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Nonlinear physics (solitons, chaos, discrete breathers)
- Erika Logan
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1 Nonlinear physics (solitons, chaos, discrete breathers) N. Theodorakopoulos Konstanz, June 2006
2 Contents Foreword vi 1 Background: Hamiltonian mechanics Lagrangian formulation of dynamics Hamiltonian dynamics Canonical momenta Poisson brackets Equations of motion Canonical transformations Point transformations Hamilton-Jacobi theory Hamilton-Jacobi equation Relationship to action Conservative systems Separation of variables Periodic motion. Action-angle variables Complete integrability Symmetries and conservation laws Homogeneity of time Homogeneity of space Galilei invariance Isotropy of space (rotational symmetry of Lagrangian) Continuum field theories Lagrangian field theories in 1+1 dimensions Symmetries and conservation laws Perturbations of integrable systems Background: Statistical mechanics Scope Formulation Phase space Liouville s theorem Averaging over time Ensemble averaging Equivalence of ensembles Ergodicity The FPU paradox The harmonic crystal: dynamics The harmonic crystal: thermodynamics The FPU numerical experiment i
3 Contents 4 The Korteweg - de Vries equation Shallow water waves Background: hydrodynamics Statement of the problem; boundary conditions Satisfying the bottom boundary condition Euler equation at top boundary A solitary wave Is the solitary wave a physical solution? KdV as a limiting case of anharmonic lattice dynamics KdV as a field theory KdV Lagrangian Symmetries and conserved quantities KdV as a Hamiltonian field theory Solving KdV by inverse scattering Isospectral property Lax pairs Inverse scattering transform: the idea The inverse scattering transform The direct problem Time evolution of scattering data Reconstructing the potential from scattering data (inverse scattering problem) IST summary Application of the IST: reflectionless potentials A single bound state Multiple bound states Integrals of motion Lemma: a useful representation of a(k) Asymptotic expansions of a(k) IST as a canonical transformation to action-angle variables Solitons in anharmonic lattice dynamics: the Toda lattice The model The dual lattice A pulse soliton Complete integrability Thermodynamics Chaos in low dimensional systems Visualization of simple dynamical systems Two dimensional phase space dimensional phase space dimensional phase space; nonautonomous systems with one degree of freedom Small denominators revisited: KAM theorem Chaos in area preserving maps Twist maps Local stability properties Poincaré-Birkhoff theorem Chaos diagnostics The standard map The Arnold cat map The baker map; Bernoulli shifts ii
4 Contents The circle map. Frequency locking Topology of chaos: stable and unstable manifolds, homoclinic points Solitons in scalar field theories Definitions and notation Lagrangian, continuum field equations Static localized solutions (general KG class) General properties Specific potentials Intrinsic Properties of kinks Linear stability of kinks Special properties of the SG field The Sine-Gordon breather Complete Integrability Atoms on substrates: the Frenkel-Kontorova model The Commensurate-Incommensurate transition The continuum approximation The special case ɛ = 0: kinks and antikinks The general case ɛ > 0: the soliton lattice Breaking of analyticity FK ground state as minimizing periodic orbit of the standard map Small amplitude motion Free end boundary conditions Metastable states: spatial chaos as a model of glassy structure Solitons in magnetic chains Introduction Classical spin dynamics Spin Poisson brackets An alternative representation Solitons in ferromagnetic chains The continuum approximation The classical, isotropic, ferromagnetic chain The easy-plane ferromagnetic chain in an external field Solitons in antiferromagnets Continuum dynamics The isotropic antiferromagnetic chain Easy axis anisotropy Easy plane anisotropy Easy plane anisotropy and symmetry-breaking field Solitons in conducting polymers Peierls instability Electrons decoupled from the lattice Electron-phonon coupling; dimerization Solitons and polarons in (CH) x A continuum approximation Dimerization The soliton The polaron iii
5 Contents 12 Solitons in nonlinear optics Background: Interaction of light with matter, Maxwell-Bloch equations Semiclassical theoretical framework and notation Dynamics Propagation at resonance. Self-induced transparency Slow modulation of the optical wave Further simplifications: Self-induced transparency Self-focusing off-resonance Off-resonance limit of the MB equations Nonlinear terms Space-time dependence of the modulation: the nonlinear Schrödinger equation Soliton solutions Solitons in Bose-Einstein Condensates The Gross-Pitaevskii equation Propagating solutions. Dark solitons Unbinding the double helix A nonlinear lattice dynamics approach Mesoscopic modeling of DNA Thermodynamics Nonlinear structures (domain walls) and DNA melting Local equilibria Thermodynamics of domain walls Pulse propagation in nerve cells: the Hodgkin-Huxley model Background The Hodgkin-Huxley model The axon membrane as an array of electrical circuit elements Ion transport via distinct ionic channels Voltage clamping Ionic channels controlled by gates Membrane activation is a threshold phenomenon A qualitative picture of ion transport during nerve activation Pulse propagation Localization and transport of energy in proteins: The Davydov soliton Background. Model Hamiltonian Energy storage in C=O stretching modes. Excitonic Hamiltonian Coupling to lattice vibrations. Analogy to polaron Born-Oppenheimer dynamics Quantum (excitonic) dynamics Lattice motion Coupled exciton-phonon dynamics The Davydov soliton The heavy ion limit. Static Solitons Moving solitons iv
6 Contents 17 Nonlinear localization in translationally invariant systems: discrete breathers The Sievers-Takeno conjecture Numerical evidence of localization Diagnostics of energy localization Internal dynamics Towards exact discrete breathers A Impurities, disorder and localization 164 A.1 Definitions A.1.1 Electrons A.1.2 Phonons A.2 A single impurity A.2.1 An exact result A.2.2 Numerical results A.3 Disorder A.3.1 Electrons in disordered one-dimensional media A.3.2 Vibrational spectra of one-dimensional disordered lattices Bibliography 173 v
