model with expanding final streaks; hydrodynamical approach is used for the intermediate stages. This paper is mainly devoted to Third Module - the one dealing with Freeze Out (FO). Two possibilities are discussed in details: (A) freeze out at the constant time hypersurface, where the statistical production model is used to describe post FO particle species; and (B) simultaneous hadronization and freeze out from supercooled QGP. For the last case the ALCOR-like algorithm for calculation of the post FO particle species is presented, due to the fact that these do not have time to reach chemical equilibrium.
Mean-field dynamo action in renovating shearing flows.
Kolekar, Sanved; Subramanian, Kandaswamy; Sridhar, S
We study mean-field dynamo action in renovating flows with finite and nonzero correlation time (τ) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and nonhelical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly nonhelical, then such mean-field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval τ. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the α(2)Ω dynamo, in the small τ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean-field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.
Robust mean field games for coupled Markov jump linear systems
NASA Astrophysics Data System (ADS)
Moon, Jun; Başar, Tamer
We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents' individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.
Mean-field versus microconvection effects in nanofluid thermal conduction.
Eapen, Jacob; Williams, Wesley C; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto
Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.
Relativistic electromagnetic mass models in spherically symmetric spacetime
NASA Astrophysics Data System (ADS)
Maurya, S. K.; Gupta, Y. K.; Ray, Saibal; Chatterjee, Vikram
Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of constructing electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Lorentz in Proc. Acad. Sci. Amst. 6, 1904). This work is in continuation of our earlier investigation of Maurya et al. (Eur. Phys. J. C 75:389, 2015a) where we developed an algorithm and found out three new solutions of electromagnetic mass model. In the present work we consider different metric potentials ν and λ and have analyzed them in a systematic way. It is observed that some of the previous solutions related to electromagnetic mass model are nothing but special cases of the presently obtained generalized solution set. We further verify the solution set and especially show that these are extremely applicable in the case of compact stars.
Thermoinertial bouncing of a relativistic collapsing sphere: A numerical model
Herrera, L.; Di Prisco, A.; Barreto, W.
We present a numerical model of a collapsing radiating sphere, whose boundary surface undergoes bouncing due to a decreasing of its inertial mass density (and, as expected from the equivalence principle, also of the 'gravitational' force term) produced by the 'inertial' term of the transport equation. This model exhibits for the first time the consequences of such an effect, and shows that under physically reasonable conditions this decreasing of the gravitational term in the dynamic equation may be large enough as to revert the collapse and produce a bouncing of the boundary surface of the sphere.
Relativistic model of anisotropic charged fluid sphere in general relativity
NASA Astrophysics Data System (ADS)
Pant, Neeraj; Pradhan, N.; Bansal, Rajeev K.
In this present paper, we present a class of static, spherically symmetric charged anisotropic fluid models of super dense stars in isotropic coordinates by considering a particular type of metric potential, a specific choice of electric field intensity E and pressure anisotropy factor Δ which involve parameters K (charge) and α (anisotropy) respectively. The solutions so obtained are utilized to construct the models for super-dense stars like neutron stars and strange quark stars. Our solutions are well behaved within the following ranges of different constant parameters. In the absence of pressure anisotropy and charge present model reduces to the isotropic model Pant et al. (Astrophys. Space Sci. 330:353-359, 2010). Our solution is well behaved in all respects for all values of X lying in the range 0< X ≤ 0.18, α lying in the range 0 ≤ α ≤6.6, K lying in the range 0< K ≤ 6.6 and Schwarzschild compactness parameter "u" lying in the range 0< u ≤ 0.38. Since our solution is well behaved for a wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to X=0.088, α=0.6 and K=4.3 for which u=0.2054 and by assuming surface density ρb = 4.6888 × 10^{14} g/cm3 the mass and radius are found to be 1.51 M_{\\varTheta} and 10.90 km respectively. Assuming surface density ρb = 2 × 10^{14} g/cm3 the mass and radius for a neutron star candidate are found to be 2.313 M_{\\varTheta} and 16.690 km respectively. Hence we obtain masses and radii that fall in the range of what is generally expected for quark stars and neutron stars.
The application of the Gibbs-Bogoliubov-Feynman inequality in mean field calculations for Markov random fields.
Zhang, J
The Gibbs-Bogoliubov-Feynman (GBF) inequality of statistical mechanics is adopted, with an information-theoretic interpretation, as a general optimization framework for deriving and examining various mean field approximations for Markov random fields (MRF's). The efficacy of this approach is demonstrated through the compound Gauss-Markov (CGM) model, comparisons between different mean field approximations, and experimental results in image restoration.
Octet Baryon Electromagnetic Form Factors in a Relativistic Quark Model
Gilberto Ramalho, Kazuo Tsushima
We study the octet baryon electromagnetic properties by applying the covariant spectator quark model, and provide covariant parametrization that can be used to study baryon electromagnetic reactions. While we use the lattice QCD data in the large pion mass regime (small pion cloud effects) to determine the parameters of the model in the valence quark sector, we use the nucleon physical and octet baryon magnetic moment data to parameterize the pion cloud contributions. The valence quark contributions for the octet baryon electromagnetic form factors are estimated by extrapolating the lattice parametrization in the large pion mass regime to the physical regime. As for the pion cloud contributions, we parameterize them in a covariant, phenomenological manner, combined with SU(3) symmetry. We also discuss the impact of the pion cloud effects on the octet baryon electromagnetic form factors and their radii.
Euclidean bridge to the relativistic constituent quark model
NASA Astrophysics Data System (ADS)
Hobbs, T. J.; Alberg, Mary; Miller, Gerald A.
Background: Knowledge of nucleon structure is today ever more of a precision science, with heightened theoretical and experimental activity expected in coming years. At the same time, a persistent gap lingers between theoretical approaches grounded in Euclidean methods (e.g., lattice QCD, Dyson-Schwinger equations [DSEs]) as opposed to traditional Minkowski field theories (such as light-front constituent quark models). Purpose: Seeking to bridge these complementary world views, we explore the potential of a Euclidean constituent quark model (ECQM). This formalism enables us to study the gluonic dressing of the quark-level axial-vector vertex, which we undertake as a test of the framework. Method: To access its indispensable elements with a minimum of inessential detail, we develop our ECQM using the simplified quark + scalar diquark picture of the nucleon. We construct a hyperspherical formalism involving polynomial expansions of diquark propagators to marry our ECQM with the results of Bethe-Salpeter equation (BSE) analyses, and constrain model parameters by fitting electromagnetic form factor data. Results: From this formalism, we define and compute a new quantity—the Euclidean density function (EDF)—an object that characterizes the nucleon's various charge distributions as functions of the quark's Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the quenched dressing effect on the proton's axial-singlet charge to be small in magnitude and consistent with zero, while use of recent determinations of unquenched BSEs results in a large suppression. Conclusions: The quark + scalar diquark ECQM is a step toward a realistic quark model in Euclidean space, and needs additional refinements. The substantial effect we obtain for the impact on the axial-singlet charge of the unquenched dressed vertex compared to the quenched demands further investigation.
Well-behaved relativistic charged super-dense star models
NASA Astrophysics Data System (ADS)
Faruqi, Shahab; Pant, Neeraj
A new class of charged super-dense star models is obtained by using an electric intensity, which involves a parameter, K. The metric describing the model shares its metric potential g 44 with that of Durgapal's fourth solution (J. Phys. A, Math. Gen. 15:2637, 1982). The pressure-free surface is kept at the density ρ b =2×1014 g/cm3 and joins smoothly with the Reissner-Nordstrom solution. The charge analogues are well-behaved for a wide range, 0≤ K≤59, with the optimum value of X=0.264 i.e. the pressure, density, pressure-density ratio and velocity of sound are monotonically decreasing and the electric intensity is monotonically increasing in nature for the given range of the parameter K. The maximum mass and the corresponding radius occupied by the neutral solution are 4.22 M Θ and 20 km, respectively for X=0.264. For the charged solution, the maximum mass and radius are defined by the expressions M≈(0.0059 K+4.22) M Θ and r b ≈-0.021464 K+20 km respectively.
Critical rotation of general-relativistic polytropic models revisited
NASA Astrophysics Data System (ADS)
Geroyannis, V.; Karageorgopoulos, V.
We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.
Collisional energy losses in relativistic nuclear collisions within an effective quasiparticle model
Tarasov, Yu. A.
We investigate the collisional energy losses of the fast gluons and light quarks in quark-gluon plasma produced in central (Au+Au) collisions at at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC) ({radical}(s{sub NN})=200 GeV). We use the effective quasiparticle model for investigation of physical characteristic of expanding plasma. We take into account the possibility of hot glue production at the first stage. We calculate these energy losses and compare them with radiative energy losses of gluons and quarks in an analogous model. We show that radiative energy losses exceed considerably the collisional energy losses.
Constrained-pairing mean-field theory. V. Triplet pairing formalism.
Ellis, Jason K; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Tsuchimochi, Takashi; Scuseria, Gustavo E
Describing strong (also known as static) correlation caused by degenerate or nearly degenerate orbitals near the Fermi level remains a theoretical challenge, particularly in molecular systems. Constrained-pairing mean-field theory has been quite successful, capturing the effects of static correlation in bond formation and breaking in closed-shell molecular systems by using singlet electron entanglement to model static correlation at mean-field computational cost. This work extends the previous formalism to include triplet pairing. Additionally, a spin orbital extension of the "odd-electron" formalism is presented as a method for understanding electron entanglement in molecules.
A Euclidean bridge to the relativistic constituent quark model
NASA Astrophysics Data System (ADS)
Hobbs, Timothy; Alberg, Mary; Miller, Gerald
We explore the potential of a Euclidean constituent quark model (ECQM) to bridge the lingering gap between Euclidean and Minkowski field theories in studies of nucleon structure. Specifically, we develop our ECQM using a simplified quark-scalar diquark picture of the nucleon as a first calculation. Our treatment in Euclidean space necessitates a hyperspherical formalism involving polynomial expansions of diquark propagators in order to marry our ECQM with results from Bethe-Salpeter Equation (BSE) analyses. From this framework, we define and compute a new quantity - a Euclidean density function (EDF) - an object that characterizes the nucleon's various charge distributions as functions of the quark's Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the quenched dressing effect on the proton's axial-singlet charge to be small in magnitude and consistent with zero, while use of recent determinations of unquenched BSEs results in a large suppression. The substantial effect we obtain for the impact on the axial-singlet charge of the unquenched dressed vertex compared to the quenched demands further investigation. Work supported by DOE grant DE-FG02-97ER-41014 and NSF Grant No. 1516105.
Generalized Mean Fields for Trapped Atomic Bose-Einstein Condensates
Proukakis, N. P.; Burnett, K.
We describe generalized time-dependent mean-field equations for partially condensed samples of trapped and evaporatively cooled atoms. These equations give a way of investigating the various order parameters that may be present as well as the existence of a mean value of the field due to condensed atoms. Our approach provides us with a closed system of self-consistent equations for the order parameters present. The equations we derive are shown to reduce to other treatments in the literature in various limits. We also show how the equation of motion method allows us to construct a formalism that can handle the evolution of these mean fields due to two-loop kinetics. PMID:27805101
Stochastic Mean-Field Dynamics For Nuclear Collisions
Ayik, Sakir
We discuss a stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. For small amplitude fluctuations, this approach gives a result for the dispersion of a one-body observable that is identical to the result obtained previously through a variational approach. Furthermore, it incorporates one-body dissipation and fluctuation mechanisms in accordance with quantal fluctuation-dissipation relation.
A mean field neural network for hierarchical module placement
NASA Technical Reports Server (NTRS)
Unaltuna, M. Kemal; Pitchumani, Vijay
This paper proposes a mean field neural network for the two-dimensional module placement problem. An efficient coding scheme with only O(N log N) neurons is employed where N is the number of modules. The neurons are evolved in groups of N in log N iteration steps such that the circuit is recursively partitioned in alternating vertical and horizontal directions. In our simulations, the network was able to find optimal solutions to all test problems with up to 128 modules.
Gluon condensate in a pion superfluid beyond the mean-field approximation
Jiang Yin; Zhuang Pengfei
We study gluon condensate in a pion superfluid by calculating the equation of state of the system in the Nambu-Jona-Lasinio model. While in mean-field approximation the growing pion condensate leads to an increasing gluon condensate, meson fluctuations reduce the gluon condensate, and the broken scalar symmetry can be smoothly restored at finite isospin density.
Numerical Simulations, Mean Field Theory and Modulational Stability Analysis of Thermohaline Intrusions
the temporal and spatial variability of the ocean circulation (Schmitt, 2003). This signifies that these thermohaline intrusions cannot be ignored...still calculating the net effects of double diffusion via crude parameterizations, the study showed that the thermohaline circulations in the model...SIMULATIONS, MEAN FIELD THEORY AND MODULATIONAL STABLITY ANALYSIS OF THERMOHALINE INTRUSIONS by Mark A. Hebert September 2011 Thesis Advisor
Structure of fluctuations near mean-field critical points and spinodals and its implication for physical processes.
Klein, W; Gould, Harvey; Gulbahce, Natali; Rundle, J B; Tiampo, K
We analyze the structure of fluctuations near critical points and spinodals in mean-field and near-mean-field systems. Unlike systems that are non-mean-field, for which a fluctuation can be represented by a single cluster in a properly chosen percolation model, a fluctuation in mean-field and near-mean-field systems consists of a large number of clusters, which we term fundamental clusters. The structure of the latter and the way that they form fluctuations has important physical consequences for phenomena as diverse as nucleation in supercooled liquids, spinodal decomposition and continuous ordering, and the statistical distribution of earthquakes. The effects due to the fundamental clusters implies that they are physical objects and not only mathematical constructs.
Relativistic blast-wave model for the rapid flux variations of AO 0235+164 and other compact radio sources
NASA Technical Reports Server (NTRS)
Marscher, A. P.
A relativistic blast-wave version of a signal-screen model is developed which can adequately explain the details of the flux-density and structural variations of compact extragalactic radio sources. The relativistic motion implied by flux variations is analyzed with respect to the synchrotron spectrum of the BL Lac object AO 0235+164 observed during outbursts, and a signal-screen model for rapidly expanding shells produced by ultrarelativistic blast waves is examined. The approximate observed structure of the blast wave at three stages in its evolution is illustrated, each stage is described, and the model is applied to the flux density outburst in AO 0235+164 observed in late 1975. The results show that a relativistic blast-wave model can in general reproduce the main features of the observed flux variations in compact sources. Some problems with the proposed model are briefly discussed.
Normalizing a relativistic model of X-ray reflection. Definition of the reflection fraction and its implementation in relxill
NASA Astrophysics Data System (ADS)
Dauser, T.; García, J.; Walton, , D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.
Aims: The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory; it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. Methods: The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an external source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamp post model, which is a focus of this paper. Results: Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamp post model, namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Conclusions: Fitting data by using the relxill model and the recently implemented reflection fraction, the geometry of a system can be constrained. The reflection fraction is independent of system parameters such as inclination and black hole spin. The reflection-fraction parameter was implemented with the name refl_frac in all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).
Normalizing a Relativistic Model of X-Ray Reflection Definition of the Reflection Fraction and Its Implementation in relxill
NASA Technical Reports Server (NTRS)
Dauser, T.; Garcia, J.; Walton, D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.
Aims. The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory; it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. Methods. The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an external source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamp post model, which is a focus of this paper. Results. Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamp post model,namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Conclusions. Fitting data by using the relxill model and the recently implemented reflection fraction, the geometry of a system can be constrained. The reflection-fraction is independent of system parameters such as inclination and black hole spin. The reflection-fraction parameter was implemented with the name reflec_frac all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).
A New Multi-dimensional General Relativistic Neutrino Hydrodynamics Code for Core-collapse Supernovae. II. Relativistic Explosion Models of Core-collapse Supernovae
NASA Astrophysics Data System (ADS)
Müller, Bernhard; Janka, Hans-Thomas; Marek, Andreas
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M ⊙ progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.
Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas E-mail: firstname.lastname@example.com
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M{sub Sun} progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.
Perera, B. B. P.; McLaughlin, M. A.; Kramer, M.; Lyne, A. G.; Stairs, I. H.; Ferdman, R. D.; Freire, P. C. C.; Possenti, A.; Burgay, M.; Breton, R. P.; Manchester, R. N.; Camilo, F.
We present the evolution of the radio emission from the 2.8 s pulsar of the double pulsar system PSR J0737- 3039A/B. We provide an update on the Burgay et al. analysis by describing the changes in the pulse profile and flux density over five years of observations, culminating in the B pulsar's radio disappearance in 2008 March. Over this time, the flux density decreases by 0.177 mJy yr{sup -1} at the brightest orbital phases and the pulse profile evolves from a single to a double peak, with a separation rate of 2.{sup 0}6 yr{sup -1}. The pulse profile changes are most likely caused by relativistic spin precession but cannot be easily explained with a circular hollow-cone beam as in the model of Clifton and Weisberg. Relativistic spin precession, coupled with an elliptical beam, can model the pulse profile evolution well and the reappearance is expected to happen in {approx}2035 with the same part of the beam or in {approx}2014 if we assume a symmetric beam shape. This particular beam shape predicts geometrical parameters for the two bright orbital phases which are consistent with and similar to those derived by Breton et al. However, the observed decrease in flux over time and B's eventual disappearance cannot be easily explained by the model and may be due to the changing influence of A on B.