7 Foreword The fact that most fundamental laws of physics, notably those of electrodynamics and quantum mechanics, have been formulated in mathematical language as linear partial differential equations has resulted historically in a preferred mode of thought within the physics community - a linear theoretical bias. The Fourier decomposition - an admittedly powerful procedure of describing an arbitrary function in terms of sines and cosines, but nonetheless a mathematical tool - has been firmly embedded in the conceptual framework of theoretical physics. Photons, phonons, magnons are prime examples of how successive generations of physicists have learned to describe properties of light, lattice vibrations, or the dynamics of magnetic crystals, respectively, during the last 100 years. This conceptual bias notwithstanding, engineers or physicists facing specific problems in classical mechanics, hydrodynamics or quantum mechanics were never shy of making particular approximations which led to nonlinear ordinary, or partial differential equations. Therefore, by the 1960 s, significant expertise had been accumulated in the field of nonlinear differential and/or integral equations; in addition, major breakthroughs had occurred on some fundamental issues related to chaos in classical mechanics (Poincaré, Birkhoff, KAM theorems). Due to the underlying linear bias however, this substantial progress took unusually long to find its way to the core of physical theory. This changed rapidly with the advent of electronic computation and the new possibilities of numerical visualization which accompanied it. Computer simulations became instrumental in catalyzing the birth of nonlinear science. This set of lectures does not even attempt to cover all areas where nonlinearity has proved to be of importance in modern physics. I will however try to describe some of the basic concepts mainly from the angle of condensed matter / statistical mechanics, an area which provided an impressive list of nonlinearly governed phenomena over the last fifty years - starting with the Fermi-Pasta-Ulam numerical experiment and its subsequent interpretation by Zabusky and Kruskal in terms of solitons ( paradox turned discovery, in the words of J. Ford). There is widespread agreement that both solitons and chaos have achieved the status of theoretical paradigm. The third concept introduced here, localization in the absence of disorder, is a relatively recent breakthrough related to the discovery of independent (nonlinear) localized modes (ILMs), a.k.a. discrete breathers. Since neither the development of the field nor its present state can be described in terms of a unique linear narrative, both the exact choice of topics and the digressions necessary to describe the wider context are to a large extent arbitrary. The latter are however necessary in order to provide a self-contained presentation which will be useful for the non-expert, i.e. typically the advanced undergraduate student with an elementary knowledge of quantum mechanics and statistical physics. Konstanz, June 2006 vi
8 1 Background: Hamiltonian mechanics Consider a mechanical system with s degrees of freedom. The state of the mechanical system at any instant of time is described by the coordinates {Q i (t), i = 1, 2,, s} and the corresponding velocities { Q i (t)}. In many applications that I will deal with, this may be a set of N point particles which are free to move in one spatial dimension. In that particular case s = N and the coordinates are the particle displacements. The rules for temporal evolution, i.e. for the determination of particle trajectories, are described in terms of Newton s law - or, in the more general Lagrangian and Hamiltonian formulations. The more general formulations are necessary in order to develop and/or make contact with fundamental notions of statistical and/or quantum mechanics. 1.1 Lagrangian formulation of dynamics The Lagrangian is given as the difference between kinetic and potential energies. particle system interacting by velocity-independent forces For a L({Q i, Q i }) = T V (1.1) T = 1 s m i Q 2 i 2 i=1 V = V ({Q i }, t). where an explicit dependence of the potential energy on time has been allowed. Lagrangian dynamics derives particle trajectories by determining the conditions for which the action integral t S(t, t 0 ) = dτl({q i, Q i, τ}) (1.2) t 0 has an extremum. The result is d L dt Q = L (1.3) i Q i which for Lagrangians of the type (1.2) becomes i.e. Newton s law. m i Qi = V Q i (1.4) 1.2 Hamiltonian dynamics Canonical momenta Hamiltonian mechanics, uses instead of velocities, the canonical momenta conjugate to the coordinates {Q i }, defined as P i = L Q i. (1.5) 1
9 1 Background: Hamiltonian mechanics In the case of (1.2) it is straightforward to express the Hamiltonian function (the total energy) H = T + V in terms of P s and Q s. The result is H({P i, Q i }) = s I=1 P 2 i 2m i + V ({Q i }). (1.6) Poisson brackets Hamiltonian dynamics is described in terms of Poisson brackets {A, B} = s i=1 { A B A } B Q i P i P i Q i (1.7) where A, B are any functions of the coordinates and momenta. The momenta are canonically conjugate to the coordinates because they satisfy the relationships Equations of motion According to Hamiltonian dynamics, the time evolution of any function A({P i, Q i }, t) is determined by the linear differential equations Ȧ da dt = {A, H} + A t. (1.8) where the second term denotes any explicit dependence of A on the time t. Application of (1.8) to the cases A = P i and A = Q i respectively leads to P i = {P i, H} Q i = {Q i, H} (1.9) which can be shown to be equivalent to (1.4). The time evolution of the Hamiltonian itself is governed by dh dt = H ( = V ). (1.10) t t Canonical transformations Hamiltonian formalism important because the symplectic structure of equations of motion (from Greek συµπλɛκω = crosslink - of momenta & coordinate variables -) remains invariant under a class of transformations obtained by a suitable generating function ( canonical transformations). Example, transformation from old coordinates & momenta {P, Q} to new ones {p, q}, via a generating function F 1 (Q, q, t) which depends on old and new coordinates (but not on old and new momenta - NB there are three more forms of generating functions - ): P i = F 1(q, Q, t) Q i p i = F 1(q, Q, t) q i K = H + F 1 t (1.11) 2
10 1 Background: Hamiltonian mechanics new coordinates are obtained by solving the first of the above eqs., and new momenta by introducing the solution in the second. It is straightforward to verify that the dynamics remains form-invariant in the new coordinate system, i.e. ṗ i = {p i, K} q i = {q i, K} (1.12) and dk(p, q, t) K(p, q, t) =. (1.13) dt t Note that if there is no explicit dependence of F 1 on time, the new Hamiltonian K is equal to the old H Point transformations A special case of canonical transformations are point transformations, generated by F 2 (Q, p, t) = i f i (Q, t)p i ; (1.14) New coordinates depend only on old coordinates - not on old momenta; in general new momenta depend on both old coordinates and momenta. A special case of point transformations are orthogonal transformations, generated by F 2 (Q, p) = i,k a ik Q k p i (1.15) where a is an orthogonal matrix. It follows that q i = k p i = k a ik Q k a ik P k. (1.16) Note that, in the case of orthogonal transformations, coordinates transform among themselves; so do the momenta. Normal mode expansion is an example of (1.16). 1.3 Hamilton-Jacobi theory Hamilton-Jacobi equation Hamiltonian dynamics consists of a system of 2N coupled first-order linear differential equations. In general, a complete integration would involve 2N constants (e.g. the initial values of coordinates and momenta). Canonical transformations enable us to play the following game: 1 Look for a transformation to a new set of canonical coordinates where the new Hamiltonian is zero and hence all new coordinates and momenta are constants of the motion. 2 Let (p, q) be the set of original momenta and coordinates in eqs of previous section, 1 Hamilton-Jacobi theory is not a recipe for integration of the coupled ODEs; nor does it in general lead to a more tractable mathematical problem. However, it provides fresh insight to the general problem, including important links to quantum mechanics and practical applications on how to deal with mechanical perturbations of a known, solved system. 2 Does this seem like too many constants? We will later explore what independent constants mean in mechanics, but at this stage let us just note that the original mathematical problem of integrating the 2N Hamiltonian equations does indeed involve 2N constants. 3
11 1 Background: Hamiltonian mechanics (α, β) the set of new constant momenta and coordinates generated by the generating function F 2 (q, α, t) which depends on the original coordinates and the new momenta. The choice of K 0 in (1.11) means that F 2 t + H(q 1, q s ; F 2 q 1,, F 2 q s ; t) = 0. (1.17) Suppose now that you can [miraculously] obtain a solution of the first-order -in general nonlinear-pde (1.17), F 2 = S(q, α, t). Note that the solution in general involves s constants {α i, i = 1,, s}. The s + 1st constant involved in the problem is a trivial one, because if S is a solution, so is S + A, where A is an arbitrary constant. It is now possible to use the defining equation of the generating function F 2 β i = S(q, α, t) α i (1.18) to obtain the new [constant] coordinates {β i, i = 1,, s}; finally, turning inside out (1.18) yields the trajectories q j = q j (α, β, t). (1.19) In other words, a solution of the Hamilton-Jacobi equation (1.17) provides a solution of the original dynamical problem Relationship to action It can be easily shown that the solution of the Hamilton-Jacobi equation satisfies or S(q, α, t) S(q, α, t 0 ) = ds dt = L, (1.20) t t 0 dτ L(q, q, τ) (1.21) where the r.h.s involves the actual particle trajectories; this shows that the solution of the Hamilton-Jacobi equation is indeed the extremum of the action function used in Lagrangian mechanics Conservative systems If the Hamiltonian does not depend explicitly on time, it is possible to separate out the time variable, i.e. S(q, α, t) = W (q, α) λ 0 t (1.22) where now the time-independent function W (q) (Hamilton s characteristic function) satisfies ( H q 1, q s ; W,, W ) = λ 0, (1.23) q 1 q s and involves s 1 independent constants, more precisely, the s constants α 1, α s depend on λ 0. 4
12 1.3.4 Separation of variables 1 Background: Hamiltonian mechanics The previous example separated out the time coordinate from the rest of the variables of the HJ function. Suppose q 1 and W q 1 enter the Hamiltonian only in the combination φ 1 (q 1, W q 1 ). The Ansatz W = W 1 (q 1 ) + W (q 2,, q s ) (1.24) in (1.23) yields H (q 2, q s ; W,, W ; φ 1 q 2 q s ( q 1, W ) ) 1 = λ 0 ; (1.25) q 1 since (1.25) must hold identically for all q, we have H ( φ 1 q 1, W ) 1 q 1 ) (q 2, q s ; W,, W ; λ 1 q 2 q s = λ 1 = λ 0. (1.26) The process can be applied recursively if the separation condition holds. Note that cyclic coordinates lead to a special case of separability; if q 1 is cyclic, then φ 1 = W q 1 = W 1 q 1, and hence W 1 (q 1 ) = λ 1 q 1. This is exactly how the time coordinate separates off in conservative systems (1.23). Complete separability occurs if we can write Hamilton s characteristic function - in some set of canonical variables - in the form W (q, α) = i W i (q i, α 1,, α s ). (1.27) Periodic motion. Action-angle variables Consider a completely separable system in the sense of (1.27). The equation p i = S q i = W i(q i, α 1,, α s ) q i (1.28) provides the phase space orbit in the subspace (q i, p i ). Now suppose that the motion in all subspaces {(q i, p i ), i = 1,, s} is periodic - not necessarily with the same period. Note that this may mean either a strict periodicity of p i, q i as a function of time (such as occurs in the bounded motion of a harmonic oscillator), or a motion of the freely rotating pendulum type, where the angle coordinate is physically significant only mod 2π. The action variables are defined as J i = 1 2π p i dq i = 1 2π dq i W i (q i, α 1,, α s ) q i (1.29) and therefore depend only on the integration constants, i.e. they are constants of the motion. If we can turn inside out (1.29), we can express W as a function of the J s instead of the α s. Then we can use the function W as a generating function of a canonical transformation to a new set of variables with the J s as new momenta, and new angle coordinates θ i = W J i = W i(q i, J 1,, J s ) J i. (1.30) 5
13 1 Background: Hamiltonian mechanics In the new set of canonical variables, Hamilton s equations of motion are J i = 0 θ i = H(J) J i ω i (J). (1.31) Note that the Hamiltonian cannot depend on the angle coordinates, since the action coordinates, the J s, are - by construction - all constants of the motion. In the set of action-angle coordinates, the motion is as trivial as it can get: J i = const θ i = ω i (J) t + const. (1.32) Complete integrability A system is called completely integrable in the sense of Liouville if it can be shown to have s independent conserved quantities in involution (this means that their Poisson brackets, taken in pairs, vanish identically). If this is the case, one can always perform a canonical transformation to action-angle variables. 1.4 Symmetries and conservation laws A change of coordinates, if it reflects an underlying symmetry of physical laws, will leave the form of the equations of motion invariant. Because Lagrangian dynamics is derived from an action principle, any such infinitesimal change which changes the particle coordinates and adds a total time derivative to the Lagrangian, i.e. q i q i = q i + ɛf i (q, t) q i q i = q i + ɛf i (q, t) (1.33) L = L + ɛ df dt, (1.34) will leave the equations of motion invariant. On the other hand, the transformed Lagrangian will generally be equal to and therefore the quantity will be conserved. L ({q i, q i}) = L({q i, q i}) = L({q i, q i }) + = L({q i, q i }) + = L({q i, q i }) + s i=1 s [ L ɛf i + L ] ɛf q i q i i s [ ( ) d L ɛf i + L ] ɛf dt q i q i i s ( ) d L f i dt q i i=1 i=1 i=1 Such underlying symmetries of classical mechanics are: L q i f i F (1.35) 6
14 1.4.1 Homogeneity of time 1 Background: Hamiltonian mechanics L = L(t + ɛ) = L(t) + ɛdl/dt, i.e. F = L; furthermore, q i = q i(t + ɛ) = q i + ɛ q i, i.e. f i = q i. As a result, the quantity s L H = q i L (1.36) q i (Hamiltonian) is conserved. i= Homogeneity of space The transformation q i q i + ɛ (hence f i = 1) leaves the Lagrangian invariant (F = 0). The conserved quantity is s L P = (1.37) q i (total momentum). i= Galilei invariance The transformation q i q i ɛt (hence f i = t) does not generally change the potential energy (if it depends only on relative particle positions). It adds to the kinetic energy a term ɛp, i.e. F = m i q i. The conserved quantity is (uniform motion of the center of mass). s m i q i P t (1.38) i= Isotropy of space (rotational symmetry of Lagrangian) Let the position of the ith particle in space be represented by the vector coordinate q i. Rotation around an axis parallel to the unit vector ˆn is represented by the transformation q i q i + ɛ f i where f i = ˆn q i. The change in kinetic energy is ɛ i q i f i = 0. If the potential energy is a function of the interparticle distances only, it too remains invariant under a rotation. Since the Lagrangian is invariant, the conserved quantity (1.35) is s i=1 L q i f i = s m i qi (ˆn q i ) = ˆn I, i=1 where is the total angular momentum. s I = m i ( q i q i ) (1.39) i=1 7