Thermal entanglement of spins in mean-field clusters
Asoudeh, M.; Karimipour, V.
We determine thermal entanglement in mean-field clusters of N spin one-half particles interacting via the anisotropic Heisenberg interaction, with and without external magnetic field. For the xxx cluster in the absence of magnetic field we prove that only the N=2 ferromagnetic cluster shows entanglement. An external magnetic field B can only entangle xxx antiferromagnetic clusters in certain regions of the B-T plane. On the other hand, the xxz clusters of size N>2 are entangled only when the interaction is ferromagnetic. Detailed dependence of the entanglement on various parameters is investigated in each case.
Cluster dynamical mean-field calculations for TiOCl
NASA Astrophysics Data System (ADS)
Saha-Dasgupta, T.; Lichtenstein, A.; Hoinkis, M.; Glawion, S.; Sing, M.; Claessen, R.; Valentí, R.
Based on a combination of cluster dynamical mean field theory (DMFT) and density functional calculations, we calculated the angle-integrated spectral density in the layered s=1/2 quantum magnet TiOCl. The agreement with recent photoemission and oxygen K-edge x-ray absorption spectroscopy experiments is found to be good. The improvement achieved with this calculation with respect to previous single-site DMFT calculations is an indication of the correlated nature and low-dimensionality of TiOCl.
Mean-Field Inference in Gaussian Restricted Boltzmann Machine
NASA Astrophysics Data System (ADS)
Takahashi, Chako; Yasuda, Muneki
A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous visible variables and a hidden layer composed of discrete hidden variables. In this paper, we derive two different inference algorithms for GRBMs based on the naïve mean-field approximation (NMFA). One is an inference algorithm for whole variables in a GRBM, and the other is an inference algorithm for partial variables in a GBRBM. We compare the two methods analytically and numerically and show that the latter method is better.
New dynamical mean-field dynamo theory and closure approach.
Blackman, Eric G; Field, George B
We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.
Mean Field Evolution of Fermions with Coulomb Interaction
NASA Astrophysics Data System (ADS)
Porta, Marcello; Rademacher, Simone; Saffirio, Chiara; Schlein, Benjamin
We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree-Fock dynamics. Our result holds under a condition on the solution of the Hartree-Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree-Fock evolution is trivial), but that we expect to hold more generally.
A mean field Ohm`s law for collisionless plasmas
Biglari, H.; Diamond, P.H. |
A mean field Ohm`s law valid for collisionless plasmas is derived kinetically. It is shown that contrary to conventional thinking, the resulting hyper-resistivity is significantly smaller than its fluid counterpart due to the fact that the turbulent decorrelation rate is linked to the rapid electron ballistic motion rather than the slower nonlinear mixing time. Moreover, the off-diagonal contributions to the parallel electron momentum flux are shown to result in Ohm`s law renormalizations that dwarf the current diffusivity and break radial parity symmetry. Thus, the conventional wisdom of tearing and twisting parity solutions appears to be vitiated in the turbulent collisionless regime.
Dynamical mean-field theory for quantum chemistry.
Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R
The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.
Advanced mean-field theory of the restricted Boltzmann machine
NASA Astrophysics Data System (ADS)
Huang, Haiping; Toyoizumi, Taro
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean-field theory based on the Bethe approximation. Our theory provides an efficient message-passing-based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling-based method.
A mean field Ohm's law for collisionless plasmas
Biglari, H. ); Diamond, P.H. )
A mean field Ohm's law valid for collisionless plasmas is derived kinetically. It is shown that contrary to conventional thinking, the resulting hyperresistivity is significantly smaller than its fluid counterpart due to the fact that the turbulent decorrelation rate is linked to the rapid electron ballistic motion rather than the slower nonlinear mixing time. Moreover, the off-diagonal contributions to the parallel electron momentum flux are shown to result in Ohm's law renormalizations that dwarf the current diffusivity and break radial parity symmetry.
Modeling the relativistic runaway electron avalanche and the feedback mechanism with GEANT4.
Skeltved, Alexander Broberg; Østgaard, Nikolai; Carlson, Brant; Gjesteland, Thomas; Celestin, Sebastien
This paper presents the first study that uses the GEometry ANd Tracking 4 (GEANT4) toolkit to do quantitative comparisons with other modeling results related to the production of terrestrial gamma ray flashes and high-energy particle emission from thunderstorms. We will study the relativistic runaway electron avalanche (RREA) and the relativistic feedback process, as well as the production of bremsstrahlung photons from runaway electrons. The Monte Carlo simulations take into account the effects of electron ionization, electron by electron (Møller), and electron by positron (Bhabha) scattering as well as the bremsstrahlung process and pair production, in the 250 eV to 100 GeV energy range. Our results indicate that the multiplication of electrons during the development of RREAs and under the influence of feedback are consistent with previous estimates. This is important to validate GEANT4 as a tool to model RREAs and feedback in homogeneous electric fields. We also determine the ratio of bremsstrahlung photons to energetic electrons Nγ /Ne . We then show that the ratio has a dependence on the electric field, which can be expressed by the avalanche time τ(E) and the bremsstrahlung coefficient α(ε). In addition, we present comparisons of GEANT4 simulations performed with a "standard" and a "low-energy" physics list both validated in the 1 keV to 100 GeV energy range. This comparison shows that the choice of physics list used in GEANT4 simulations has a significant effect on the results.
Mean-field limit of systems with multiplicative noise.
Muñoz, Miguel A; Colaiori, Francesca; Castellano, Claudio
A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise intensity (weak, intermediate, and strong noise) are identified by performing a self-consistent calculation on a fully connected lattice. The most interesting, strong-noise, regime is shown to be intrinsically unstable with respect to the inclusion of fluctuations, as a Ginzburg criterion shows. On the other hand, the self-consistent approach is shown to be valid only in the thermodynamic limit, while for finite systems the critical behavior is found to be different. In this last case, the self-consistent field itself is broadly distributed rather than taking a well defined mean value; its fluctuations, described by an effective zero-dimensional multiplicative noise equation, govern the critical properties. These findings are obtained analytically for a fully connected graph, and verified numerically both on fully connected graphs and on random regular networks. The results presented here shed some doubt on what is the validity and meaning of a standard mean-field approach in systems with multiplicative noise in finite dimensions, where each site does not see an infinite number of neighbors, but a finite one. The implications of all this on the existence of a finite upper critical dimension for multiplicative noise and Kardar-Parisi-Zhang problems are briefly discussed.
Nonextensive statistical effects in the quark-gluon plasma formation at relativistic heavy-ion collisions energies
NASA Astrophysics Data System (ADS)
Gervino, Gianpiero; Lavagno, Andrea; Pigato, Daniele
We investigate the relativistic equation of state of hadronic matter and quark-gluon plasma at finite temperature and baryon density in the framework of the non-extensive statistical mechanics, characterized by power-law quantum distributions. We impose the Gibbs conditions on the global conservation of baryon number, electric charge and strangeness number. For the hadronic phase, we study an extended relativistic mean-field theoretical model with the inclusion of strange particles (hyperons and mesons). For the quark sector, we employ an extended MIT-Bag model. In this context we focus on the relevance of non-extensive effects in the presence of strange matter.
A relativistic self-consistent model for studying enhancement of space charge limited emission due to counter-streaming ions
NASA Astrophysics Data System (ADS)
Lin, M. C.; Verboncoeur, J.
A maximum electron current transmitted through a planar diode gap is limited by space charge of electrons dwelling across the gap region, the so called space charge limited (SCL) emission. By introducing a counter-streaming ion flow to neutralize the electron charge density, the SCL emission can be dramatically raised, so electron current transmission gets enhanced. In this work, we have developed a relativistic self-consistent model for studying the enhancement of maximum transmission by a counter-streaming ion current. The maximum enhancement is found when the ion effect is saturated, as shown analytically. The solutions in non-relativistic, intermediate, and ultra-relativistic regimes are obtained and verified with 1-D particle-in-cell simulations. This self-consistent model is general and can also serve as a comparison for verification of simulation codes, as well as extension to higher dimensions.
Relativistic scalar-vector models of the N-N and N-nuclear interactions
Green, A.E.S.
This paper for the Proceedings of Conference an Anti-Nucleon and Nucleon-Nucleus Interactions summarizes work by the principal investigator and his collaborators on the nucleon-nucleon (N-N) and nucleon-nuclear (N-eta) interactions. It draws heavily on a paper presented at the Many Body Conference in Rome in 1972 but also includes a brief review of our phenomenological N-eta interaction studies. We first summarize our 48-49 generalized scalar-vector meson field theory model of the N-N interactions. This is followed by a brief description of our phenomenological work in the 50's on the N-eta interaction sponsored by the Atomic Energy Commission (the present DOE). This work finally led to strong velocity dependent potentials with spin orbit and isospin terms for shell and optical model applications. This is followed by a section on the Emergence of One-Boson Exchange Models describing developments in the 60's of quantitative generalized one boson exchange potentials (GOBEP) including our purely relativistic N-N analyses. Then follows a section on the application of this meson field model to the N-eta interaction, in particular to spherical closed shell nuclei. This work was sponsored by AFOSR but funding was halted with the Mansfield amendment. We conclude with a discussion of subsequent collateral work by former colleagues and by others who have converged upon scalar-vector relativistic models of N-N, antiN-N, N-eta and antiN-eta interactions and some lessons learned from this extended endeavor. 61 refs.
The Limits of Mean-Field Heterozygosity Estimates under Spatial Extension in Simulated Plant Populations
Kitchen, James L.; Allaby, Robin G.
Computational models of evolutionary processes are increasingly required to incorporate multiple and diverse sources of data. A popular feature to include in population genetics models is spatial extension, which reflects more accurately natural populations than does a mean field approach. However, such models necessarily violate the mean field assumptions of classical population genetics, as do natural populations in the real world. Recently, it has been questioned whether classical approaches are truly applicable to the real world. Individual based models (IBM) are a powerful and versatile approach to achieve integration in models. In this study an IBM was used to examine how populations of plants deviate from classical expectations under spatial extension. Populations of plants that used three different mating strategies were placed in a range of arena sizes giving crowded to sparse occupation densities. Using a measure of population density, the pollen communication distance (Pcd), the deviation exhibited by outbreeding populations differed from classical mean field expectations by less than 5% when Pcd was less than 1, and over this threshold value the deviation significantly increased. Populations with an intermediate mating strategy did not have such a threshold and deviated directly with increasing isolation between individuals. Populations with a selfing strategy were influenced more by the mating strategy than by increased isolation. In all cases pollen dispersal was more influential than seed dispersal. The IBM model showed that mean field calculations can be reasonably applied to natural outbreeding plant populations that occur at a density in which individuals are less than the average pollen dispersal distance from their neighbors. PMID:22952655
Viallet, Maxime; Meakin, Casey; Mocak, Miroslav; Arnett, David
We present three-dimensional implicit large eddy simulations of the turbulent convection in the envelope of a 5 M{sub Sun} red giant star and in the oxygen-burning shell of a 23 M{sub Sun} supernova progenitor. The numerical models are analyzed in the framework of one-dimensional Reynolds-Averaged Navier-Stokes equations. The effects of pressure fluctuations are more important in the red giant model, owing to larger stratification of the convective zone. We show how this impacts different terms in the mean-field equations. We clarify the driving sources of kinetic energy, and show that the rate of turbulent dissipation is comparable to the convective luminosity. Although our flows have low Mach numbers and are nearly adiabatic, our analysis is general and can be applied to photospheric convection as well. The robustness of our analysis of turbulent convection is supported by the insensitivity of the mean-field balances to linear mesh resolution. We find robust results for the turbulent convection zone and the stable layers in the oxygen-burning shell model, and robust results everywhere in the red giant model, but the mean fields are not well converged in the narrow boundary regions (which contain steep gradients) in the oxygen-burning shell model. This last result illustrates the importance of unresolved physics at the convective boundary, which governs the mixing there.
The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization
NASA Astrophysics Data System (ADS)
Bogolubov, Nikolai N.; Prykarpatsky, Anatoliy K.
The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079-1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed.
Coughlin, Eric R.; Begelman, Mitchell C. E-mail: email@example.com
Using the relativistic equations of radiation hydrodynamics in the viscous limit, we analyze the boundary layers that develop between radiation-dominated jets and their environments. In this paper we present the solution for the self-similar, 2D, plane-parallel two-stream problem, wherein the jet and the ambient medium are considered to be separate, interacting fluids, and we compare our results to those of previous authors. (In a companion paper we investigate an alternative scenario, known as the free-streaming jet model.) Consistent with past findings, we show that the boundary layer that develops between the jet and its surroundings creates a region of low-density material. These models may be applicable to sources such as super-Eddington tidal disruption events and long gamma-ray bursts.
Density Functional Plus Dynamical Mean Field Theory of Correlated Oxides
NASA Astrophysics Data System (ADS)
Millis, Andrew
The density functional plus dynamical mean field method is outlined and a few recent successes including applications to spin crossover molecules, oxide superlattices and metal-insulator transitions in bulk transition metals are outlined. Insights from the method into the essential role played by lattice distortions (both rotations and bond length changes) in determining the phase diagrams of correlated materials are presented. The key theoretical issue of the double counting correction is outlined, different approaches are compared, and a connection to the energy level differences between strongly and weakly correlated orbitals is presented. Charge transfer across oxide interfaces shown to depend crucially on the double counting correction, suggesting that experiments on oxide superlattices may provide insights into this important problem. Future directions are discussed. This work is performed in collaboration with Jia Chen, Hung Dang, Hyowon Park and Chris Marianetti. This research supported by the DOE Office of Science, Grant ER 046169.
Extended time-dependent mean-field approximation
Portes, D.A. Jr. |; Kodama, T.; de Toledo Piza, A.F.
The time-dependent mean-field approximation for two dynamically coupled subsystems is extended to include correlation effects between the subsystems, allowing for decorrelation processes to develop in the reduced density matrices. The extended scheme is formulated in terms of the truncation to {ital M} terms of the Schmidt decomposition of the full density matrix. This {ital M} natural orbitals truncation scheme is compared to the exact numerical solution for a system of two coupled anharmonic oscillators in a factorized initial state. It is found that the approximation {ital M}=3 gives a good approximation to the exact results over several characteristic times of the system. {copyright} {ital 1996 The American Physical Society.}
Bödeker, Dietrich; Wörmann, Mirco E-mail: firstname.lastname@example.com
In many phenomenologically interesting models of thermal leptogenesis the heavy neutrinos are non-relativistic when they decay and produce the baryon asymmetry of the Universe. We propose a non-relativistic approximation for the corresponding rate equations in the non-resonant case, and a systematic way for computing relativistic corrections. We determine the leading order coefficients in these equations, and the first relativistic corrections. The non-relativistic approximation works remarkably well. It appears to be consistent with results obtained using a Boltzmann equation taking into account the momentum distribution of the heavy neutrinos, while being much simpler. We also compute radiative corrections to some of the coefficients in the rate equations. Their effect is of order 1% in the regime favored by neutrino oscillation data. We obtain the correct leading order lepton number washout rate in this regime, which leads to large ( ∼ 20%) effects compared to previous computations.
Modelling the high-energy emission from gamma-ray binaries using numerical relativistic hydrodynamics
NASA Astrophysics Data System (ADS)
Dubus, G.; Lamberts, A.; Fromang, S.
Context. Detailed modelling of the high-energy emission from gamma-ray binaries has been propounded as a path to pulsar wind physics. Aims: Fulfilling this ambition requires a coherent model of the flow and its emission in the region where the pulsar wind interacts with the stellar wind of its companion. Methods: We have developed a code that follows the evolution and emission of electrons in the shocked pulsar wind based on inputs from a relativistic hydrodynamical simulation. The code is used to model the well-documented spectral energy distribution and orbital modulations from LS 5039. Results: The pulsar wind is fully confined by a bow shock and a back shock. The particles are distributed into a narrow Maxwellian, emitting mostly GeV photons, and a power law radiating very efficiently over a broad energy range from X-rays to TeV gamma rays. Most of the emission arises from the apex of the bow shock. Doppler boosting shapes the X-ray and very high energy (VHE) lightcurves, constraining the system inclination to i ≈ 35°. There is tension between the hard VHE spectrum and the level of X-ray to MeV emission, which requires differing magnetic field intensities that are hard to achieve with constant magnetisation σ and Lorentz factor Γp of the pulsar wind. Our best compromise implies σ ≈ 1 and Γp ≈ 5 × 103, so respectively higher and lower than the typical values in pulsar wind nebulae. Conclusions: The high value of σ derived here, where the wind is confined close to the pulsar, supports the classical picture that has pulsar winds highly magnetised at launch. However, such magnetisations will require that further investigations are based on relativistic MHD simulations. Movies associated to Figs. A.1-A.4 are available in electronic form at http://www.aanda.org
Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume
Briceno, Raul A.; Hansen, Maxwell T.
We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less
Relativistic Quark-Model Results for Baryon Ground and Resonant States
Plessas, W.; Melde, T.
Latest results from a study of baryon ground and resonant states within relativistic constituent quark models are reported. After recalling some typical spectral properties, the description of ground states, especially with regard to the nucleon and hyperon electromagnetic structures, is addressed. In the following, recent covariant predictions for pion, eta, and kaon partial decay widths of light and strange baryon resonances below 2 GeV are summarized. These results exhibit a characteristic pattern that is distinct from nonrelativistic or relativized decay studies performed so far. Together with a detailed analysis of the spin, flavor, and spatial structures of the wave functions, it supports a new and extended classification scheme of baryon ground and resonant states into SU(3) flavor multiplets.