15 1.5 Continuum field theories 1 Background: Hamiltonian mechanics Lagrangian field theories in 1+1 dimensions Given a Lagrangian in 1+1 dimensions, L = dxl(φ, φ x, φ t ) (1.40) where the Lagrangian density L depends only on the field φ and first space and time derivatives, the equations of motion can be derived by minimizing the total action S = dtdxl (1.41) and have the form d dt ( L φ t ) + d ( ) L L dx φ x φ = 0. (1.42) Symmetries and conservation laws The form (1.42) remains invariant under a transformation which adds to the Lagrangian density a term of the form ɛ µ J µ (1.43) where the implied summation is over µ = 0, 1, because this adds only surface boundary terms to the action integral. If the transformation changes the field by δφ, and the derivatives by δφ x, δφ t, the same argument as in discrete systems leads us to conclude that L L δφ + δφ x + L ( dj0 δφ t = ɛ φ φ x φ t dt + dj ) 1 (1.44) dx which can be transformed, using the equations of motion, to ( ) d L δφ + L δφ t + d ( ) L δφ + L ( dj0 δφ x = ɛ dt φ t φ t dx φ x φ x dt + dj ) 1 dx (1.45) Examples: 1. homogeneity of space (translational invariance) x x + ɛ δφ = φ(x + ɛ) φ(x) = φ x ɛ δφ t = φ t (x + ɛ) φ t (x) = φ xt ɛ δφ x = φ x (x + ɛ) φ x (x) = φ xx ɛ δl = dl dl δx = dx dx ɛ J 1 = L, J 0 = 0. (1.46) Eq. (1.45) becomes ( ) d L φ x + L φ xt + d ( ) L φ x + L φ xx = dl dt φ t φ t dx φ x φ x dx or (1.47) ( ) d L φ x + d ( ) L φ x L = 0 ; (1.48) dt φ t dx φ x 8
16 1 Background: Hamiltonian mechanics integrating over all space, this gives dx L φ x P φ t (1.49) i.e. the total momentum is a constant. 2. homogeneity of time t t + ɛ δφ = φ(t + ɛ) φ(t) = φ t ɛ δφ t = φ t (t + ɛ) φ t (t) = φ tt ɛ δφ x = φ x (t + ɛ) φ x (t) = φ xt ɛ δl = dl dl δt = dt dt ɛ J 0 = L, J 1 = 0. (1.50) Eq. (1.45) becomes ( ) d L φ t + L φ tt + d ( ) L φ t + L φ tx = dl dt φ t φ t dx φ x φ x dt or (1.51) ( ) d L φ t L + d ( ) L φ t = 0 ; (1.52) dt φ t dx φ x integrating over all space, this gives [ ] L dx φ t L H (1.53) φ t i.e. the total energy is a constant. 3. Lorentz invariance 1.6 Perturbations of integrable systems Consider a conservative Hamiltonian system H 0 (J) which is completely integrable, i.e. it possesses s independent integrals of motion. Note that I use the action-angle coordinates, so that H 0 is a function of the (conserved) action coordinates J j. The angles θ j are cyclic variables, so they do not appear in H 0. Suppose now that the system is slightly perturbed, by a time-independent perturbation Hamiltonian µh 1 (µ 1) A sensible question to ask is: what exactly happens to the integrals of motion? We know of course that the energy of the perturbed system remains constant - since H 1 has been assumed to be time independent. But what exactly happens to the other s 1 constants of motion? The question was first addressed by Poincaré in connection with the stability of the planetary system. He succeeded in showing that there are no analytic invariants of the perturbed system, i.e. that it is not possible, starting from a constant Φ 0 of the unperturbed system, to construct quantities Φ = Φ 0 (J) + µφ 1 (J, θ) + µ 2 Φ 2 (J, θ), (1.54) where the Φ n s are analytic functions of J, θ, such that {Φ, H} = 0 (1.55) 9
17 1 Background: Hamiltonian mechanics holds, i.e. Φ is a constant of motion of the perturbed system. The proof of Poincaré s theorem is quite general. The only requirement on the unperturbed Hamiltonian is that it should have functionally independent frequencies ω j = H 0 / J j. Although the proof itself is lengthy and I will make no attempt to reproduce it, it is fairly straightforward to see where the problem with analytic invariants lies. To second order in µ, the requirement (1.55) implies {Φ 0 + µφ 1 + µ 2 Φ 2, H 0 + µh 1 } = 0 {Φ 0, H 0 } + µ ({Φ 1, H 0 } + {Φ 0, H 1 }) + µ 2 ({Φ 2, H 0 } + {Φ 1, H 1 }) = 0. The coefficients of all powers must vanish. Note that the zeroth order term vanishes by definition. The higher order terms will do so, provided {Φ 1, H 0 } = {Φ 0, H 1 } (1.56) {Φ 2, H 0 } = {Φ 1, H 1 }. The process can be continued iteratively to all orders, by requiring {Φ n, H 0 } = {Φ n+1, H 1 }. (1.57) Consider the lowest-order term generated by (1.57). Writing down the Poisson brackets gives s ( Φ1 H 0 Φ ) 1 H 0 s ( Φ0 H 1 = Φ ) 0 H 1. (1.58) θ i J i J i θ i θ i J i J i θ i j=1 The second term on the left hand side and the first term on the right-hand side vanish because the θ s are cyclic coordinates in the unperturbed system. The rest can be rewritten as s j=1 ω i (J) Φ 1 θ i = j=1 s j=1 Φ 0 J i H 1 θ i. (1.59) For notational simplicity, let me now restrict myself to the case of two degrees of freedom. The perturbed Hamiltonian can be written in a double Fourier series H 1 = n 1,n 2 A n1,n 2 (J 1, J 2 ) cos(n 1 θ 1 + n 2 θ 2 ). (1.60) Similarly, one can make a double Fourier series ansatz for Φ 1, Φ 1 = n 1,n 2 B n1,n 2 (J 1, J 2 ) cos(n 1 θ 1 + n 2 θ 2 ). (1.61) Now apply (1.59) to the case Φ 0 (J) = J 1. Using the double Fourier series I obtain B (J n 1) 1 n 1,n 2 = A n1,n n 1 ω 1 + n 2 ω 2, (1.62) 2 which in principle determines the first-order term in the µ expansion of the constant of motion J 1 which should replace J 1 in the new system. It is straightforward to show, using the same process for J 2, that the perturbed Hamiltonian can be written in terms of the new constants J 1 as H = H 0 (J 1, J 2) + O(µ 2 ). (1.63) Unfortunately, what looks like the beginning of a systematic expansion suffers from a fatal flaw. If the frequencies are functionally independent, the denominator in (1.62) will in general vanish on a denumerably infinite number of surfaces in phase space. This however means that Φ 1 cannot be an analytic function of J 1, J 2. Analytic invariants are not possible. All integrals of motion - other than the energy - are irrevocably destroyed by the perturbation. 10
18 2 Background: Statistical mechanics 2.1 Scope Classical statistical mechanics attempts to establish a systematic connection between microscopic theory which governs the dynamical motion of individual entities (atoms, molecules, local magnetic moments on a lattice) and the macroscopically observed behavior of matter. Microscopic motion is described - depending on the particular scale of the problem - either by classical or quantum mechanics. The rules of macroscopically observed behavior under conditions of thermal equilibrium have been codified in the study of thermodynamics. Thermodynamics will tell you which processes are macroscopically allowed, and can establish relationships between material properties. In principle, it can reduce everything - everything which can be observed under varying control parameters ( temperature, pressure or other external fields) to the equation of state which describes one of the relevant macroscopic observables as a function of the control parameters. Deriving the form of the equation of state is beyond thermodynamics. It needs a link to microscopic theory - i.e. to the underlying mechanics of the individual particles. This link is provided by equilibrium statistical mechanics. A more general theory of non-equilibrium statistical mechanics is necessary to establish a link between non-equilibrium macroscopic behavior (e.g. a steady state flow) and microscopic dynamics. Here I will only deal with equilibrium statistical mechanics. 2.2 Formulation A statistical description always involves some kind of averaging. Statistical mechanics is about systematically averaging over hopefully nonessential details. What are these details and how can we show that they are nonessential? In order to decide this you have to look first at a system in full detail and then decide what to throw out - and how to go about it consistently Phase space An Hamiltonian system with s degrees of freedom is fully described at any given time if we know all coordinates and momenta, i.e. a total of 2s quantities (=6N if we are dealing with point particles moving in three-dimensional space). The microscopic state of the system can be viewed as a point, a vector in 2s dimensional space. The dynamical evolution of the system in time can be viewed as a motion of this point in the 2s dimensional space (phase space). I will use the shorthand notation Γ (q i, p i, i = 1, s) to denote a point in phase space. More precisely, Γ(t) will denote a trajectory in phase space with the initial condition Γ(t 0 ) = Γ Note that trajectories in phase space do not cross. A history of a Hamiltonian system is determined by differential equations which are first-order in time, and is therefore reversible - and hence unique. 11
19 2.2.2 Liouville s theorem 2 Background: Statistical mechanics Consider an element of volume dσ 0 in phase space; the set of trajectories starting at time t 0 at some point Γ 0 dσ 0 lead, at time t to points Γ dσ. Liouville s theorem asserts that dσ = dσ 0. (invariance of phase space volume). The proof consists of showing that the Jacobi determinant (q, p) D(t, t 0 ) (q 0, p 0 (2.1) ) corresponding to the coordinate transformation (q 0, p 0 ) (q, p), is equal to unity. Using general properties of Jacobians (q, p) (q, p) (q 0, p 0 = ) (q 0, p) (q 0, p) (q 0, p 0 ) = (q) (p) (q 0 ) p=const (p 0 ) (2.2) q=const and D(t, t 0 t = t=t0 s i=1 ( qi + ṗ ) i = q i p i t=t0 s i=1 ( 2 H q i p i ) 2 H = 0, (2.3) p i q i and noting that D(t 0, t 0 ) = 1, it follows that D(t, t 0 ) = 1 at all times Averaging over time Consider a function A(Γ) of all coordinates and momenta. If you want to compute its longtime average under conditions of thermal equilibrium, you need to follow the state of the system over a long time, record it, evaluate the function A at each instant of time, and take a suitable average. Following the trajectory of the point in phase space allows us to define a long-time average 1 T Ā = lim dta[γ(t)]. (2.4) T T 0 Since the system is followed over infinite time this can then be regarded as a true equilibrium average. More on this later Ensemble averaging On the other hand, we could consider an ensemble of identically prepared systems and attempt a series of observations. One system could be in the state Γ 1, another in the state Γ 2. Then perhaps we could determine the distribution of states ρ(γ), i.e. the probability ρ(γ)δγ, that the state vector is in the neighborhood (Γ, Γ + δγ). The average of A in this case would be < A >= dγρ(γ)a(γ) (2.5) Note that since ρ is a probability distribution, its integral over all phase space should be normalized to unity: dγρ(γ) = 1 (2.6) A distribution in phase space must obey further restrictions. Liouville s theorem states that if we view the dynamics of a Hamiltonian system as a flow in phase space, elements of volume are invariant - in other words the fluid is incompressible: d dt ρ(γ, t) = {ρ, H} + ρ(γ, t) = 0. (2.7) t 12
20 2 Background: Statistical mechanics For a stationary distribution ρ(γ) - as one expects to obtain for a system at equilibrium - {ρ, H} = 0, (2.8) i.e. ρ can only depend on the energy 2. This is a very severe restriction on the forms of allowed distribution functions in phase space. Nonetheless it still allows for any functional dependence on the energy. A possible choice (Boltzmann) is to assume that any point on the phase space hypersurface defined by H(Γ) = E may occur with equal probability. This corresponds to ρ(γ) = 1 δ {H(Γ) E} (2.9) Ω(E) where Ω(E) = dγ δ {H(Γ) E} (2.10) is the volume of the hypersurface H(Γ) = E. This is the microcanonical ensemble. Other choices are possible - e.g. the canonical (Gibbs) ensemble defined as ρ(γ) = 1 Z(β) e βh(γ) (2.11) where the control parameter β can be identified with the inverse temperature and Z(β) = dγe βh(γ) (2.12) is the classical partition function Equivalence of ensembles The choice of ensemble, although it may appear arbitrary, is meant to reflect the actual experimental situation. For example, the Gibbs ensemble may be derived - in the sense that it can be shown to correspond to a small (but still macroscopic) system in contact with a much larger reservoir of energy - which in effect holds the smaller system at a fixed temperature T = 1/β. Ensembles must - and to some extent can - be shown to be equivalent, in the sense that the averages computed using two different ensembles coincide if the control parameters are appropriately chosen. For example a microcanonical average of a function A(Γ) over the energy surface H(Γ) = ɛ will be equal with the canonical average at a certain temperature T if we choose ɛ to be equal to the canonical average of the energy at that temperature, i.e. < A(Γ) > micro ɛ =< A(Γ) > canon T if ɛ =< H(Γ) > canon T. If ensembles can be shown to be equivalent to each other in this sense, we do not need to perform the actual experiment of waiting and observing the realization of a large number of identical systems as postulated in the previous section. We can simply use the most convenient ensemble for the problem at hand as a theoretical tool for calculating averages. In general one uses the canonical ensemble, which is designed for computing average quantities as functions of temperature Ergodicity The usage of ensemble averages - and therefore of the whole edifice of classical statistical mechanics - rests on the implicit assumption that they somehow coincide with the more physical time averages. Since the various ensembles can be shown to be equivalent (cf. 2 or - in principle - on other conserved quantities; in dealing with large systems it may well be necessary to account for other macroscopically conserved quantities in defining a proper distribution function. 13
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Archive Listing
September 28, 2008 - September 21, 2008
. The maestro is in the news a couple of ways this week. First,
it seems there's been a rediscovery of a lost
manuscript: Predictably, it's being used to make lesser men feel
less lesser:
Nobody can play the music yet, because he left out information like the
key and so forth that mere mortals have to have before they can
orchestrate a deathless doodle.