Modeling the QCD Equation of State in Relativistic Heavy Ion Collisions on BlueGene/L
Soltz, R; Grady, J; Hartouni, E P; Gupta, R; Vitev, I; Mottola, E; Petreczky, P; Karsch, F; Christ, N; Mawhinney, R; Bass, S; Mueller, B; Vranas, P; Levkova, L; Molnar, D; Teaney, D; De Tar, C; Toussaint, D; Sugar, R
On 9,10 Feb 2006 a workshop was held at LLNL to discuss how a 10% allocation of the ASC BG/L supercomputer performing a finite temperature Lattice QCD (LQCD) calculation of the equation of state and non-equilibrium properties of the quark-gluon state of matter could lead to a breakthrough in our understanding of recent data from the Relativistic Heavy Ion Collider at Brookhaven National Lab. From this meeting and subsequent discussions we present a detailed plan for this calculation, including mechanisms for working in a secure computing environment and inserting the resulting equation of state into hydrodynamic transport models that will be compared directly to the RHIC data. We discuss expected benefits for DOE Office of Science research programs within the context of the NNSA mission.
Relativistic density functional theory modeling of plutonium and americium higher oxide molecules.
Zaitsevskii, Andréi; Mosyagin, Nikolai S; Titov, Anatoly V; Kiselev, Yuri M
The results of electronic structure modeling of plutonium and americium higher oxide molecules (actinide oxidation states VI through VIII) by two-component relativistic density functional theory are presented. Ground-state equilibrium molecular structures, main features of charge distributions, and energetics of AnO3, AnO4, An2On (An=Pu, Am), and PuAmOn, n = 6-8, are determined. In all cases, molecular geometries of americium and mixed plutonium-americium oxides are similar to those of the corresponding plutonium compounds, though chemical bonding in americium oxides is markedly weaker. Relatively high stability of the mixed heptoxide PuAmO7 is noticed; the Pu(VIII) and especially Am(VIII) oxides are expected to be unstable.
Relativistic density functional theory modeling of plutonium and americium higher oxide molecules
NASA Astrophysics Data System (ADS)
Zaitsevskii, Andréi; Mosyagin, Nikolai S.; Titov, Anatoly V.; Kiselev, Yuri M.
The results of electronic structure modeling of plutonium and americium higher oxide molecules (actinide oxidation states VI through VIII) by two-component relativistic density functional theory are presented. Ground-state equilibrium molecular structures, main features of charge distributions, and energetics of AnO3, AnO4, An2On (An=Pu, Am), and PuAmOn, n = 6-8, are determined. In all cases, molecular geometries of americium and mixed plutonium-americium oxides are similar to those of the corresponding plutonium compounds, though chemical bonding in americium oxides is markedly weaker. Relatively high stability of the mixed heptoxide PuAmO7 is noticed; the Pu(VIII) and especially Am(VIII) oxides are expected to be unstable.
Statistical thermodynamics of protein folding: Comparison of a mean-field theory with Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Hao, Ming-Hong; Scheraga, Harold A.
A comparative study of protein folding with an analytical theory and computer simulations, respectively, is reported. The theory is based on an improved mean-field formalism which, in addition to the usual mean-field approximations, takes into account the distributions of energies in the subsets of conformational states. Sequence-specific properties of proteins are parametrized in the theory by two sets of variables, one for the energetics of mean-field interactions and one for the distribution of energies. Simulations are carried out on model polypeptides with different sequences, with different chain lengths, and with different interaction potentials, ranging from strong biases towards certain local chain states (bond angles and torsional angles) to complete absence of local conformational preferences. Theoretical analysis of the simulation results for the model polypeptides reveals three different types of behavior in the folding transition from the statistical coiled state to the compact globular state; these include a cooperative two-state transition, a continuous folding, and a glasslike transition. It is found that, with the fitted theoretical parameters which are specific for each polypeptide under a different potential, the mean-field theory can describe the thermodynamic properties and folding behavior of the different polypeptides accurately. By comparing the theoretical descriptions with simulation results, we verify the basic assumptions of the theory and, thereby, obtain new insights about the folding transitions of proteins. It is found that the cooperativity of the first-order folding transition of the model polypeptides is determined mainly by long-range interactions, in particular the dipolar orientation; the local interactions (e.g., bond-angle and torsion-angle potentials) have only marginal effect on the cooperative characteristic of the folding, but have a large impact on the difference in energy between the folded lowest-energy structure and
Modeling the relativistic runaway electron avalanche and the feedback mechanism with GEANT4
Skeltved, Alexander Broberg; Østgaard, Nikolai; Carlson, Brant; Gjesteland, Thomas; Celestin, Sebastien
This paper presents the first study that uses the GEometry ANd Tracking 4 (GEANT4) toolkit to do quantitative comparisons with other modeling results related to the production of terrestrial gamma ray flashes and high-energy particle emission from thunderstorms. We will study the relativistic runaway electron avalanche (RREA) and the relativistic feedback process, as well as the production of bremsstrahlung photons from runaway electrons. The Monte Carlo simulations take into account the effects of electron ionization, electron by electron (Møller), and electron by positron (Bhabha) scattering as well as the bremsstrahlung process and pair production, in the 250 eV to 100 GeV energy range. Our results indicate that the multiplication of electrons during the development of RREAs and under the influence of feedback are consistent with previous estimates. This is important to validate GEANT4 as a tool to model RREAs and feedback in homogeneous electric fields. We also determine the ratio of bremsstrahlung photons to energetic electrons Nγ/Ne. We then show that the ratio has a dependence on the electric field, which can be expressed by the avalanche time τ(E) and the bremsstrahlung coefficient α(ε). In addition, we present comparisons of GEANT4 simulations performed with a "standard" and a "low-energy" physics list both validated in the 1 keV to 100 GeV energy range. This comparison shows that the choice of physics list used in GEANT4 simulations has a significant effect on the results. Key Points Testing the feedback mechanism with GEANT4 Validating the GEANT4 programming toolkit Study the ratio of bremsstrahlung photons to electrons at TGF source altitude PMID:26167437
NASA Astrophysics Data System (ADS)
Dunkel, Jörn; Hänggi, Peter
Over the past one hundred years, Brownian motion theory has contributed substantially to our understanding of various microscopic phenomena. Originally proposed as a phenomenological paradigm for atomistic matter interactions, the theory has since evolved into a broad and vivid research area, with an ever increasing number of applications in biology, chemistry, finance, and physics. The mathematical description of stochastic processes has led to new approaches in other fields, culminating in the path integral formulation of modern quantum theory. Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special relativity, we review, here, recent progress in the phenomenological description of relativistic diffusion processes. After a brief historical overview, we will summarize basic concepts from the Langevin theory of nonrelativistic Brownian motions and discuss relevant aspects of relativistic equilibrium thermostatistics. The introductory parts are followed by a detailed discussion of relativistic Langevin equations in phase space. We address the choice of time parameters, discretization rules, relativistic fluctuation-dissipation theorems, and Lorentz transformations of stochastic differential equations. The general theory is illustrated through analytical and numerical results for the diffusion of free relativistic Brownian particles. Subsequently, we discuss how Langevin-type equations can be obtained as approximations to microscopic models. The final part of the article is dedicated to relativistic diffusion processes in Minkowski spacetime. Since the velocities of relativistic particles are bounded by the speed of light, nontrivial relativistic Markov processes in spacetime do not exist; i.e., relativistic generalizations of the nonrelativistic diffusion equation and its Gaussian solutions
Computation of masses and binding energies of some hadrons and bosons according to the rotating lepton model and the relativistic Newton equation
NASA Astrophysics Data System (ADS)
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
We compute analytically the masses, binding energies and hamiltonians of gravitationally bound Bohr-type states via the rotating relativistic lepton model which utilizes the de Broglie wavelength equation in conjunction with special relativity and Newton's relativistic gravitational law. The latter uses the inertial-gravitational masses, rather than the rest masses, of the rotating particles. The model also accounts for the electrostatic charge- induced dipole interactions between a central charged lepton, which is usually a positron, with the rotating relativistic lepton ring. We use three rotating relativistic neutrinos to model baryons, two rotating relativistic neutrinos to model mesons, and a rotating relativistic electron neutrino - positron (or electron) pair to model the W± bosons. It is found that gravitationally bound ground states comprising three relativistic neutrinos have masses in the baryon mass range (∼⃒ 0.9 to 1 GeV/c2), while ground states comprising two neutrinos have masses in the meson mass range (∼⃒ 0.4 to 0.8 GeV/c2). It is also found that the rest mass values of quarks are in good agreement with the heaviest neutrino mass value of 0.05 eV/c2 and that the mass of W± bosons (∼⃒ 81 GeV/c2) corresponds to the mass of a rotating gravitationally confined e± — ve pair. A generalized expression is also derived for the gravitational potential energy of such relativistic Bohr-type structures.
Relativistic effects on plasma expansion
Benkhelifa, El-Amine; Djebli, Mourad
The expansion of electron-ion plasma is studied through a fully relativistic multi-fluids plasma model which includes thermal pressure, ambipolar electrostatic potential, and internal energy conversion. Numerical investigation, based on quasi-neutral assumption, is performed for three different regimes: nonrelativistic, weakly relativistic, and relativistic. Ions' front in weakly relativistic regime exhibits spiky structure associated with a break-down of quasi-neutrality at the expanding front. In the relativistic regime, ion velocity is found to reach a saturation limit which occurs at earlier stages of the expansion. This limit is enhanced by higher electron velocity.
More is the Same; Phase Transitions and Mean Field Theories
NASA Astrophysics Data System (ADS)
Kadanoff, Leo P.
This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the names of "singularity", "order parameter", "mean field theory", "variational method", "correlation length", "universality class", "scale changes", and "renormalization". The first four of these will be considered here. In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in some statistical variable. The discontinuous property is called the order parameter. Each phase transition has its own order parameter. The possible order parameters range over a tremendous variety of physical properties. These properties include the density of a liquid-gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when the discontinuity in the jump approaches zero. This article is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of phase transition phenomena. Much of the material in this review was first prepared for the Royal Netherlands Academy of Arts and
Nonuniversal behavior for aperiodic interactions within a mean-field approximation.
Faria, Maicon S; Branco, N S; Tragtenberg, M H R
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.
Mean Field Limit of Interacting Filaments and Vector Valued Non-linear PDEs
NASA Astrophysics Data System (ADS)
Bessaih, Hakima; Coghi, Michele; Flandoli, Franco
Families of N interacting curves are considered, with long range, mean field type, interaction. They generalize models based on classical interacting point particles to models based on curves. In this new set-up, a mean field result is proven, as N→ ∞. The limit PDE is vector valued and, in the limit, each curve interacts with a mean field solution of the PDE. This target is reached by a careful formulation of curves and weak solutions of the PDE which makes use of 1-currents and their topologies. The main results are based on the analysis of a nonlinear Lagrangian-type flow equation. Most of the results are deterministic; as a by-product, when the initial conditions are given by families of independent random curves, we prove a propagation of chaos result. The results are local in time for general interaction kernel, global in time under some additional restriction. Our main motivation is the approximation of 3D-inviscid flow dynamics by the interacting dynamics of a large number of vortex filaments, as observed in certain turbulent fluids; in this respect, the present paper is restricted to smoothed interaction kernels, instead of the true Biot-Savart kernel.
Self-consistent slave rotor mean-field theory for strongly correlated systems
NASA Astrophysics Data System (ADS)
Zhao, E.; Paramekanti, A.
Building on the work by Florens and Georges [Phys. Rev. B 70, 035114 (2004)], we formulate and study a self-consistent slave rotor mean-field theory for strongly correlated systems. This approach views the electron, in the strong correlation regime, as a composite of a neutral spinon and a charged rotor field. We solve the coupled spinon-rotor model self-consistently using a cluster mean-field theory for the rotors and various Ansätze for the spinon ground state. We illustrate this approach with a number of examples relevant to ongoing experiments in strongly correlated electronic systems such as (i) the phase diagram of the isotropic triangular lattice organic Mott insulators, (ii) quasiparticle excitations and tunneling asymmetry in the weakly doped cuprate superconductors, and (iii) the cyclotron mass of carriers in commensurate spin-density wave and U(1) staggered flux (or d -density wave) normal states of the underdoped cuprates. We compare the estimated cyclotron mass with results from recent quantum oscillation experiments on ortho-II YBa2Cu3O6.5 by Doiron-Leyraud [Nature (London) 447, 565 (2007)] which appear to find Fermi pockets in the magnetic field induced normal state. We comment on the relation of this normal ground state to Fermi arcs seen in photoemission experiments above Tc . This slave rotor mean-field theory can be generalized to study inhomogeneous states and strongly interacting models relevant to ultracold atoms in optical lattices.
Mean Field Limit of Interacting Filaments and Vector Valued Non-linear PDEs
NASA Astrophysics Data System (ADS)
Bessaih, Hakima; Coghi, Michele; Flandoli, Franco
Families of N interacting curves are considered, with long range, mean field type, interaction. They generalize models based on classical interacting point particles to models based on curves. In this new set-up, a mean field result is proven, as N→ ∞. The limit PDE is vector valued and, in the limit, each curve interacts with a mean field solution of the PDE. This target is reached by a careful formulation of curves and weak solutions of the PDE which makes use of 1-currents and their topologies. The main results are based on the analysis of a nonlinear Lagrangian-type flow equation. Most of the results are deterministic; as a by-product, when the initial conditions are given by families of independent random curves, we prove a propagation of chaos result. The results are local in time for general interaction kernel, global in time under some additional restriction. Our main motivation is the approximation of 3D-inviscid flow dynamics by the interacting dynamics of a large number of vortex filaments, as observed in certain turbulent fluids; in this respect, the present paper is restricted to smoothed interaction kernels, instead of the true Biot-Savart kernel.
Spectral Synthesis via Mean Field approach to Independent Component Analysis
NASA Astrophysics Data System (ADS)
Hu, Ning; Su, Shan-Shan; Kong, Xu
We apply a new statistical analysis technique, the Mean Field approach to Independent Component Analysis (MF-ICA) in a Bayseian framework, to galaxy spectral analysis. This algorithm can compress a stellar spectral library into a few Independent Components (ICs), and the galaxy spectrum can be reconstructed by these ICs. Compared to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, the MF-ICA approach offers a large improvement in efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter recovery for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters derived with galaxies from the Sloan Digital Sky Survey. We find that our MF-ICA method can not only fit the observed galaxy spectra efficiently, but can also accurately recover the physical parameters of galaxies. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find it can provide excellent fitting results for low signal-to-noise spectra.
You Bei; Cao Xinwu; Yuan Yefei E-mail: firstname.lastname@example.com
We calculate the structure of a standard accretion disk with a corona surrounding a massive Kerr black hole in the general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields generated in the cold accretion disk. The emergent spectra of accretion disk-corona systems are calculated by using the relativistic ray-tracing method. We propose a new method to calculate the emergent Comptonized spectra from the coronae. The spectra of disk-corona systems with a modified {alpha}-magnetic stress show that both the hard X-ray spectral index and the hard X-ray bolometric correction factor L{sub bol}/L{sub X,2-10keV} increase with the dimensionless mass accretion rate, which is qualitatively consistent with the observations of active galactic nuclei. The fraction of the power dissipated in the corona decreases with increasing black hole spin parameter a, which leads to lower electron temperatures of the coronae for rapidly spinning black holes. The X-ray emission from the coronae surrounding rapidly spinning black holes becomes weak and soft. The ratio of the X-ray luminosity to the optical/UV luminosity increases with the viewing angle, while the spectral shape in the X-ray band is insensitive to the viewing angle. We find that the spectral index in the infrared waveband depends on the mass accretion rate and the black hole spin a, which deviates from the f{sub {nu}}{proportional_to}{nu}{sup 1/3} relation expected by the standard thin disk model.
Relativistic Effects and Polarization in Three High-Energy Pulsar Models
NASA Technical Reports Server (NTRS)
Dyks, J.; Harding, Alice K.; Rudak, B.
We present the influence of the special relativistic effects of aberration and light travel time delay on pulsar high-energy lightcurves and polarization characteristics predicted by three models: the two-pole caustic model, the outer gap model, and the polar cap model. Position angle curves and degree of polarization are calculated for the models and compared with the optical data on the Crab pulsar. The relative positions of peaks in gamma-ray and radio lightcurves are discussed in detail for the models. We find that the two-pole caustic model can reproduce qualitatively the optical polarization characteristics of the Crab pulsar - fast swings of the position angle and minima in polarization degree associated with both peaks. The anticorrelation between the observed flux and the polarization degree (observed in the optical band also for B0656+14) naturally results from the caustic nature of the peaks which are produced in the model due to the superposition of radiation from many different altitudes, ie. polarized at different angles. The two-pole caustic model also provides an acceptable interpretation of the main features in the Crab's radio profile. Neither the outer gap model nor the polar cap model are able to reproduce the optical polarization data on the Crab. Although the outer gap model is very successful in reproducing the relative positions of gamma-ray and radio peaks in pulse profiles, it can reproduce the high-energy lightcurves only when photon emission from regions very close to the light cylinder is included.