Second, there's news about the long-disputed skull currently in the possession of an Austrian foundation. We may soon have a better idea about whether it belonged to Wolfgang or somebody else..
The scuttlebutt has it that the gravedigger who buried Mozart
subsequently stole his skull and sold it. Scientists have managed to
procure the thighbone of an aunt to use it in DNA comparisons. We'll
Scientists are never satisfied, of course. Without their dumb tests,
they're adrift. It doesn't matter that jettisoned body parts have served as soothsayers to millions over the years, capable of
answering every "yes or no" question put to them.
Oh? You doubt it? Then give it a try. Frame your question and prepare to hear the voice of the greatest genius yet born in the -- what d'you call it? -- Common Era?
You'll see.
. Frankly, we can't make out many of the details in what's
going on out there. All that's clear is that everyone's involved and
everyone's getting dirty. Anyone who can decipher some real highlights
of the action is free to offer them in the Comment section. I'm not
even going to try.
Meanwhile, gas prices keep going up, the financial system keeps melting down, people on the gulf coast are still mired in mud of their own, Pakistan is imploding, Iran is toiling away nonstop on its atom bomb, our own leftist loons are applauding Ahdumjihad for blaming the U.S. financial crisis on the War in Iraq, and tragically, Horatio Caine is not really dead. (Bret Favre and the Jets, on the other hand, just might be.)
I'm sure all the campaign geniuses know what they're doing and why it's better than acting like a grownup. Maybe they'll explain it all to us one day. Until then, here's the best advice a lone blogger can give you.
Things will get better. They do that. Sometimes they do. But not CSI Miami.
Thank God we can trust the government
to look out for us, you know? It wasn't always this way. Here's
something of a prophecy from nearly 20 years ago. It's from The
Boomer Bible.� Which continues to be right about a lot
of things.
Here endeth today's lesson. Unless you're prepared to consider even
more evidence
that InstaPunk is always right.
Nah. You don't want to do that. Think about Hope and Change instead.
P.S. Time capsule moment. If you follow the "InstaPunk is always right" link, note that while I anticipated a Hillary nomination, I also suggested the electorate might be in the mood for a "super-smart" candidate. Isn't that really the basis of the Obama campaign? No experience. No accomplishments. No plans to speak of. But he's just "super-smart." Newt would have taken him apart in three debates. (And I mean absolutely nothing left moving on the field of battle larger than a toe...) But read the comments on that post. Everyone telling me I was wrong because they just knew conservatives had to bend their principles this time for the sake of getting elected. And the commenters weren't alone. Somewhat later in the day I crossed swords with Weekly Standard wunderkind Dean Barnett, who still hasn't regained any credibility after his long infatuation with Mitt Romney. When you look at just how nasty this campaign is getting, does anyone really think Mitt's sunny banality would play with the negative ads he'd have to be running by now?
So there's a second lesson of the day. Conservatives blew it this time, Because they had no guts. Their convictions and principles weren't proof against their fears and their media-induced anxiousness to compromise on issues that -- as I predicted -- would no longer be the determining factors in the 2008 election. The bad news? We may very well get ZERObama for president. That's an outcome that could have been avoided with a show of character by all you 'pragmatic' Romney, Giuliani, Thompson, and McCain supporters. (Peter: Don't you dare. Ron Paul was never a candidate; he was always only a badly written fictional character, Eugene McCarthy rewritten as a graphic novel for for the solipsistic I-pod set.)
Disgusted. Yeah, I'm voting McCain. But I'm still d-i-s-g-u-s-t-e-d.

subset: commoncrawl


text: School-Age Shop Online at www.RedleafPress.org Whether your program operates before or after school, on non-school days, or during the summer, this book will help you create a dymanic place where everyone enjoys spending time. It takes you through all of the considerations that affect your program and then lays out a process to help you improve the Great Afterschool Programs and temporal, interpersonal, Spaces That Wow! and physical dimensions #541228 $44.95 of your environment. (E-book #542546 $44.95) Hundreds of ideas are included! Age focus: 5–12. Softbound, 240 pgs. LI S H E D BY ESS PUB These true-to-life stories of bullying are told from all perspectives: the role of the target, the bystander, and the person doing the bullying. Each book concludes with activity pages for kids and information for adults. Does your program have the wow factor? R ED PR Bullying from three third graders' perspectives LEAF 101 treasure hunt cards Weird! Colorful, polka-dotted Luisa changes everything about herself to avoid being bullied, and she learns a valuable lesson in the process. Age focus: 5–9. Hardcover, 48 pgs. #423982 $15.95 Sharpen observation skills, build vocabulary, and develop thinking skills with this treasure hunt game. Age focus: 4 and up. Treasure Hunt for Primary Ages in a Jar #429595 $9.95 Dare! When Jayla witnesses her friend being bullied, she is too scared to stand up for her, but she soon finds the courage to do what's right. Age focus: 5–9. Hardcover, 48 pgs. 101 brainteasers #423999 $15.95 Brain Games in a Jar #429755 $9.95 Tough! Sam bullies kids at school before realizing it only makes her feel worse, and there are caring people who can help her change. Age focus: 5–9. Hardcover, 48 pgs. #424002 $15.95 Save almost $4 when you buy the set One copy each of Dare!, Wierd!, and Tough! Dare! Weird! Tough! Set #424000 $43.95 Pg38&39.All.WS14.indd 2 Use the brainteasers, word-play puzzles, and brain boosters to challenge kids to think creatively. Age focus: 6 and up. NEW! 10 things to know to improve your work with children In this audio program, national speaker, educational consultant, and behavioral health therapist Jim Harris uses his vast knowledge of children, excellent storytelling, and a real world approach to help you be more effective in your work with children. CD, 80 min. 10 Things You Need to Know About Kids #326366 $14.95 39 11/4/13 1:51 PM


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Urban Meyer Health Problems? Top 10 Foods That Cause Heartburn
One time, we spent an excruciating 45 minutes at a family dinner thinking a tapeworm was chewing up our insides. Turns out we just had a mean case of heartburn.
Maybe Urban Meyer has the same problem.
Saturday, the University of Florida's Gators football team's head coach resigned from the football program for undefined health related reasons.
A day later, Urban changed his mind and decided to stay on board, but to take a leave of absence of indeterminate length starting after the Gators' Sugarbowl game against Cincinnati later this week.
So what's up with Urban Meyer's health? We don't know, but if it has got anything to do with heartburn here's our advice to him.
These are our top ten foods that cause heartburn.
10. Chili Cheese Fries
Can you taste the reflux just thinking about it?
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"$100, right?" asks Josh West as he takes money from photogragpher George Ce in this second scene of Titan Men's latest by director Joe Gage, Chain Reaction. "Now what do you want?" George starts filming the bearded stranger, who is dressed in a cutoff flannel and cowboy hat. "Open your shirt," George orders, the first of many that have Josh finally stripped down to his jockstrap - his balls peeking out as his boner throbs. "Wanna see what's inside?" he asks, slowly releasing his monster. George continues to film the action, tension building as Josh repeatedly lifts up his beast and lets it bounce down, the impressive weight of his heavy cock getting George even more hot and bothered. George opens wide and swallow's as much of Josh's cock as he can, and soon feeding his own uncut beauty to Josh - who gags on it. George whips his dick on the sucker's fuzzy face. He offers his ass which Josh greedily eats before shoving his cock inside, working up a hot rhythm: "You like this? This is a cowboy fuck!" The bottom turns over for more - and is soon covered in cum, Josh's hot load running down the middle of the stud's tatted chest.
Tags: fucking (1454), Titan Men (139), cumshot (295), cowboy (7), big cock (1196),


text:
Sterling Silver Small and Medium Ball Stud and Hoop Earrings Set
Item# 19935352
Three great looks -- one great price! All fashioned of sterling silver, this set includes both small and medium ball-shaped studs as well as a pair of charming Bali hoops. These polished stud earrings secure with friction backs; the Bali hoops earrings secure with wire backs.
Special Offers
Typographic errors are subject to correction. Merchandise enlarged to show detail and may not always be exactly as pictured. Promotions, prices, styles and availability may vary by store and online.


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You have an important occasion coming in your way, for which you want to wear your favourite dress. You will try your favourite dress and it will not fit you! A total disappointment! How do you lose that extra flab to fit into that dress? Well, try the banana-milk diet, which would surely help you lose some weight in an easy and effective way.
The banana-milk diet has been proved to be an effective weight loss method that would require you to practice it only for 3 to 4 days and you would surely see incredible results!
[ Read: Does Banana Shake Help To Gain Weight ]
How Does It Work?
The banana and milk diet program was first developed by Dr. George Harrop in 1934. The idea behind this diet plan was to let the body consume lesser calories and still stay healthy. The diet involves consuming 2 to 3 bananas along with one cup fat-free milk for each meal. There is some flexibility here as you may consume the bananas before or after having the milk or even blend the two together to make a banana smoothie. One thing that you need to consume along with this diet is lots and lots of water.
Following this diet plan helps one lose the excess fat in the body along with the muscle mass. This milk and banana diet allows you to consume lesser than 1000 calories each day and thus the body can easily shed weight at a fast pace.
Here Is The Maths:
Each banana contains around 100 calories and a cup of milk would not contain more than 80 calories. Hence, consuming a meal of this diet thrice would not let you have more than 900 calories per day.
[ Read: Milk Diet for Weight Loss ]
The Benefits Of Banana And Milk Diet:
Banana's Portion Of Benefits:
- Bananas, as we all know, are a highly nutritious fruit laden with vitamins and minerals, especially potassium (about 422 mg in one banana) which is vital for the normal functioning of the body.
- They also contain fibers (about 3 gms in one banana), which help the body get rid of the toxins that are accumulated in it.
- These also give a satiated feeling, making one feel hungry after long hours. Above all, they are tastier and consuming them is easier.
Milk's Portion Of Benefits:
- Fat-free milk is a quintessential element of our daily diet. It is rich in calcium and proteins and contains no fat.
- The calcium in it helps in the development and retention of bone strength. It also help in the normal functioning of hormones.
- It also contains proteins that are required for the development of the body muscles.
Combined Benefits:
- Put together, bananas and milk provide the body with ample doses of proteins, vitamins, fibres and minerals without any fat!
- The nutrients received from this diet are enough to supply the body with a sufficient amount of energy to sustain for a period of 3 to 4 days.
[ Read: Benefits Of Banana Juice For Health ]
Some Points Of Caution:
A banana and milk diet regime can be followed by anyone who wants to lose weight in an emergency situation. However, there are a few things that one should keep in mind when following it:
- Initially, one might feel a bit weak as the calorie intake gets reduced incredibly during this diet. The weakness is not difficult enough to manage, but if in case it does get tough to manage, you could consume one proper meal per day. Still, try to keep the fat intake less for this meal.
- The banana-milk diet is not recommended to be followed by women during their menstrual cycle. This diet lacks minerals like iron, zinc, copper and some vitamins that are quite important to be consumed during this time. Still, if the diet has to be taken at this time, make sure you have some vitamin and mineral supplements along with it.
- The banana-milk diet plan should not be followed for more than 4 days as some of the vital elements required for the body are missing in it. Following this diet for 4 days helps one lose around 4 kgs of body weight easily. If one wants to lose more weight, he/she could take a gap of about one week and undertake another round of this diet plan.
Is this diet sounding helpful? Hope you would definitely try this banana and milk diet plan for weight loss! Feel free to share your thoughts or experiences with us in the comment section.
Recommended Articles:
- The Banana Diet: Bananas For Weight Loss
- This Remarkable Diet Can Make You Lose 10 Pounds In Just 3 Weeks!
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No. 9 Kentucky Takes Down Louisiana-Lafayette 5-2
Feb. 29, 2012
LEXINGTON, Ky. - The ninth-ranked University of Kentucky men's tennis team won the doubles point and then claimed four of the six singles matches to earn a convincing 5-2 win over Louisiana-Lafayette on Wednesday in Lafayette, La.
The win over the Ragin Cajuns improves Kentucky's record to 11-3 as it prepares to begin its difficult Southeastern Conference schedule starting Friday. The Wildcats will start the SEC slate at No. 17 LSU at 4 p.m. ET before traveling to No. 47 Arkansas on Sunday at 12:30 p.m. ET. A complete preview for the weekend will be posted Thursday on UKathletics.com.
"This was a really hard-fought win," UK head coach Dennis Emery said. "We felt coming into today that Louisiana was a top-50 team at the end of the year and they showed that today with how well they played. They had a big, enthusiast crowd and were even better than we thought they would be. Hopefully, this match will help prepare us for this weekend as we open up conference play."