Newtonian self-gravitating system in a relativistic huge void universe model
NASA Astrophysics Data System (ADS)
Nishikawa, Ryusuke; Nakao, Ken-ichi; Yoo, Chul-Moon
We consider a test of the Copernican Principle through observations of the large-scale structures, and for this purpose we study the self-gravitating system in a relativistic huge void universe model which does not invoke the Copernican Principle. If we focus on the the weakly self-gravitating and slowly evolving system whose spatial extent is much smaller than the scale of the cosmological horizon in the homogeneous and isotropic background universe model, the cosmological Newtonian approximation is available. Also in the huge void universe model, the same kind of approximation as the cosmological Newtonian approximation is available for the analysis of the perturbations contained in a region whose spatial size is much smaller than the scale of the huge void: the effects of the huge void are taken into account in a perturbative manner by using the Fermi-normal coordinates. By using this approximation, we derive the equations of motion for the weakly self-gravitating perturbations whose elements have relative velocities much smaller than the speed of light, and show the derived equations can be significantly different from those in the homogeneous and isotropic universe model, due to the anisotropic volume expansion in the huge void. We linearize the derived equations of motion and solve them. The solutions show that the behaviors of linear density perturbations are very different from those in the homogeneous and isotropic universe model.
The cumulative overlap distribution function in spin glasses: mean field vs. three dimensions
NASA Astrophysics Data System (ADS)
Yllanes, David; Billoire, Alain; Maiorano, Andrea; Marinari, Enzo; Martin-Mayor, Victor
We use a sample-dependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution in spin glasses. Using analytical and numerical mean-field results for the Sherrington-Kirkpatrick model, as well as data from toy models, we show that this approach is an effective tool to distinguish the low-temperature behavior of replica symmmetry breaking systems from that expected in the droplet picture. An application of the method to the three-dimensional Edwards-Anderson models shows agreement with the replica symmetry breaking predictions. Supported by ERC Grant No. 247328 and from MINECO (Spain), Contract No. FIS2012-35719-C02.
Comparisons and connections between mean field dynamo theory and accretion disc theory
NASA Astrophysics Data System (ADS)
Blackman, E. G.
The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory.
Mean-Field Approximation to the Hydrophobic Hydration in the Liquid-Vapor Interface of Water.
Abe, Kiharu; Sumi, Tomonari; Koga, Kenichiro
A mean-field approximation to the solvation of nonpolar solutes in the liquid-vapor interface of aqueous solutions is proposed. It is first remarked with a numerical illustration that the solvation of a methane-like solute in bulk liquid water is accurately described by the mean-field theory of liquids, the main idea of which is that the probability (Pcav) of finding a cavity in the solvent that can accommodate the solute molecule and the attractive interaction energy (uatt) that the solute would feel if it is inserted in such a cavity are both functions of the solvent density alone. It is then assumed that the basic idea is still valid in the liquid-vapor interface, but Pcav and uatt are separately functions of different coarse-grained local densities, not functions of a common local density. Validity of the assumptions is confirmed for the solvation of the methane-like particle in the interface of model water at temperatures between 253 and 613 K. With the mean-field approximation extended to the inhomogeneous system the local solubility profiles across the interface at various temperatures are calculated from Pcav and uatt obtained at a single temperature. The predicted profiles are in excellent agreement with those obtained by the direct calculation of the excess chemical potential over an interfacial region where the solvent local density varies most rapidly.
General relativistic considerations of the field shedding model of fast radio bursts
NASA Astrophysics Data System (ADS)
Punsly, Brian; Bini, Donato
Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic `hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 1011-1013 G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.
Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach
NASA Astrophysics Data System (ADS)
Pramanik, Souvik; Ghosh, Subir
We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.
Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach
NASA Astrophysics Data System (ADS)
Pramanik, Souvik; Ghosh, Subir
We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.
Black hole thermodynamics as seen through a microscopic model of a relativistic Bose gas
NASA Astrophysics Data System (ADS)
Skákala, Jozef; Shankaranarayanan, S.
Equations of gravity when projected on spacetime horizons resemble Navier-Stokes equation of a fluid with a specific equation of state [T. Damour, Surface effects of black hole physics, in Proc. M. Grossman Meeting (North Holland, 1982), p. 587, T. Padmanabhan, Phys. Rev. D 83 (2011) 044048, arXiv:gr-qc/1012.0119, S. Kolekar and T. Padmanabhan, Phys. Rev. D 85 (2011) 024004, arXiv:gr-qc/1012.5421]. We show that this equation of state describes massless ideal relativistic gas. We use these results, and build an explicit and simple molecular model of the fluid living on the Schwarzschild and Reissner-Nordström black hole horizons. For the spin zero Bose gas, our model makes two predictions: (i) The horizon area/entropy is quantized as given by Bekenstein's quantization rule, (ii) The model explains the correct type of proportionality between horizon area and entropy. However, for the physically relevant range of parameters, the proportionality constant is never equal to 1/4.
Double occupancy in dynamical mean-field theory and the dual boson approach
NASA Astrophysics Data System (ADS)
van Loon, Erik G. C. P.; Krien, Friedrich; Hafermann, Hartmut; Stepanov, Evgeny A.; Lichtenstein, Alexander I.; Katsnelson, Mikhail I.
We discuss the calculation of the double occupancy using dynamical mean-field theory in finite dimensions. The double occupancy can be determined from the susceptibility of the auxiliary impurity model or from the lattice susceptibility. The former method typically overestimates, whereas the latter underestimates the double occupancy. We illustrate this for the square-lattice Hubbard model. We propose an approach for which both methods lead to identical results by construction and which resolves this ambiguity. This self-consistent dual boson scheme results in a double occupancy that is numerically close to benchmarks available in the literature.
Mean-field theory for confinement transitions and magnetization plateaux in spin ice
NASA Astrophysics Data System (ADS)
Powell, Stephen
We study phase transitions in classical spin ice at nonzero magnetization, by introducing a mean-field theory designed to capture the interplay between confinement and topological constraints. The method is applied to a model of spin ice in an applied magnetic field along the ≤ft[1 0 0\\right] crystallographic direction and yields a phase diagram containing the Coulomb phase as well as a set of magnetization plateaux. We argue that the lobe structure of the phase diagram, strongly reminiscent of the Bose–Hubbard model, is generic to Coulomb spin liquids.
Mean field mutation dynamics and the continuous Luria-Delbrück distribution.
Kashdan, Eugene; Pareschi, Lorenzo
The Luria-Delbrück mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker-Planck equations for the mutants distribution whose solutions are given by the corresponding Luria-Delbrück distribution. Numerical results confirming the theoretical analysis are also presented.
Weakly relativistic plasma expansion
Fermous, Rachid Djebli, Mourad
Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamical multi-fluid equations, we investigated the expansion of both dense and under-dense plasmas. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. Numerical investigations have shown that relativistic effects are important for under-dense plasma and are characterized by a finite ion front velocity. Dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.
Modeling of relativistic plasmas with the Particle-In-Cell method
NASA Astrophysics Data System (ADS)
Vay, Jean-Luc; Godfrey, Brendan B.
Standard methods employed in relativistic electromagnetic Particle-In-Cell codes are reviewed, as well as novel techniques that were introduced recently. Advances in the analysis and mitigation of the numerical Cherenkov instability are also presented with comparison between analytical theory and numerical experiments. The algorithmic and numerical analytic advances are expanding the range of applicability of the method in the ultra-relativistic regime in particular, where the numerical Cherenkov instability is the strongest without corrective measures.
Modeling relativistic soliton interactions in overdense plasmas: a perturbed nonlinear Schrödinger equation framework.
Siminos, E; Sánchez-Arriaga, G; Saxena, V; Kourakis, I
We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude.
A class of exact isotropic solutions of Einstein's equations and relativistic stellar models in general relativity
NASA Astrophysics Data System (ADS)
Murad, Mohammad Hassan; Pant, Neeraj
In this paper we have studied a particular class of exact solutions of Einstein's gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/ c 2 R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538-52, LMC X-4, SAX J1808.4-3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.
Superheavy Element Chemistry by Relativistic Density Functional Theory Electronic Structure Modeling
NASA Astrophysics Data System (ADS)
Zaitsevskii, A. V.; Polyaev, A. V.; Demidov, Yu. A.; Mosyagin, N. S.; Lomachuk, Yu. V.; Titov, A. V.
Two-component density functional theory in its non-collinear formulation combined with the accurate relativistic electronic structure model defined by shape-consistent small-core pseudopotentials (PP/RDFT) provides a robust basis of efficient computational schemes for predicting energetic and structural properties of complex polyatomic systems including superheavy elements (SHEs). Because of the exceptional role of thermochromatography in the experiments on the "chemical" identification of SHEs with atomic numbers Z ≥ 112, we focus on the description of the adsorption of single SHE atoms on the surfaces of solids through cluster modeling of adsorption complexes. In some cases our results differ significantly from those of previous theoretical studies. The results of systematic comparative studies on chemical bonding in simple molecules of binary compounds of SHEs and their nearest homologs with most common light elements, obtained at the PP/RDFT level and visualized through the "chemical graphs", provide the understanding of the general chemistry of SHEs which at present cannot be derived from the experimental data. These results are used to discuss the main trends in changing chemical properties of the elements in the given group of the periodic table and demonstrate the specificity of SHEs.
Semileptonic decays of Λb baryons in the relativistic quark model
NASA Astrophysics Data System (ADS)
Faustov, R. N.; Galkin, V. O.
Semileptonic Λb decays are investigated in the framework of the relativistic quark model based on the quasipotential approach and the quark-diquark picture of baryons. The decay form factors are expressed through the overlap integrals of the initial and final baryon wave functions. All calculations are done without employing nonrelativistic and heavy quark expansions. The momentum transfer dependence of the decay form factors is explicitly determined in the whole accessible kinematical range without any extrapolations or model assumptions. Both the heavy-to-heavy Λb→Λcℓνℓ and heavy-to-light Λb→p ℓνℓ decay branching fractions are calculated. The results agree within error bars with the experimental value of the branching fraction of the Λb→Λc+l-ν¯l decay. From the recent LHCb data on the ratio of the branching fractions of the heavy-to-light and heavy-to-heavy semileptonic Λb decays the ratio of the Cabibbo-Kobayashi-Maskawa matrix elements |Vu b|/|Vc b| is obtained. It is consistent with the corresponding ratio determined from the inclusive B meson decays.
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Competitive adsorption and ordered packing of counterions near highly charged surfaces: From mean-field theory to Monte Carlo simulations.
Wen, Jiayi; Zhou, Shenggao; Xu, Zhenli; Li, Bo
Competitive adsorption of counterions of multiple species to charged surfaces is studied by a size-effect-included mean-field theory and Monte Carlo (MC) simulations. The mean-field electrostatic free-energy functional of ionic concentrations, constrained by Poisson's equation, is numerically minimized by an augmented Lagrangian multiplier method. Unrestricted primitive models and canonical ensemble MC simulations with the Metropolis criterion are used to predict the ionic distributions around a charged surface. It is found that, for a low surface charge density, the adsorption of ions with a higher valence is preferable, agreeing with existing studies. For a highly charged surface, both the mean-field theory and the MC simulations demonstrate that the counterions bind tightly around the charged surface, resulting in a stratification of counterions of different species. The competition between mixed entropy and electrostatic energetics leads to a compromise that the ionic species with a higher valence-to-volume ratio has a larger probability to form the first layer of stratification. In particular, the MC simulations confirm the crucial role of ionic valence-to-volume ratios in the competitive adsorption to charged surfaces that had been previously predicted by the mean-field theory. The charge inversion for ionic systems with salt is predicted by the MC simulations but not by the mean-field theory. This work provides a better understanding of competitive adsorption of counterions to charged surfaces and calls for further studies on the ionic size effect with application to large-scale biomolecular modeling.
Magnetic material in mean-field dynamos driven by small scale helical flows
NASA Astrophysics Data System (ADS)
Giesecke, A.; Stefani, F.; Gerbeth, G.
We perform kinematic simulations of dynamo action driven by a helical small scale flow of a conducting fluid in order to deduce mean-field properties of the combined induction action of small scale eddies. We examine two different flow patterns in the style of the G O Roberts flow but with a mean vertical component and with internal fixtures that are modelled by regions with vanishing flow. These fixtures represent either rods that lie in the center of individual eddies, or internal dividing walls that provide a separation of the eddies from each other. The fixtures can be made of magnetic material with a relative permeability larger than one which can alter the dynamo behavior. The investigations are motivated by the widely unknown induction effects of the forced helical flow that is used in the core of liquid sodium cooled fast reactors, and from the key role of soft iron impellers in the von-Kármán-sodium dynamo. For both examined flow configurations the consideration of magnetic material within the fluid flow causes a reduction of the critical magnetic Reynolds number of up to 25%. The development of the growth-rate in the limit of the largest achievable permeabilities suggests no further significant reduction for even larger values of the permeability. In order to study the dynamo behavior of systems that consist of tens of thousands of helical cells we resort to the mean-field dynamo theory (Krause and Rädler 1980 Mean-field Magnetohydrodynamics and Dynamo Theory (Oxford: Pergamon)) in which the action of the small scale flow is parameterized in terms of an α- and β-effect. We compute the relevant elements of the α- and the β-tensor using the so called testfield method. We find a reasonable agreement between the fully resolved models and the corresponding mean-field models for wall or rod materials in the considered range 1\\leqslant {{\\mu }_{r}}\\leqslant 20. Our results may be used for the development of global large scale models with recirculation
The D-D-bar mesons matter in Walecka's mean field theory
Farias Freire, M. L. de; Rodrigues da Silva, R.
We study the D-D-bar mesons matter in the framework of {sigma} and {omega} meson exchange model using Walecka's mean field theory. We choose the equal number of D and anti-D meson then we get <{omega}{sup 0}> = 0 and the <{sigma}> field exhibits a critical temperature around 1.2 GeV. We investigate effective mass and pressure. We conclude that this matter is a gas and these results are not favorable for the existence of D-D-bar bound state.
Study of shape transitions in N{approx}90 isotopes with beyond mean field calculations
Rodriguez, Tomas R.; Egido, J. L.
We study the spherical to prolate-deformed shape transition in {sup 144-158}Sm and {sup 146-160}Gd isotopes with modern calculations beyond the mean field with the Gogny D1S force. We compare the results with the shape-phase transition predicted by the collective Hamiltonian model and with the experimental data. Our calculations do not support the existence of a first order phase transition in these isotopic chains in the viewpoint of the Bohr Hamiltonian neither the interpretation of the nuclei N = 90 as critical points.
A mean-field limit for a class of queueing networks
NASA Astrophysics Data System (ADS)
Baccelli, F.; Karpelevich, F. I.; Kelbert, M. Ya.; Puhalskii, A. A.; Rybko, A. N.; Suhov, Yu. M.
A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limit N → ∞ is discussed, where N is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.
Cluster Monte Carlo and numerical mean field analysis for the water liquid-liquid phase transition
NASA Astrophysics Data System (ADS)
Mazza, Marco G.; Stokely, Kevin; Strekalova, Elena G.; Stanley, H. Eugene; Franzese, Giancarlo
Using Wolff's cluster Monte Carlo simulations and numerical minimization within a mean field approach, we study the low temperature phase diagram of water, adopting a cell model that reproduces the known properties of water in its fluid phases. Both methods allow us to study the thermodynamic behavior of water at temperatures, where other numerical approaches - both Monte Carlo and molecular dynamics - are seriously hampered by the large increase of the correlation times. The cluster algorithm also allows us to emphasize that the liquid-liquid phase transition corresponds to the percolation transition of tetrahedrally ordered water molecules.
Outline of the concept of stable relativistic radiation sphere. A model of quasar?
NASA Astrophysics Data System (ADS)
Neslušan, L.
The new possibilities to construct the stable relativistic compact objects were opened by Ni in 2011, after his discovery of new solution of the Einstein field equations for the spherically symmetric distribution of matter. The solution occurs to be the super-class of the well-known Tolman-Oppenheimer-Volkoff solution published in 1939. In the presented work, we consider the equation of state for a radiation fluid and use the Ni's solution to construct the massive objects consisting of radiation. We describe their fundamental properties. Since there is no upper constraint of energy/mass of the Ni's object, the formally calculated gravitational mass (from gravitational effects) of these objects can be as high as observed for the super-massive compact objects in the centers of galaxies and even in the most massive quasars. In the solution by Ni, the gravitational acceleration is not linearly proportional to the energy concentrated in the object. Actually, the models indicate that the objects should be extremely luminous, as quasars. The most massive of them can have enough energy to emit the radiation with a quasar luminosity during the age of the universe. And, it is predicted that they must possess an extremely extended "corona" with the gravitational effects resembling those, which are assigned to a dark matter.
Modeling the Physics of Sliding Objects on Rotating Space Elevators and Other Non-relativistic Strings
NASA Astrophysics Data System (ADS)
Golubovic, Leonardo; Knudsen, Steven
We consider general problem of modeling the dynamics of objects sliding on moving strings. We introduce a powerful computational algorithm that can be used to investigate the dynamics of objects sliding along non-relativistic strings. We use the algorithm to numerically explore fundamental physics of sliding climbers on a unique class of dynamical systems, Rotating Space Elevators (RSE). Objects sliding along RSE strings do not require internal engines or propulsion to be transported from the Earth's surface into outer space. By extensive numerical simulations, we find that sliding climbers may display interesting non-linear dynamics exhibiting both quasi-periodic and chaotic states of motion. While our main interest in this study is in the climber dynamics on RSEs, our results for the dynamics of sliding object are of more general interest. In particular, we designed tools capable of dealing with strongly nonlinear phenomena involving moving strings of any kind, such as the chaotic dynamics of sliding climbers observed in our simulations.
Electroexcitation of the Δ(1232)32+ and Δ(1600)32+ in a light-front relativistic quark model
Aznauryan, Inna G.; Burkert, Volker D.
Here, the magnetic-dipole form factor and the ratios REM and RSM for the γ* N → Δ(1232)3/2+ transition are predicted within light-front relativistic quark model up to photon virtuality Q2=12 GeV2. Furthermore, we predict the helicity amplitudes of the γ* N → Δ(1600)3/2+ transition assuming the Δ(1600)3/2+ is the first radial excitation of the ground state Delta(1232)3/2+.
relline: Relativistic line profiles calculation
NASA Astrophysics Data System (ADS)
Dauser, Thomas
relline calculates relativistic line profiles; it is compatible with the common X-ray data analysis software XSPEC (ascl:9910.005) and ISIS (ascl:1302.002). The two basic forms are an additive line model (RELLINE) and a convolution model to calculate relativistic smearing (RELCONV).
Point form relativistic quantum mechanics and relativistic SU(6)
NASA Technical Reports Server (NTRS)
Klink, W. H.
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
Finite-size critical scaling in Ising spin glasses in the mean-field regime
NASA Astrophysics Data System (ADS)
Aspelmeier, T.; Katzgraber, Helmut G.; Larson, Derek; Moore, M. A.; Wittmann, Matthew; Yeo, Joonhyun
We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.
GENERAL: Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure
NASA Astrophysics Data System (ADS)
Yang, Xu-Hua; Sun, Bao; Wang, Bo; Sun, You-Xian
Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks (BTNs) evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper.
Phase-space moment-equation model of highly relativistic electron-beams in plasma-wakefield accelerators
Robson, R.E.; Mehrling, T.; Osterhoff, J.
We formulate a new procedure for modelling the transverse dynamics of relativistic electron beams with significant energy spread when injected into plasma-based accelerators operated in the blow-out regime. Quantities of physical interest, such as the emittance, are furnished directly from solution of phase space moment equations formed from the relativistic Vlasov equation. The moment equations are closed by an Ansatz, and solved analytically for prescribed wakefields. The accuracy of the analytic formulas is established by benchmarking against the results of a semi-analytic/numerical procedure which is described within the scope of this work, and results from a simulation with the 3D quasi-static PIC code HiPACE.
Review of modeling of losses and sources of relativistic electrons in the outer radiation belt I: Radial transport
NASA Astrophysics Data System (ADS)
Shprits, Yuri Y.; Elkington, Scot R.; Meredith, Nigel P.; Subbotin, Dmitriy A.
In this paper, we focus on the modeling of radial transport in the Earth's outer radiation belt. A historical overview of the first observations of the radiation belts is presented, followed by a brief description of radial diffusion. We describe how resonant interactions with poloidal and toroidal components of the ULF waves can change the electron's energy and provide radial displacements. We also present radial diffusion and guiding center simulations that show the importance of radial transport in redistributing relativistic electron fluxes and also in accelerating and decelerating radiation belt electrons. We conclude by presenting guiding center simulations of the coupled particle tracing and magnetohydrodynamic (MHD) codes and by discussing the origin of relativistic electrons at geosynchronous orbit. Local acceleration and losses and 3D simulations of the dynamics of the radiation belt fluxes are discussed in the companion paper [Shprits, Y.Y., Subbotin, D.A., Meredith, N.P., Elkington, S.R., 2008. Review of modeling of losses and sources of relativistic electrons in the outer radiation belt II: Local acceleration and loss. Journal of Atmospheric and Solar-Terrestrial Physics, this issue. doi:10.1016/j.jastp.2008.06.014].
Non-mean-field theory of anomalously large double layer capacitance.
Loth, M S; Skinner, Brian; Shklovskii, B I
Mean-field theories claim that the capacitance of the double layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double layer capacitor is substantially smaller. We propose an alternate non-mean-field theory of the ionic double layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our "one-component plasma" model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudocapacitance.
Mean-field theory for pedestrian outflow through an exit
NASA Astrophysics Data System (ADS)
Yanagisawa, Daichi; Nishinari, Katsuhiro
The average pedestrian flow through an exit is one of the most important indices in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model using cellular automata, is extended by taking into account realistic behavior of pedestrians around the exit. The model is studied by both numerical simulations and cluster analysis to obtain a theoretical expression for the average pedestrian flow through the exit. It is found quantitatively that the effects of exit door width, the wall, and the pedestrian mood of competition or cooperation significantly influence the average flow. The results show that there is a suitable width and position of the exit according to the pedestrians' mood.
Phase transitions of nuclear matter beyond mean field theory
Tran Huu Phat; Nguyen Tuan Anh; Nguyen Van Long; Le Viet Hoa
The Cornwall-Jackiw-Tomboulis (CJT) effective action approach is applied to study the phase transition of nuclear matter modeled by the four-nucleon interaction. It is shown that in the Hartree-Fock approximation (HFA) a first-order phase transition takes place at low temperature, whereas the phase transition is of second order at higher temperature.
Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations.
Vrettas, Michail D; Opper, Manfred; Cornford, Dan
This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.
Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models
NASA Astrophysics Data System (ADS)
Kawazura, Yohei; Miloshevich, George; Morrison, Philip J.
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to Comisso et al., Phys. Rev. Lett. 113, 045001 (2014) for the electron-positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked contrast to nonrelativistic Hall MHD that does satisfy the frozen-in condition. We also find the violation of the frozen-in condition is accompanied by freezing-in of an alternative flux determined by a generalized vector potential. Finally, we derive a more general 3 + 1 Poisson bracket for nonrelativistic extended MHD, one that does not assume smallness of the electron ion mass ratio.
A Simple Relativistic Bohr Atom
ERIC Educational Resources Information Center
Terzis, Andreas F.
A simple concise relativistic modification of the standard Bohr model for hydrogen-like atoms with circular orbits is presented. As the derivation requires basic knowledge of classical and relativistic mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics. In addition, it can be shown in a class that…
Mean field spin glasses treated with PDE techniques
NASA Astrophysics Data System (ADS)
Barra, Adriano; Del Ferraro, Gino; Tantari, Daniele
Following an original idea of Guerra, in these notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of the model (e.g. solving for the free energy) to well-known partial differential equation (PDE) problems (in suitable spaces). The plan is then to solve the related PDE using techniques involved in their native field and lastly bringing back the solution in the proper statistical mechanics framework. Within this strand, after a streamlined test-case on the Curie-Weiss model to highlight the methods more than the physics behind, we solve the SK both at the replica symmetric and at the 1-RSB level, obtaining the correct expression for the free energy via an analogy to a Fourier equation and for the self-consistencies with an analogy to a Burger equation, whose shock wave develops exactly at critical noise level (triggering the phase transition). Our approach, beyond acting as a new alternative method (with respect to the standard routes) for tackling the complexity of spin glasses, links symmetries in PDE theory with constraints in statistical mechanics and, as a novel result from the theoretical physics perspective, we obtain a new class of polynomial identities (namely of Aizenman-Contucci type, but merged within the Guerra's broken replica measures), whose interest lies in understanding, via the recent Panchenko breakthroughs, how to force the overlap organization to the ultrametric tree predicted by Parisi.
From effective field theories to effective density functionals in and beyond the mean field
NASA Astrophysics Data System (ADS)
Grasso, M.; Lacroix, D.; van Kolck, U.
Since the 1975 Nobel Prize in Physics, nuclear theory has evolved along two main directions. On the one hand, the energy-density functional (EDF) theory was established, which presently encompasses (by enlarging the EDF framework) all the mean-field and beyond-mean-field theories based on energy functionals produced by effective phenomenological interactions. Highly sophisticated structure and reaction models are currently available for the treatment of medium-mass and heavy nuclei. On the other hand, effective field theories (EFTs) have rendered possible the formulation of QCD as a low-energy hadronic theory. Ab initio methods have recently achieved remarkable success in the application of EFT or EFT-inspired potentials to structure analyses of light nuclei. Different but complementary competences have been developed during the past few decades in the EDF and EFT communities. Bridges and connections have in some cases been identified and constructed. We review here some of the developments that have been performed within the EDF theory and the EFT during recent years, with some emphasis on analogies and connections that may one day provide a unified picture of the two theories. Illustrations are given for infinite matter and finite nuclei.
Atomically flat superconducting nanofilms: multiband properties and mean-field theory
NASA Astrophysics Data System (ADS)
Shanenko, A. A.; Aguiar, J. Albino; Vagov, A.; Croitoru, M. D.; Milošević, M. V.
Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Pérot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.
Quantum de Finetti theorems and mean-field theory from quantum phase space representations
NASA Astrophysics Data System (ADS)
Trimborn, F.; Werner, R. F.; Witthaut, D.
We introduce the number-conserving quantum phase space description as a versatile tool to address fundamental aspects of quantum many-body systems. Using phase space methods we prove two alternative versions of the quantum de Finetti theorem for finite-dimensional bosonic quantum systems, which states that a reduced density matrix of a many-body quantum state can be approximated by a convex combination of product states where the error is proportional to the inverse particle number. This theorem provides a formal justification for the mean-field description of many-body quantum systems, as it shows that quantum correlations can be neglected for the calculation of few-body observables when the particle number is large. Furthermore we discuss methods to derive the exact evolution equations for quantum phase space distribution functions as well as upper and lower bounds for the ground state energy. As an important example, we consider the Bose-Hubbard model and show that the mean-field dynamics is given by a classical phase space flow equivalent to the discrete Gross-Pitaevskii equation.
Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field.
Vladimirski, Boris B; Tabak, Joël; O'Donovan, Michael J; Rinzel, John
Many developing neural systems exhibit spontaneous activity (O'Donovan, Curr Opin Neurobiol 9:94-104, 1999; Feller, Neuron 22:653-656, 1999) characterized by episodes of discharge (active phases) when many cells are firing, separated by silent phases during which few cells fire. Various models exhibit features of episodic behavior by means of recurrent excitation for supporting an episode and slow activity-dependent depression for terminating one. The basic mechanism has been analyzed using mean-field, firing-rate models. Firing-rate models are typically formulated ad hoc, not derived from a spiking network description, and the effects of substantial heterogeneity amongst the units are not usually considered. Here we develop an excitatory network of spiking neurons (N-cell model) with slow synaptic depression to model episodic rhythmogenesis. This N-cell model displays episodic behavior over a range of heterogeneity in bias currents. Important features of the episodic behavior include orderly recruitment of individual cells during silent phases and existence of a dynamical process whereby a small critical subpopulation of intermediate excitability conveys synaptic drive from active to silent cells. We also derive a general self-consistency equation for synaptic drive that includes cell heterogeneity explicitly. We use this mean-field description to expose the dynamical bistability that underlies episodic behavior in the heterogeneous network. In a systematic numerical study we find that the robustness of the episodic behavior improves with increasing heterogeneity. Furthermore, the heterogeneity of depression variables (imparted by the heterogeneity in cellular firing thresholds) plays an important role in this improvement: it renders the network episodic behavior more robust to variations in excitability than if depression is uniformized. We also investigate the effects of noise vs. heterogeneity on the robustness of episodic behavior, especially important for the
Mean field theory of directed polymers with random complex weights
NASA Astrophysics Data System (ADS)
Derrida, B.; Evans, M. R.; Speer, E. R.
We show that for the problem of directed polymers on a tree with i.i.d. random complex weights on each bond, three possible phases can exist; the phase of a particular system is determined by the distribution ρ of the random weights. For each of these three phases, we give the expression of the free energy per unit length in the limit of infinitely long polymers. Our proofs require several hypotheses on the distribution ρ, most importantly, that the amplitude and the phase of each complex weight be statistically independent. The main steps of our proofs use bounds on noninteger moments of the partition function and self averaging properties of the free energy. We illustrate our results by some examples and discuss possible generalizations to a larger class of distributions, to Random Energy Models, and to the finite dimensional case. We note that our results are not in agreement with the predictions of a recent replica approach to a similar problem.
Mean-Field Theory of Intra-Molecular Charge Ordering in (TTM--TTP)I3
NASA Astrophysics Data System (ADS)
Omori, Yukiko; Tsuchiizu, Masahisa; Suzumura, Yoshikazu
We examine an intra-molecular charge-ordered (ICO) state in the multi-orbital molecular compound (TTM--TTP)I3 on the basis of an effective two-orbital model derived from ab initio calculations. Representing the model in terms of the fragment molecular-orbital (MO) picture, the ICO state is described as the charge disproportionation on the left and right fragment MOs. By applying the mean-field theory, the phase diagram of the ground state is obtained as a function of the inter-molecular Coulomb repulsion and the intra-molecular transfer integral. The ICO state is stabilized by large inter-fragment Coulomb interactions, and the small intra-molecular transfer energy between two fragment MOs. Furthermore, we examine the finite-temperature phase diagram. The relevance to the experimental observations in the molecular compound of (TTM--TTP)I3 is also discussed.
β-decay of magic nuclei: Beyond mean-field description
Niu, Yifei; Niu, Zhongming; Colò, Gianluca; Vigezzi, Enrico
Nuclear β-decay plays an important role not only in nuclear physics but also in astrophysics. The widely used self-consistent Random Phase Approximation (RPA) models tend to overestimate the half-lives of magic nuclei. To overcome this problem, we go beyond the mean-field description and include the effects of particle-vibration coupling (PVC) on top of the RPA model. The β-decay half-lives of {sup 34}Si, {sup 68}Ni, {sup 78}Ni, and {sup 132}Sn are studied within this approach in the case of the Skyrme interaction SkM*. It is found that the low-lying Gamow-Teller (GT) strength is shifted downwards with the inclusion of the PVC effect, and as a consequence, the half-lives are reduced due to the increase of the phase space available for β-decay, which leads to a good agreement between theoretical and experimental lifetimes.
Dynamical Mean-Field Equations for a Neural Network with Spike Timing Dependent Plasticity
NASA Astrophysics Data System (ADS)
Mayer, Jörg; Ngo, Hong-Viet V.; Schuster, Heinz Georg
We study the discrete dynamics of a fully connected network of threshold elements interacting via dynamically evolving synapses displaying spike timing dependent plasticity. Dynamical mean-field equations, which become exact in the thermodynamical limit, are derived to study the behavior of the system driven with uncorrelated and correlated Gaussian noise input. We use correlated noise to verify that our model gives account to the fact that correlated noise provides stronger drive for synaptic modification. Further we find that stochastic independent input leads to a noise dependent transition to the coherent state where all neurons fire together, most notably there exists an optimal noise level for the enhancement of synaptic potentiation in our model.
Mean-field state population study for iron-based superconductors
NASA Astrophysics Data System (ADS)
Wang, Zhigang; Fu, Zhen-Guo; Zheng, Fa-Wei; Zhang, Ping
The occupation number distribution in momentum space are theoretically studied within a two-orbital model, which can be unified describing the low-energy physics of the iron pnictides and iron chalcogenides. The mean-field approximation of Hubbard interaction is employed. By tuning the hopping parameters, the difference between the iron pnictides and iron chalcogenides in their occupation number distribution behavior can be clearly observed. The results show that when the pairing interaction tends to zero, the occupation number n (k) ≈ 0 at Γ point for iron chalcogenides while n (k) ≈ 2 at Γ point for iron pnictides. By increasing the strength of the pairing interaction to a large value, the change of n (k) at Γ point for iron chalcogenides (pnictides) is remarkable (unremarkable). In addition, we find that the effect of the nearest-neighbor coupling between the two layers, contained in the S4 model [Hu and Hao, (2012) [33
Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach
Petrovici, A.; Andrei, O.
Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.
Generalized mean-field theory for Ising spins in small world networks.
Meilikhov, E Z; Farzetdinova, R M
A generalization of mean-field theory for random systems is described. The results of that analytic model could be reconciled with the results of numerical calculations of the Curie temperature for a system of Ising spins in small world (SW) networks by introducing the effective interaction energy associated with long-range links which exceeds the real energy of spin interaction. Such a model describes qualitatively well the increasing Curie temperature T(C) with the growth of the long-range links fraction p in the two-dimensional SW system with fixed coordination number. On the basis of simple physical considerations, concentration dependences T(C)(p) are found for SW systems of different dimensions.
The glass crossover from mean-field Spin-Glasses to supercooled liquids
NASA Astrophysics Data System (ADS)
Rizzo, Tommaso
Stochastic-Beta-Relaxation provides a characterisation of the glass crossover in discontinuous Spin-Glasses and supercoooled liquid. Notably it can be derived through a rigorous computation from a dynamical Landau theory. In this paper, I will discuss the precise meaning of this connection in a language that does not require familiarity with statistical field theory. I will discuss finite-size corrections in mean-field Spin-Glass models and loop corrections in finite-dimensional models that are both described by the dynamical Landau theory considered. Then I will argue that the same Landau theory can be associated to supercooled liquid described by Mode-Coupling Theory invoking a physical principle of time-scale invariance.
How deep cells feel: Mean-field Computations and Experiments
NASA Astrophysics Data System (ADS)
Buxboim, Amnon; Sen, Shamik; Discher, Dennis E.
Most cells in solid tissues exert contractile forces that mechanically couple them to elastic surroundings and that significantly influence cell adhesion, cytoskeletal organization and differentiation. However, strains within the depths of matrices are often unclear and are likely relevant to thin matrices, such as basement membranes, relative to cell size as well as to defining how far cells can ``feel.'' We present experimental results for cell spreading on thin, ligand- coated gels and for prestress in stem cells in relation to gel stiffness. Matrix thickness affects cell spread area, focal adhesions and cytoskeleton organization in stem cells, which we will compare to differentiated cells. We introduce a finite element computation to estimate the elastostatic deformations within the matrix on which a cell is placed. Interfacial strains between cell and matrix show large deviations only when soft matrices are a fraction of cell dimensions, proving consistent with experiments. 3-D cell morphologies that model stem cell-derived neurons, myoblasts, and osteoblasts show that a cylinder-shaped myoblast induces the highest strains, consistent with the prominent contractility of muscle. Groups of such cells show a weak crosstalk via matrix strains only when cells are much closer than a cell-width. Cells thus feel on length scales closer to that of adhesions than on cellular scales.
Mean-field analysis of an inductive reasoning game: application to influenza vaccination.
Breban, Romulus; Vardavas, Raffaele; Blower, Sally
Recently we have introduced an inductive reasoning game of voluntary yearly vaccination to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. Here, we analyze our model to describe the dynamics of the collective yearly vaccination uptake. We discuss the mean-field equations of our model and first order effects of fluctuations. We explain why our model predicts that severe epidemics are periodically expected even without the introduction of pandemic strains. We find that fluctuations in the collective yearly vaccination uptake induce severe epidemics with an expected periodicity that depends on the number of independent decision makers in the population. The mean-field dynamics also reveal that there are conditions for which the dynamics become robust to the fluctuations. However, the transition between fluctuation-sensitive and fluctuation-robust dynamics occurs for biologically implausible parameters. We also analyze our model when incentive-based vaccination programs are offered. When a family-based incentive is offered, the expected periodicity of severe epidemics is increased. This results from the fact that the number of independent decision makers is reduced, increasing the effect of the fluctuations. However, incentives based on the number of years of prepayment of vaccination may yield fluctuation-robust dynamics where severe epidemics are prevented. In this case, depending on prepayment, the transition between fluctuation-sensitive and fluctuation-robust dynamics may occur for biologically plausible parameters. Our analysis provides a practical method for identifying how many years of free vaccination should be provided in order to successfully ameliorate influenza epidemics.
Mean-field analysis of an inductive reasoning game: Application to influenza vaccination
NASA Astrophysics Data System (ADS)
Breban, Romulus; Vardavas, Raffaele; Blower, Sally
Recently we have introduced an inductive reasoning game of voluntary yearly vaccination to establish whether or not a population of individuals acting in their own self-interest would be able to prevent influenza epidemics. Here, we analyze our model to describe the dynamics of the collective yearly vaccination uptake. We discuss the mean-field equations of our model and first order effects of fluctuations. We explain why our model predicts that severe epidemics are periodically expected even without the introduction of pandemic strains. We find that fluctuations in the collective yearly vaccination uptake induce severe epidemics with an expected periodicity that depends on the number of independent decision makers in the population. The mean-field dynamics also reveal that there are conditions for which the dynamics become robust to the fluctuations. However, the transition between fluctuation-sensitive and fluctuation-robust dynamics occurs for biologically implausible parameters. We also analyze our model when incentive-based vaccination programs are offered. When a family-based incentive is offered, the expected periodicity of severe epidemics is increased. This results from the fact that the number of independent decision makers is reduced, increasing the effect of the fluctuations. However, incentives based on the number of years of prepayment of vaccination may yield fluctuation-robust dynamics where severe epidemics are prevented. In this case, depending on prepayment, the transition between fluctuation-sensitive and fluctuation-robust dynamics may occur for biologically plausible parameters. Our analysis provides a practical method for identifying how many years of free vaccination should be provided in order to successfully ameliorate influenza epidemics.
Biopolymers under large external forces and mean-field RNA virus evolutionary dynamics
NASA Astrophysics Data System (ADS)
Ahsan, Syed Amir
The modeling of the mechanical response of single-molecules of DNA and RNA under large external forces through statistical mechanical methods is central to this thesis with a small portion devoted to modeling the evolutionary dynamics of positive-sense single-stranded RNA viruses. In order to develop and test models of biopolymer mechanics and illuminate the mechanisms underlying biological processes where biopolymers undergo changes in energy on the order of the thermal energy, , entails measuring forces and lengths on the scale of piconewtons (pN) and nanometers (nm), respectively. A capacity achieved in the past two decades at the single-molecule level through the development of micromanipulation techniques such as magnetic and optical tweezers, atomic force microscopy, coupled with advances in micro- and nanofabrication. The statistical mechanical models of biopolymers developed in this dissertation are dependent upon and the outcome of these advancements and resulting experiments. The dissertation begins in chapter 1 with an introduction to the structure and thermodynamics of DNA and RNA, highlighting the importance and effectiveness of simple, two-state models in their description as a prelude to the emergence of two-state models in the research manuscripts. In chapter 2 the standard models of the elasticity of polymers and of a polymer gel are reviewed, characterizing the continuum and mean-field models, including the scaling behavior of DNA in confined spaces. The research manuscript presented in the last section of chapter 2 (section 2.5), subsequent to a review of a Flory gel and in contrast to it, is a model of the elasticity of RNA as a gel, with viral RNA illustrating an instance of such a network, and shown to exhibit anomalous elastic behavior, a negative Poisson ratio, and capable of facilitating viral RNA encapsidation with further context provided in section 5.1. In chapter 3 the experimental methods and behavior of DNA and RNA under mechanical
Weiss mean-field approximation for multicomponent stochastic spatially extended systems.
Kurushina, Svetlana E; Maximov, Valerii V; Romanovskii, Yurii M
We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system, which describes a well-known model of autocatalytic chemical reaction (brusselator) with spatially correlated multiplicative noise, and to study the evolution of probability density and statistical characteristics of the system in the process of spatial pattern formation. We propose the finite-difference method for the numerical solving of a general class of multivariate nonlinear self-consistent time-dependent Fokker-Planck equations. We illustrate the accuracy and reliability of the method by applying it to an exactly solvable nonlinear Fokker-Planck equation (NFPE) for the Shimizu-Yamada model [Prog. Theor. Phys. 47, 350 (1972)] and nonlinear Fokker-Planck equation [Desai and Zwanzig, J. Stat. Phys. 19, 1 (1978)] obtained for a nonlinear stochastic mean-field model introduced by Kometani and Shimizu [J. Stat. Phys. 13, 473 (1975)]. Taking the problems indicated above as an example, the accuracy of the method is compared with the accuracy of Hermite distributed approximating functional method [Zhang et al., Phys. Rev. E 56, 1197 (1997)]. Numerical study of the NFPE solutions for a stochastic brusselator shows that in the region of Turing bifurcation several types of solutions exist if noise intensity increases: unimodal solution, transient bimodality, and an interesting solution which involves multiple "repumping" of probability density through bimodality. Additionally, we study the behavior of the order parameter of the system under consideration and show that the second type of solution arises in the supercritical region if noise intensity values are close to the values appropriate for the transition from bimodal stationary probability density for the order parameter to the unimodal one.
Convergence of the self-energy in a relativistic chiral quark model: excited nucleon and Δ sector
NASA Astrophysics Data System (ADS)
Tursunov, E. M.
A convergence of the valence quark self-energies in the 1S, 2S, 1P1/2, 1P3/2 orbits induced by pion- and gluon-field configurations is shown in the frame of a relativistic chiral quark model. It is shown that in order to reach a convergence, one needs to include the contribution of the intermediate quark and anti-quark states with the total momentum up to j = 25/2. It is argued that a restriction to the lowest mode when estimating the self-energy is not a good approximation.
Exploring center strings in S U (2 ) and S U (3 ) relativistic Yang-Mills-Higgs models
NASA Astrophysics Data System (ADS)
Oxman, L. E.; Vercauteren, D.
We develop numerical tools and apply them to solve the relativistic Yang-Mills-Higgs equations in a model where the S U (N ) symmetry is spontaneously broken to its center. In S U (2 ) and S U (3 ), we obtain the different field profiles for infinite and finite center strings, with end points at external monopole sources. Exploration of parameter space permits the detection of a region where the equations get Abelianized. Finally, a general parametrization of the color structure of S U (2 ) fields leads us to a reference point where an Abelian-like Bogomol'nyi-Prasad-Sommereld (BPS) bound is reconciled with N -ality.
Relativistically-Compressed Exploding White-Dwarf Model for Sgr A East
Dearborn, D P; Wilson, J R; Mathews, G J
Recently, a new mechanism for Type I supernovae has been proposed whereby relativistic terms enhance the self gravity of a carbon-oxygen white dwarf as it passes near a black hole. It was suggested but not confirmed that this relativistic compression can cause the central density to exceed the threshold for pycnonuclear reactions so that a thermonuclear runaway ensues. Here, we present numerical studies of such relativistically induced explosions of white dwarfs and red giant cores of various mass (particularly a typical 0.6 M{sub {circle_dot}} white dwarf) as they pass near a 3.7 x 10{sup 6} black hole like Sgr A* in the Galactic center. We confirm by hydrodynamic thermonuclear burn simulations in three spatial dimensions that white dwarfs and red giant cores do indeed ignite and explode. In fact they seem to explode even farther from the black hole than earlier estimates due to increased internal temperatures from adiabatic heating as the stars are compressed. We find that the compression is sufficiently fast that red giant cores, or young (< 10{sup 8} yr) white dwarfs can even be heated to thermonuclear rather than pychnonuclear ignition. We propose that such an event might explain the observed ''mixed-morphology'' Sgr A East supernova remnant in the Galactic center.
Probing relevant ingredients in mean-field approaches for the athermal rheology of yield stress materials.
Puosi, Francesco; Olivier, Julien; Martens, Kirsten
Although the notion of mechanical noise is expected to play a key role in the non-linear rheology of athermally sheared amorphous systems, its characterization has so far remained elusive. Here, we show using molecular dynamic simulations that in spite of the presence of strong spatio-temporal correlations in the system, the local stress exhibits normal diffusion under the effect of the mechanical noise in the finite driving regime. The diffusion constant appears to be proportional to the mean plastic activity. Our data suggests that the corresponding proportionality constant is density independent, and can be directly related to the specific form of the rheological flow curve, pointing the way to a generic way of modeling mechanical noise in mean-field equations.
Predicting the mean fields of compressible turbulent boundary layer via a symmetry approach
NASA Astrophysics Data System (ADS)
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su
A symmetry approach for canonical wall turbulence is extended to develop mean-field predictions for compressible turbulent boundary layer (CTBL). A stress length and a weighted heat flux length are identified to obey the multilayer dilation symmetry of canonical flows, giving rise to predictions of the mean velocity and temperature profiles for a range of Reynolds number (Re), Mach number (Ma) and wall temperature (Tw). Also predicted are the streamwise developments of the shape factor, the boundary layer edge velocity and the boundary layer thicknesses, etc. Only three parameters are involved in the predictions, which have sound physics and organized behaviors with respect to the Re, Ma and Tw effects. The predictions are extensively validated by direct numerical simulation and experimental data, showing better accuracies than the previous theories. The results provide new quantifications that can be used to assess computations, measurements and turbulence models of CTBL, as well as to provide new insights for the CTBL physics.
The role of the Hall current in mean-field dynamo theory
NASA Astrophysics Data System (ADS)
Bhattacharjee, Amitava; Lingam, Manasvi
It is now well established that the Hall current plays a significant role in astrophysical environments. Hence, the role of the Hall term in classical mean-field dynamo theory is investigated. The standard alpha coefficient is modified, and shown to vanish only when a specific double Beltrami state (an outcome of certain Hall MHD relaxation theories) is attained. The dynamics of alpha quenching is also elaborated, and shown to exhibit both similarities and dissimilarities with its resistive MHD counterpart. A noteworthy and unusual feature of this analysis is the emergence of a turbulent resistivity that is not necessarily positive-definite. It implies that, even in the absence of shear and rotation, Hall effects may enable the growth of large-scale magnetic fields. Connections with the Hall MRI dynamo are also briefly discussed via a heuristic model. DOE Grant No. DE-AC02- 09CH-11466 and NSF Grant No. AGS-1338944.
Interacting motile agents: taking a mean-field approach beyond monomers and nearest-neighbor steps.
Penington, Catherine J; Hughes, Barry D; Landman, Kerry A
We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.
Compression induced phase transition of nematic brush: A mean-field theory study
Tang, Jiuzhou; Zhang, Xinghua; Yan, Dadong
Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.
Compression induced phase transition of nematic brush: A mean-field theory study
NASA Astrophysics Data System (ADS)
Tang, Jiuzhou; Zhang, Xinghua; Yan, Dadong
Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.
Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.
Chou, Yen-Liang; Ihle, Thomas
Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.
Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
NASA Astrophysics Data System (ADS)
Chou, Yen-Liang; Ihle, Thomas
Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013), 10.1103/PhysRevE.88.052309] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N -particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8 , followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.
Zero-Temperature, Mean-Field Theory of Atomic Bose-Einstein Condensates
Edwards, Mark; Dodd, R. J.; Clark, Charles W.; Burnett, K.
We review the application of zero-temperature, mean-field theory to current experimental atomic Bose-Einstein condensates. We assess the validity of the approximations made by comparing the mean-field results with a variety of experimental data. PMID:27805108
Tetrahedral shapes of neutron-rich Zr isotopes from a multidimensionally constrained relativistic Hartree-Bogoliubov model
NASA Astrophysics Data System (ADS)
Zhao, Jie; Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
We develop a multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model in which the pairing correlations are taken into account by making the Bogoliubov transformation. In this model, the nuclear shape is assumed to be invariant under the reversion of x and y axes; i.e., the intrinsic symmetry group is V4 and all shape degrees of freedom βλ μ with even μ are included self-consistently. The RHB equation is solved in an axially deformed harmonic oscillator basis. A separable pairing force of finite range is adopted in the MDC-RHB model. The potential energy curves of neutron-rich even-even Zr isotopes are calculated with relativistic functionals DD-PC1 and PC-PK1 and possible tetrahedral shapes in the ground and isomeric states are investigated. The ground state shape of 110Zr is predicted to be tetrahedral with both functionals and so is that of 112Zr with the functional DD-PC1. The tetrahedral ground states are caused by large energy gaps around Z =40 and N =70 when β32 deformation is included. Although the inclusion of the β30 deformation can also reduce the energy around β20=0 and lead to minima with pear-like shapes for nuclei around 110Zr, these minima are unstable due to their shallowness.
Mean-field interactions between nucleic-acid-base dipoles can drive the formation of the double helix
He, Yi; Maciejczyk, Maciej; Ołdziej, Stanisław; Scheraga, Harold A.; Liwo, Adam
A proposed coarse-grained model of nucleic acids demonstrates that average interactions between base dipoles, together with chain connectivity and excluded-volume interactions, are sufficient to form double-helical structures of DNA and RNA molecules. Additionally, local interactions determine helix handedness and direction of strand packing. This result, and earlier research on reduced protein models, suggest that mean-field multipole-multipole interactions are the principal factors responsible for the formation of regular structure of biomolecules. PMID:23496746
Towards the island of stability with relativistic energy density functionals
Prassa, V.; Niksic, T.; Lalazissis, G. A.; Vretenar, D.
Relativistic energy density functionals (REDF) provide a complete and accurate, global description of nuclear structure phenomena. Modern semi-empirical functionals, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, are applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison to empirical masses, quadrupole deformations, and energy barriers of actinide nuclei. The model is used in a self-consistent mean-field calculation of spherical, axial and triaxial shapes of superheavy nuclei, alpha-decay energies and lifetimes. The effect of explicit treatment of collective correlations is analyzed in calculations that consistently use a collective Hamiltonian model based on REDFs.
Allen, M.A.; Azuma, O.; Callin, R.S.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Fowkes, W.R.; Herrmannsfeldt, W.B.; Hoag, H.A.; Koontz, R.F.
Experimental work is underway by a SLAC-LLNL-LBL collaboration to investigate the feasibility of using relativistic klystrons as a power source for future high gradient accelerators. Two different relativistic klystron configurations have been built and tested to date: a high grain multicavity klystron at 11.4 GHz and a low gain two cavity subharmonic buncher driven at 5.7 GHz. In both configurations power is extracted at 11.4 GHz. In order to understand the basic physics issues involved in extracting RF from a high power beam, we have used both a single resonant cavity and a multi-cell traveling wave structure for energy extraction. We have learned how to overcome our previously reported problem of high power RF pulse shortening, and have achieved peak RF power levels of 170 MW with the RF pulse of the same duration as the beam current pulse. 6 refs., 3 figs., 3 tabs.
NASA Astrophysics Data System (ADS)
Flury, J.
Quantum metrology enables new applications in geodesy, including relativistic geodesy. The recent progress in optical atomic clocks and in long-distance frequency transfer by optical fiber together pave the way for using measurements of the gravitational frequency redshift for geodesy. The remote comparison of frequencies generated by calibrated clocks will allow for a purely relativistic determination of differences in gravitational potential and height between stations on Earth surface (chronometric leveling). The long-term perspective is to tie potential and height differences to atomic standards in order to overcome the weaknesses and inhomogeneity of height systems determined by classical spirit leveling. Complementarily, gravity measurements with atom interferometric setups, and satellite gravimetry with space borne laser interferometers allow for new sensitivities in the measurement of the Earth's gravity field.
NASA Astrophysics Data System (ADS)
Jones, Bernard J. T.; Markovic, Dragoljub
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Theory and modeling of a relativistic klystron amplifier with high space charge for microsecond applications
Carlsten, B.E.; Fazio, M.V.; Faehl, R.J.; Kwan, T.J.; Rickel, D.G.; Stringfield, R.M.
We discuss basic Relativistic Klystron Amplifier physics. We show that in the intense space-charge regime the maximum power extraction does not coincide with the maximum harmonic bunching. In addition, we show that as the beam is bunched, the additional power stored in the Coulomb fields does not add significantly to the overall power extraction. Because of these effects, the power extraction at 1.3 GHz for a 500 kV, 5 kA beam with reasonable beam-to-wall spacing is limited to around 35%. 3 refs., 17 figs.
Exact mean-field theory of ionic solutions: non-Debye screening
NASA Astrophysics Data System (ADS)
Varela, Luis M.; García, Manuel; Mosquera, Víctor
The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hückel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory
Validity of the relativistic phase shift model for the extrinsic spin Hall effect in dilute metal alloys.
Johansson, A; Herschbach, C; Fedorov, D V; Gradhand, M; Mertig, I
Recently, a generalized relativistic phase shift model was proposed (Fedorovet al 2013 Phys. Rev. B 88 085116) for the description of the skew-scattering contribution to the spin Hall effect caused by impurities. Here, we inspect this model by means of a systematic comparison with the results of first-principles calculations performed for several metallic host systems with different substitutional impurities. It is found that for its proper application, the differences between impurity and host phase shifts should be used as input parameters. Generally, the model provides good qualitative agreement with ab initio results for hosts with a free-electron-like Fermi surface and a relatively weak spin-orbit coupling, but fails otherwise.
Corona, Jet, and Relativistic Line Models for Suzaku/RXTE/Chandra-HETG Observations of the Cygnus X-1 Hard State
NASA Astrophysics Data System (ADS)
Nowak, Michael A.; Hanke, Manfred; Trowbridge, Sarah N.; Markoff, Sera B.; Wilms, Jörn; Pottschmidt, Katja; Coppi, Paolo; Maitra, Dipankar; Davis, John E.; Tramper, Frank
Using Suzaku and the Rossi X-ray Timing Explorer (RXTE), we have conducted a series of four simultaneous observations of the galactic black hole candidate Cyg X-1 in what were historically faint and spectrally hard "low states." Additionally, all of these observations occurred near superior conjunction with our line of sight to the X-ray source passing through the dense phases of the "focused wind" from the mass donating secondary. One of our observations was also simultaneous with observations by the Chandra-High Energy Transmission Grating (HETG). These latter spectra are crucial for revealing the ionized absorption due to the secondary's focused wind. Such absorption is present and must be accounted for in all four spectra. These simultaneous data give an unprecedented view of the 0.8-300 keV spectrum of Cyg X-1, and hence bear upon both corona and X-ray emitting jet models of black hole hard states. Three models fit the spectra well: coronae with thermal or mixed thermal/non-thermal electron populations and jets. All three models require a soft component that we fit with a low temperature disk spectrum with an inner radius of only a few tens of GM/c 2. All three models also agree that the known spectral break at 10 keV is not solely due to the presence of reflection, but each gives a different underlying explanation for the augmentation of this break. Thus, whereas all three models require that there is a relativistically broadened Fe line, the strength and inner radius of such a line is dependent upon the specific model, thus making premature line-based estimates of the black hole spin in the Cyg X-1 system. We look at the relativistic line in detail, accounting for the narrow Fe emission and ionized absorption detected by HETG. Although the specific relativistic parameters of the line are continuum dependent, none of the broad line fits allow for an inner disk radius that is >40 GM/c 2.
Corona, Jet, and Relativistic Line Models for Suzaku/RXTE/Chandra-HETG Observations of the Cygnus X-1 Hard State
NASA Technical Reports Server (NTRS)
Nowak, Michael A.; Hanke, Manfred; Trowbridge, Sarah N.; Markoff, Sera B.; Wilms, Joern; Pottschmidt, Katja; Coppi, Paolo; Maitra, Dipankar; Davis, Jhn E.; Tramper, Frank
Using Suzaku and the Rossi X-ray Timing Explorer (RXTE), we have conducted a series of four simultaneous observations of the galactic black hole candidate Cyg X-1 in what were historically faint and spectrally hard "low states". Additionally, all of these observations occurred near superior conjunction with our line of sight to the X-ray source passing through the dense phases of the "focused wind" from the mass donating secondary. One of our observations was also simultaneous with observations by the Chandra-High Energy Transmission Grating (HETG). These latter spectra are crucial for revealing the ionized absorption due to the secondary s focused wind. Such absorption is present and must be accounted for in all four spectra. These simultaneous data give an unprecedented view of the 0.8-300 keV spectrum of Cyg X-1, and hence bear upon both corona and X-ray emitting jet models of black hole hard states. Three models fit the spectra well: coronae with thermal or mixed thermal/non-thermal electron populations, and jets. All three models require a soft component that we fit with a low temperature disk spectrum with an inner radius of only a few tens of GM/c2. All three models also agree that the known spectral break at 10 keV is not solely due to the presence of reflection, but each gives a different underlying explanation for the augmentation of this break. Thus whereas all three models require that there is a relativistically broadened Fe line, the strength and inner radius of such a line is dependent upon the specific model, thus making premature line-based estimates of the black hole spin in the Cyg X-1 system. We look at the relativistic line in detail, accounting for the narrow Fe emission and ionized absorption detected by HETG. Although the specific relativistic parameters of the line are continuum-dependent, none of the broad line fits allow for an inner disk radius that is > 40 GM/c(sup 2).
Solvable light-front model of the electromagnetic form factor of the relativistic two-body bound state in 1+1 dimensions
Mankiewicz, L. ); Sawicki, M. )
Within a relativistically correct yet analytically solvable model of light-front quantum mechanics we construct the electromagnetic form factor of the two-body bound state and we study the validity of the static approximation to the full form factor. Upon comparison of full form factors calculated for different values of binding energy we observe an unexpected effect that for very strongly bound states further increase in binding leads to an increase in the size of the bound system. A similar effect is found for another quantum-mechanical model of relativistic dynamics.
Beyond-mean-field corrections within the second random-phase approximation
NASA Astrophysics Data System (ADS)
Grasso, M.; Gambacurta, D.; Engel, J.
A subtraction procedure, introduced to overcome double-counting problems in beyond-mean-field theories, is used in the second random-phase approximation (SRPA). Doublecounting problems arise in the energy-density functional framework in all cases where effective interactions tailored at leading order are used for higher-order calculations, such as those done in the SRPA model. It was recently shown that this subtraction procedure also guarantees that the stability condition related to the Thouless theorem is verified in extended RPA models. We discuss applications of the subtraction procedure, introduced within the SRPA model, to the nucleus 16O. The application of the subtraction procedure leads to: (i) stable results that are weakly cutoff dependent; (ii) a considerable upwards correction of the SRPA spectra (which were systematically shifted downwards by several MeV with respect to RPA spectra, in all previous calculations). With this important implementation of the model, many applications may be foreseen to analyze the genuine impact of 2 particle-2 hole configurations (without any cutoff dependences and anomalous shifts) on the excitation spectra of medium-mass and heavy nuclei.
A relativistic self-consistent model for studying enhancement of space charge limited field emission due to counter-streaming ions
NASA Astrophysics Data System (ADS)
Lin, M. C.; Lu, P. S.; Chang, P. C.; Ragan-Kelley, B.; Verboncoeur, J. P.
Recently, field emission has attracted increasing attention despite the practical limitation that field emitters operate below the Child-Langmuir space charge limit. By introducing counter-streaming ion flow to neutralize the electron charge density, the space charge limited field emission (SCLFE) current can be dramatically enhanced. In this work, we have developed a relativistic self-consistent model for studying the enhancement of SCLFE by a counter-streaming ion current. The maximum enhancement is found when the ion effect is saturated, as shown analytically. The solutions in non-relativistic, intermediate, and ultra-relativistic regimes are obtained and verified with 1-D particle-in-cell simulations. This self-consistent model is general and can also serve as a benchmark or comparison for verification of simulation codes, as well as extension to higher dimensions.
A relativistic self-consistent model for studying enhancement of space charge limited field emission due to counter-streaming ions
Lin, M. C. Lu, P. S.; Chang, P. C.; Ragan-Kelley, B.; Verboncoeur, J. P.
Recently, field emission has attracted increasing attention despite the practical limitation that field emitters operate below the Child-Langmuir space charge limit. By introducing counter-streaming ion flow to neutralize the electron charge density, the space charge limited field emission (SCLFE) current can be dramatically enhanced. In this work, we have developed a relativistic self-consistent model for studying the enhancement of SCLFE by a counter-streaming ion current. The maximum enhancement is found when the ion effect is saturated, as shown analytically. The solutions in non-relativistic, intermediate, and ultra-relativistic regimes are obtained and verified with 1-D particle-in-cell simulations. This self-consistent model is general and can also serve as a benchmark or comparison for verification of simulation codes, as well as extension to higher dimensions.
Spectral properties and phase diagram of correlated lattice bosons in an optical cavity within bosonic dynamical mean-field theory
NASA Astrophysics Data System (ADS)
Panas, Jaromir; Kauch, Anna; Byczuk, Krzysztof
We use the Bose-Hubbard model with an effective infinite-range interaction to describe the correlated lattice bosons in an optical cavity. We study both static and spectral properties of such system within the bosonic dynamical mean-field theory, which is the state-of-the-art method for strongly correlated bosonic systems. Both similarities and differences are found and discussed between our results and those obtained within different theoretical methods and experiment.
Relativistic impulse dynamics.
Swanson, Stanley M
Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion.
Pipin, V. V.; Kuzanyan, K. M.; Zhang, H.; Kosovichev, A. G.
We study the dynamical and statistical properties of turbulent cross-helicity (correlation of the aligned fluctuating velocity and magnetic field components). We derive an equation governing generation and evolution of the turbulent cross-helicity and discuss its meaning for the dynamo. Using the symmetry properties of the problem we suggest a general expression for the turbulent cross-helicity. Effects of the density stratification, large-scale magnetic fields, differential rotation, and turbulent convection are taken into account. We investigate the relative contribution of these effects to the cross-helicity evolution for two kinds of dynamo models of the solar cycle: a distributed mean-field model and a flux-transport dynamo model. We show that the contribution from the density stratification follows the evolution of the radial magnetic field, while large-scale electric currents produce a more complicated pattern of the cross-helicity of comparable magnitude. The pattern of the cross-helicity evolution strongly depends on details of the dynamo mechanism. Thus, we anticipate that direct observations of the cross-helicity on the Sun may serve for the diagnostic purpose of the solar dynamo process.
Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics
NASA Astrophysics Data System (ADS)
Zsargo, J.; Petrovay, K.
It is widely known that a sufficient condition for the applicability of quasilinear-type approximations (e.g. the second-order correlation approximation or SOCA) in mean-field electrodynamics is that Utau << min {l, H} where l, H, U and tau are characteristic horizontal and vertical scale lengths, velocity, and time, respectively. A necessary condition for their validity is however not known. In order to check the validity of the quasilinear results in cases where the above condition is not satisfied, as well as to study qualitative and quantitative differences between the quasilinear results and the actual solutions, we numerically solve the MHD induction equation for the kinematical case in a series of simplified "toy" model flows and then compare the results with the corresponding quasilinear solutions. Our model flows are two-dimensional two-component flows with simple (exponential or linear) stratifications. For conceptual clarity, in each model only one independent physical quantity (initial magnetic field, density, or velocity amplitude, respectively) has an inhomogeneous distribution. Solutions are computed for several widely differing values of the l/H horizontal/vertical scale length ratio. In all cases we find that the computed turbulent electromotive force does not differ from the quasilinear value by more than an order-of-unity factor, as long as Utau does not greatly exceed min {l, H}.
A Relativistic Model for Data Processing of High-precision Astrometry and a Test of Alternative Gravity Theories
NASA Astrophysics Data System (ADS)
Deng, X. M.
With the development of the unprecedented techniques for observation and the improvement of the advanced methods for measurement, it is time for astrometry to unfold a new era indubitably. Presently, the satellite laser ranging like LAser GEOdynamics Satellite (LAGEOS) has achieved a precision of 0.5 mas for orbit determination, the precision of Lunar Laser Ranging (LLR) has approached one millimeter, and Very Long Baseline Interferometry (VLBI) has attained the precision of 0.1 mas or even better. Beyond the current thresholds, astrometric observation will be able to attain the precision of a few μas or higher for some astrometric missions in the near future, such as Global Astrometric Interferometer for Astrophysics (GAIA) and Space Interferometry Mission (SIM). With the modern continuous improvement of the observational accuracy, we realize that Newtonian mechanics has already deviated from the high-precision astronomical observation. A relativistic model for data processing of high-precision astrometry needs to be established. On the other hand, the continued failure in merging gravity with quantum mechanics and recent cosmological observations indicate that Einstein's general relativity needs some modifications. Thus, we are motivated by testing alternative gravity theories and parameterizing relativistic model. We mainly try to research these deeply. Firstly, it is shown that the parameterized post-Newtonian parameter γ≠1 for Moffat's STVG by using Chandrasekhar's approach, and the theory is then ruled out by the experiments in the solar system. Then we propose a modified theory, MSTVG, to solve this problem. Besides, we use binary pulsar data to constrain two parameters in MSTVG. Secondly, a parameterized 2PN framework for light propagation is developed based on the previous works in our research. By considering the non-static gravitational field of the solar system, the influences of all kinds of relativistic terms with different physical origins on
Neural networks with excitatory and inhibitory components: Direct and inverse problems by a mean-field approach
NASA Astrophysics Data System (ADS)
di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro
We study the dynamics of networks with inhibitory and excitatory leak-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a heterogeneous mean-field approximation, which allows us to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, which give rise to a rich dynamical phase diagram as a function of the fraction of inhibitory neurons. Using the same mean-field approach, we study and solve a global inverse problem: reconstructing the degree probability distributions of the inhibitory and excitatory components and the fraction of inhibitory neurons from the knowledge of the average synaptic activity field. This approach unveils new perspectives on the numerical study of neural network dynamics and the possibility of using these models as a test bed for the analysis of experimental data.
Towards a quasi-periodic mean field theory for globally coupled oscillators
NASA Astrophysics Data System (ADS)
Banaji, Murad; Glendinning, Paul
We show how a quasi-periodic mean field theory may be used to understand the chaotic dynamics and geometry of globally coupled complex Ginzburg-Landau equations. The Poincaré map of the mean field equations appears to have saddlenode-homoclinic bifurcations leading to chaotic motion, and the attractor has the characteristic ρ shape identified by numerical experiments on the full equations.
NASA Astrophysics Data System (ADS)
Valente, Giovanni; Owen Weatherall, James
Relativity theory is often taken to include, or to imply, a prohibition on superluminal propagation of causal processes. Yet, what exactly the prohibition on superluminal propagation amounts to and how one should deal with its possible violation have remained open philosophical problems, both in the context of the metaphysics of causation and the foundations of physics. In particular, recent work in philosophy of physics has focused on the causal structure of spacetime in relativity theory and on how this causal structure manifests itself in our most fundamental theories of matter. These topics were the subject of a workshop on "Relativistic Causality in Quantum Field Theory and General Relativity" that we organized (along with John Earman) at the Center for Philosophy of Science in Pittsburgh on April 5-7, 2013. The present Special Issue comprises contributions by speakers in that workshop as well as several other experts exploring different aspects of relativistic causality. We are grateful to the journal for hosting this Special Issue, to the journal's managing editor, Femke Kuiling, for her help and support in putting the issue together, and to the authors and the referees for their excellent work.
Lin, Da-Bin; Gu, Wei-Min; Hou, Shu-Jin; Liu, Tong; Sun, Mou-Yuan; Lu, Ju-Fu E-mail: firstname.lastname@example.com
Rapid temporal variability has been widely observed in the light curves of gamma-ray bursts (GRBs). One possible mechanism for such variability is related to the relativistic eddies in the jet. In this paper, we include the contribution of the inter-eddy medium together with the eddies to the gamma-ray emission. We show that the gamma-ray emission can either lead or lag behind the observed synchrotron emission, where the latter originates in the inter-eddy medium and provides most of the seed photons for producing gamma-ray emission through inverse Compton scattering. As a consequence, we argue that the lead/lag found in non-stationary short-lived light curves may not reveal the intrinsic lead/lag of different emission components. In addition, our results may explain the lead of gamma-ray emission with respect to optical emission observed in GRB 080319B.
Relativistic geometric quantum phases from the Lorentz symmetry violation effects in the CPT-even gauge sector of Standard Model Extension
NASA Astrophysics Data System (ADS)
Bakke, K.; Belich, H.
We discuss the appearance of geometric quantum phases for a Dirac neutral particle in the context of relativistic quantum mechanics based on possible scenarios of the Lorentz symmetry violation tensor background in the CPT-even gauge sector of Standard Model Extension. We assume that the Lorentz symmetry breaking is determined by a tensor background given by (KF)μναβ, then, relativistic analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the parity-even and parity-odd sectors of the tensor (KF)μναβ.
Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons.
Baladron, Javier; Fasoli, Diego; Faugeras, Olivier; Touboul, Jonathan
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the FitzHugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons' initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes place, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is a solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations or non-local partial differential equations resembling the McKean-Vlasov-Fokker-Planck equations. We prove the well-posedness of the McKean-Vlasov equations, i.e. the existence and uniqueness of a solution. We also show the results of some numerical experiments that indicate that the mean-field equations are a good representation of the mean activity of a finite size network, even for modest sizes. These experiments also indicate that the McKean-Vlasov-Fokker-Planck equations may be a good way to understand the mean-field dynamics through, e.g. a bifurcation analysis.Mathematics Subject Classification (2000): 60F99, 60B10, 92B20, 82C32, 82C80, 35Q80.
Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the FitzHugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons' initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes place, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is a solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations or non-local partial differential equations resembling the McKean-Vlasov-Fokker-Planck equations. We prove the well-posedness of the McKean-Vlasov equations, i.e. the existence and uniqueness of a solution. We also show the results of some numerical experiments that indicate that the mean-field equations are a good representation of the mean activity of a finite size network, even for modest sizes. These experiments also indicate that the McKean-Vlasov-Fokker-Planck equations may be a good way to understand the mean-field dynamics through, e.g. a bifurcation analysis. Mathematics Subject Classification (2000): 60F99, 60B10, 92B20, 82C32, 82C80, 35Q80. PMID:22657695
The nuclear mean field of sulfur from -80 to +80 MeV
Al-Ohali, M.A. |
Neutron elastic-scattering differential cross section {sigma}({theta}) and analyzing power Ay({theta}) {delta}{alpha}{tau}{alpha} for {sup 32}S have been measured at incident neutron energies of 15.5 and 19 MeV. These data were combined with previous n-{sup 32}S scattering data (Ay({theta}), {sigma}({theta}) and total cross section) to form a large database in the energy range from 1 to 80 MeV. In addition, information about binding energies of the single-particle bound states for the n-{sup 32}S system was incorporated to extend the database to negative energies (down to {minus}80 MeV). The entire database was analyzed in the framework of the nuclear mean field (NMF). The NMF was derived from a Dispersive Optical Model (DOM) analysis that incorporates explicitly the dispersion relation which connects the real and the imaginary parts of the NMF. The extension of the DOM potential from positive to negative energy provides the shell-model potential used for predicting the binding energies of single-particle bound states. The DOM describes the scattering data very well in the energy range between 8 - 80 MeV, but it overestimates the total cross section for energies less than 8 MeV. The DOM predicts reasonably well the observed binding energies of the single-particle states.
Cluster Dynamical Mean Field Methods and the Momentum-selective Mott transition
NASA Astrophysics Data System (ADS)
Gull, Emanuel
Innovations in methodology and computational power have enabled cluster dynamical mean field calculations of the Hubbard model with interaction strengths and band structures representative of high temperature copper oxide superconductors, for clusters large enough that the thermodyamic limit behavior may be determined. We present the methods and show how extrapolations to the thermodynamic limit work in practice. We show that the Hubbard model with next-nearest neighbor hopping at intermediate interaction strength captures much of the exotic behavior characteristic of the high temperature superconductors. An important feature of the results is a pseudogap for hole doping but not for electron doping. The pseudogap regime is characterized by a gap for momenta near Brillouin zone face and gapless behavior near the zone diagonal. for dopings outside of the pseudogap regime we find scattering rates which vary around the fermi surface in a way consistent with recent transport measurements. Using the maximum entropy method we calculate spectra, self-energies, and response functions for Raman spectroscopy and optical conductivities, finding results also in good agreement with experiment. Olivier Parcollet, Philipp Werner, Nan Lin, Michel Ferrero, Antoine Georges, Andrew J. Millis; NSF-DMR-0705847.
Thermal conduction in polymeric nanofluids under mean field approximation: role of interfacial adsorption layers
NASA Astrophysics Data System (ADS)
Nisha, M. R.; Philip, J.
Polymeric nanofluids of TiO2/PVA (polyvinyl alcohol) and Cu/PVA have been prepared by dispersing nanoparticles of TiO2 or metallic copper in PVA. The thermal diffusivities and thermal conductivities of these nanofluids have been measured as a function of particle loading following a thermal wave interference technique in a thermal wave resonant cavity. It is found that in both cases thermal conductivity increases with particle concentration, with Cu/PVA nanofluids showing a much larger increase. The results have been compared with the corresponding values calculated following different theoretical models. Comparison of the results with model-based calculations shows that the thermal conductivity variations in these nanofluids are within the framework of the classical mean field theory including the formation of thin interfacial adsorption layers around nanoparticles. Although the molecular weight of PVA is very high, it is found that the adsorption layer thickness is limited by the hydrodynamic radius of the nanoparticles. It is found that particle clustering followed by interfacial layering accounts for the larger increase in thermal conductivity found for Cu/PVA compared to TiO2/PVA.
Perturbative Calculation of Quasi-Potential in Non-equilibrium Diffusions: A Mean-Field Example
NASA Astrophysics Data System (ADS)
Bouchet, Freddy; Gawȩdzki, Krzysztof; Nardini, Cesare
of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators (Prog Theoret Phys 75:1105-1110, [74]). This is one of few systems for which non-equilibrium free energies can be computed and analyzed in an effective way, at least perturbatively.
Relativistic effects in atom gravimeters
NASA Astrophysics Data System (ADS)
Tan, Yu-Jie; Shao, Cheng-Gang; Hu, Zhong-Kun
Atom interferometry is currently developing rapidly, which is now reaching sufficient precision to motivate laboratory tests of general relativity. Thus, it is extremely significant to develop a general relativistic model for atom interferometers. In this paper, we mainly present an analytical derivation process and first give a complete vectorial expression for the relativistic interferometric phase shift in an atom interferometer. The dynamics of the interferometer are studied, where both the atoms and the light are treated relativistically. Then, an appropriate coordinate transformation for the light is performed crucially to simplify the calculation. In addition, the Bordé A B C D matrix combined with quantum mechanics and the "perturbation" approach are applied to make a methodical calculation for the total phase shift. Finally, we derive the relativistic phase shift kept up to a sensitivity of the acceleration ˜1 0-14 m/s 2 for a 10 -m -long atom interferometer.
Diffuse phase transition in ferroelectrics with mesoscopic heterogeneity: Mean-field theory
Li, S.; Eastman, J.A.; Newnham, R.E.; Cross, L.E.
The diffuse phase transition in ferroelectrics with mesoscopic heterogeneity has been discussed within the context of a superparaelectric model by using the Ginzburg-Landau formalism. In the Curie region ferroelectrics with mesoscopic heterogeneity are treated as {open_quotes}superparaelectrics{close_quotes} consisting of a mass of polar clusters, each of which has Ising character. Based on the mean-field theory, the influence of the finite-size effects of polar clusters on their structural instability has been discussed by considering a coherent lattice coupling between two structurally different regions. In particular, we have analytically derived the explicit solutions of the distribution of local polarizations. In turn, the processes of polar nanophase precipitation and coarsening have been also discussed in conjunction with the local chemical or structural inhomogeneity. Moreover, we have also analyzed the relationship between the local polarization distribution and the static dielectric susceptibility in ferroelectrics with the nanometric scale heterogeneity. The width of the Curie region is dependent upon the distribution of the sum of localized correlation length, which reflects the size distribution of heterogeneity. The presented analysis reveals that the diffuse phase transition is closely associated with the existence of nanometric polar clusters and their physical size distribution. Intriguingly, our theoretical results bear a very close resemblance to most experimental observations. {copyright} {ital 1997} {ital The American Physical Society}
Investigation of single- and double-Λ hypernuclei using a beyond-mean-field approach
NASA Astrophysics Data System (ADS)
Cui, Ji-Wei; Zhou, Xian-Rong; Guo, Li-Xin; Schulze, Hans-Josef
A beyond-mean-field approach consisting of angular momentum projection techniques and generator coordinate method based on Skyrme-Hartree-Fock calculations is employed to investigate single- and double-Λ hypernuclear systems. The density-dependent N Λ interactions derived from the Nijmegen soft-core potentials are used. Rotational energy spectra and electric-quadrupole transition strengths B (E 2 ) of the hypernuclei 13CΛ, 14CΛ Λ, 21Ne21Λ, and 22NeΛ Λ are presented and compared with those of the corresponding core nuclei 12C and 20Ne. The shrinkage effect of the Λ s is demonstrated by the B (E 2 ) values, the charge radii, and the shape deformation β of the nuclear core. It is found that the reduction of the B (E 2 ) values in 13CΛ and 14CΛΛ is mainly caused by the shrinkage of the charge radii of the nuclear cores, while the reduced shape deformations also play important roles; but the contrary is the case in Ne21Λ and 22NeΛΛ. Comparison between this and other theoretical models are made, and the differences between them are illuminated.
Autonomously Responsive Pumping by a Bacterial Flagellar Forest: A Mean-field Approach
NASA Astrophysics Data System (ADS)
Martindale, James; Fu, Henry C.
The design and fabrication of microscale pumps using magnetically actuated bacterial flagella opens the door for many applications such as the pumping and regulation of chemicals. Here, we discuss simulations for a pump consisting of a regular two-dimensional array of rigid helices. Recent work investigating the flows above a small, finite array by numerically calculating the full dynamics showed that having random phase differences between helices seems essential to produce the flow patterns observed in experiments. We developed a model which allows us to treat random phase differences in an infinite array. Using a mean-field approach we define pumping as the existence of a self-consistent tilt angle of the array. Pumping is then examined numerically as a function of several parameters in the magnetic actuation and helical geometry. We demonstrate how this pumping flow may be mechanically halted by way of magnetic actuation or autonomously halted by the polymorphic transformation of bacterial flagella in response to environmental stimuli.
Mean-field Density Functional Theory of a Three-Phase Contact Line
NASA Astrophysics Data System (ADS)
Lin, Chang-You
A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive over-relaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change. We develop a geometrical interpretation to generalize our potential in order to study less symmetric systems as occur in some practical phase diagrams. A set of special cases of this new potential are linear transformations from our original potential. In those special cases, we can obtain solutions by scaling of our former results.
Correlated cluster mean-field theory for spin-glass systems
NASA Astrophysics Data System (ADS)
Zimmer, F. M.; Schmidt, M.; Magalhaes, S. G.
The competition between cluster spin glass (CSG) and ferromagnetism or antiferromagnetism is studied in this work. The model considers clusters of spins with short-range ferromagnetic or antiferromagnetic (FE-AF) interactions (J0) and long-range disordered couplings (J) between clusters. The problem is treated by adapting the correlated cluster mean-field theory of D. Yamamoto [Phys. Rev. B 79, 144427 (2009), 10.1103/PhysRevB.79.144427]. Phase diagrams T /J×J0/J are obtained for different cluster sizes ns. The results show that the CSG phase is found below the freezing temperature Tf for lower intensities of J0/J. The increase of short-range FE interaction can favor the CSG phase, while the AF one reduces the CSG region by decreasing the Tf. However, there are always critical values of J0 where AF or FE orders become stable. The results also indicate a strong influence of the cluster size in the competition of magnetic phases. For AF cluster, the increase of ns diminishes Tf reducing the CSG phase region, which indicates that the cluster surface spins can play an important role in the CSG arising.
Microscopic theory of dissipation for slowly time-dependent mean field potentials
NASA Astrophysics Data System (ADS)
Aleshin, V. P.
We study the dissipation rate Q˙ in systems of nucleons bound by a slowly time-dependent mean-field potential and slightly interacting between themselves. Starting from the many-body linear response formula we evaluate an expression for Q˙ in terms of the pure shell-model quantities and the nucleon-nucleon collision rate Γ. The application of the classical sum rule leads then to an expression for Q˙ in terms of the classical-path integral with the weighting function including Γ. For vanishing Γ this expression reduces to the Koonin-Randrup Knudsen-gas formula. For simplified Skyrme interactions the classical approximation for the Γ itself is obtained. In leptodermous systems the classical-path expression for Q˙ decomposes into the wall formula and the multiple-reflection term owing to incomplete randomization of particle motion between consecutive encounters with the boundary. The mean-free path and temperature dependence of dissipation is analyzed for small-amplitude distortions of spherical cavities.
Cluster mean-field signature of entanglement entropy in bosonic superfluid-insulator transitions
NASA Astrophysics Data System (ADS)
Zhang, Li; Qin, Xizhou; Ke, Yongguan; Lee, Chaohong
Entanglement entropy (EE), a fundamental concept in quantum information for characterizing entanglement, has been extensively employed to explore quantum phase transitions (QPTs). Although the conventional single-site mean-field (MF) approach successfully predicts the emergence of QPTs, it fails to include any entanglement. Here, in the framework of a cluster MF treatment, we extract the signature of EE in bosonic superfluid-insulator (SI) transitions. We consider a trimerized Kagomé lattice of interacting bosons, in which each trimer is treated as a cluster, and implement the cluster MF treatment by decoupling all intertrimer hopping. In addition to superfluid and integer insulator phases, we find that fractional insulator phases appear when the tunneling is dominated by the intratrimer part. To quantify the residual bipartite entanglement in a cluster, we calculate the second-order Rényi entropy, which can be experimentally measured by quantum interference of many-body twins. The second-order Rényi entropy itself is continuous everywhere, however, the continuousness of its first-order derivative breaks down at the phase boundary. This means that the bosonic SI transitions can still be efficiently captured by the residual entanglement in our cluster MF treatment. Besides to the bosonic SI transitions, our cluster MF treatment may also be used to capture the signature of EE for other QPTs in quantum superlattice models.
The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models
NASA Technical Reports Server (NTRS)
Thorne, K. S.; Zytkow, A. N.
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."
Modeling Relativistic Electron Precipitation Bremsstrahlung X-Ray Intensities at 10-100 km Manned Vehicle Altitudes
NASA Astrophysics Data System (ADS)
Habash Krause, L.; Gilchrist, B. E.; Nishikawa, K.; Williams, A.
Relativistic electron precipitation (REP) events occur when beams or bunches of relativistic electrons of magnetospheric origin enter the Earth's atmosphere, typically at auroral latitudes. REP events are associated with a variety of space weather effects, including production of transitional and bremsstrahlung radiation, catalytic depletion of stratospheric ozone, and scintillation of transionospheric radio waves. This study examines the intensities of x-rays produced at airliner, manned balloon, and suborbital Reusable Launch Vehicle (sRLV) altitudes. The monoenergetic beam is modeled in cylindrical symmetry using the paraxial ray equation. Bremsstrahlung photon production is calculated using the traditional Sauter-Elwert cross-section, providing x-ray emission spectra differential in energy and angle. Attenuation is computed for a plane-stratified standard atmosphere, and the loss processes include photoionization, Rayleigh and Compton scattering, electron-positron pair production, and photonuclear interaction. Peak altitudes of electron energy deposition and bremsstrahlung x-ray production were calculated for beams of energies from 1 MeV through 100 MeV. The altitude peak of bremsstrahlung deposition was consistently and significantly lower that that of the electron deposition due to the longer mean free paths of x-rays compared to electrons within the atmosphere. For example, for a nadir-directed monoenergetic 5 MeV beam, the peak deposition altitude was calculated to be 42 km, but the resulting bremmstrahlung deposition peaked at 25 km. This has implications for crew and passenger safety, especially with the growth of the space tourism industry that relies on sRLVs with a nominal apogee of 100 km. A survey of results covering the 1-100 MeV spectrum for the three altitude ranges of interest will be presented.
Real-space, mean-field algorithm to numerically calculate long-range interactions
NASA Astrophysics Data System (ADS)
Cadilhe, A.; Costa, B. V.
Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.
Ising spin-glass transition in a magnetic field outside the limit of validity of mean-field theory.
Leuzzi, L; Parisi, G; Ricci-Tersenghi, F; Ruiz-Lorenzo, J J
The spin-glass transition in a magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to changing the dimension in spin-glass short-range models. Evidence for a spin-glass transition in a magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension in a zero magnetic field.
Connection between the nuclear matter mean-field equation of state and the quark and gluon condensates at high density
Malheiro, M.; Dey, M.; Delfino, A.; Dey, J. |||
It is known now that chiral symmetry restoration requires the meson-nucleon couplings to be density-dependent in nuclear-matter mean-field models. We further show that, quite generally, the quark and gluon condensates in medium are related to the trace of the energy-momentum tensor of nuclear matter and in these models the incompressibility K must be less than 3 times the chemical potential {mu}. In the critical density {rho}{sub c}, the gluon condensate is only reduced by 20{percent}, indicating a larger effective nucleon mass. {copyright} {ital 1997} {ital The American Physical Society}
A relativistic correction to semiclassical charmonium
NASA Astrophysics Data System (ADS)
Weiss, J.
It is shown that the relativistic linear potentials, introduced by the author within the particle à la Wheeler-Feynman direct-interaction (AAD) theory, applied to the semiclassically quantized charmonium, yield energy spectrum comparable to that of some known models. Using the expansion of the relativistic linear AAD potentials in powers ofc -1, the charmonium spectrum, given as a rule by Bohr-Sommerfeld quantization of circular orbits, is extended up to the second order of relativistic corrections.
A General Stochastic Maximum Principle for SDEs of Mean-field Type
Buckdahn, Rainer; Djehiche, Boualem; Li Juan
We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng's-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966-979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order adjoint equation remains the same as in Peng's stochastic maximum principle.