The match started with the Wildcats taking the doubles point behind wins on all three courts. Junior Anthony Rossi and sophomore Tom Jomby grabbed an 8-5 win at No. 1 doubles over Rick DeGroot and Carlin Murray, while sophomore Grant Roberts and senior Alex Musialek posted an 8-5 win over Brandon Farine and Yanick Mandl at No. 2 doubles. The Wildcats won a close contest at No. 3 doubles when sophomores Ryuji Hirooka and Panav Jha defeated Damian Farinola and Jarred Wynan 9-8 (7-4).
UK continued to perform well in singles action, claiming four of the six singles matches. Musialek, who is ranked 16th in the nation in singles, posted a come-from-behind 4-6, 6-2, 6-2 win at No. 1 singles over DeGroot. No. 98 Jomby scored a straight-sets win at No. 3 singles over Mandl 7-5, 6-3, while No. 107 Alejandro Gomez won a three-set thriller 2-6, 6-3, 6-4 at No. 4 singles over Ted Nilsson. Kentucky's fifth point came at No. 6 singles when Roberts took down Wynan 6-3, 6-4.
Louisiana posted wins at Nos. 2 and 5 singles. Murray defeated Kentucky's No. 14 Rossi in three sets 5-7, 6-4, 6-3 at court two, while Farinola defeated Jha 6-4, 6-4 at court five.
For more information on the Kentucky men's tennis team, follow "UKmentennis" on Twitter or "University of Kentucky men's tennis team" on Facebook.
No. 9 Kentucky 5, Louisiana 2
Wednesday, Feb. 29, 2012
Lafayette, La.
Singles competition
1. #16 Musialek, Alex (UK) def. DeGroot, Rick (UL) 4-6, 6-2, 6-2
2. Murray, Carlin (UL) def. #14 Rossi, Anthony (UK) 5-7, 6-4, 6-3
3. #98 Jomby, Tom (UK) def. Mandl, Yanick (UL) 7-5, 6-3
4. #107 Gomez, Alejandro (UK) def. Nilsson, Ted (UL) 2-6, 6-3, 6-4
5. Farinola, Damian (UL) def. Jha, Panav (UK) 6-4, 6-4
6. Roberts, Grant (UK) def. Wynan, Jarred (UL) 6-3, 6-4
Doubles competition
1. Rossi, Anthony/Jomby, Tom (UK) def. DeGroot, Rick/Murray, Carlin (UL) 8-5
2. Roberts, Grant/Musialek, Alex (UK) def. Farine, Brandon/Mandl, Yanick (UL) 8-6
3. Hirooka, Ryuji/Jha, Panav (UK) def. Farinola, Damian/Wynan, Jarred (UL) 9-8 (7-4)


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Stalin's Nervous Collapse
Published: May 31, 1992
To the Editor:
Reviewing Alan Bullock's "Hitler and Stalin: Parallel Lives" (March 22), Norman Davies faults the author for discussing the June 1941 Nazi invasion of the Soviet Union "without reference to recent suggestions from some Russians that Stalin was poised to launch an offensive against Germany at the same juncture." Perhaps the reason for this omission is that the overwhelming weight of historical evidence points to the conclusion that, far from being poised to attack, Stalin was completely unprepared for the sudden Nazi onslaught.
Stalin made it clear throughout the period of the Nazi-Soviet pact (1939-41) that he had an important stake in maintaining the alliance with Hitler. He shipped large quantities of raw materials and foodstuffs to Germany and even went so far as to deliver up scores of German Communist exiles to certain death at the hands of the Nazis. In order to avoid provoking Berlin, German reconnaissance flights over the western Soviet Union were allowed to go unchallenged up to the day of the invasion.
Detailed British and American warnings of an impending Nazi attack were dismissed by Stalin as a provocation, and similar reports by Soviet intelligence agents were also disregarded. When the invasion finally came, the Red Army simply collapsed along the entire front. For nearly two weeks after the invasion, Stalin neither appeared in public nor addressed the nation by radio. The consensus among historians is that he suffered a nervous collapse following his betrayal by an ally to whom he had shown such loyalty. LOUIS JAY HERMAN New York


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A big thank you goes out to all of our fantastic Early Beta User Group participants. We have been making incredible improvements since our last feature release that would not have been possible without them, and I'd like to highlight just a few of those.
- International Time Zones / Date & Time Formats
Finally! A major request from our friends outside the United States was the ability to set their time zones so date and time can be viewed in other time formats! Now, users will be able set and change the way that their dates and times are displayed (from MM/DD/YYYY to DD/MM/YYYY and AM/PM to the 24-hour format). Thanks Louis, Noerman, and Robert!
- Linking Existing
Many of you, and rightfully so, have asked for the ability to add emails, actions, and more to exiting project(s). We've answered your request and have improved on it! Now in IQTELL, you'll be able to add any entry type to another existing entry.
The basics will be configured for you already – e.g., adding emails and actions to existing projects; adding emails to existing actions – but the sky is the limit. With IQTELL, if you have an idea, share it with us and we'll tackle it together. A special thanks to Grace, Louis, and Ian!
- Calendar Syncing
One of the most highly requested features from our Beta users was the ability to connect a Google and Yahoo Calendar to their IQTELL account. It's still one we're working on carefully at the moment – we can see the light! (Exchange calendar support will be coming soon).
This will not be your standard synch; within IQTELL, you'll actually be able to pull all of your calendars into one super calendar.
- GTD Inbox
For our GTD users, we were happy to implement a GTD Inbox where you can add items as they come to mind and deal with each item individually at a later time, now available on our iPhone app as well. Thanks Robert!
- Evernote Anyone?
This is perhaps the most widely anticipated feature. It's something we have not seen anywhere else! Evernote is one of the best applications we've seen; and many of our users are also Evernote users.
We hope to release this feature by the end of January 2012. You will be able to view, modify and access all of your Evernote notebooks and notes within IQTELL with real time synchronization. Users will be able to leverage IQTELL's functionality on Evernote notes, adding reminders, calendar events, actions, projects, and more! Thanks to Ian and Stewart!
We are still working on some other highly requested features, such as keyboard shortcuts, tagging, and dashboard customization. We greatly appreciate all of the excellent feedback, so keep it coming! If you have any questions, suggestions, feedback (good or otherwise), feel free to let us know!
You can also follow us and get updates via our Facebook Page or our Twitter account. See you there :)
* GTD® is a registered trademark of the David Allen Company. IQTELL is not affiliated with the David Allen Company.


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Donald A. Eisner, Ph.D. J.D., is a licensed attorney and psychologist. Dr. Eisner has served as an expert witness in State and Federal Court as well as in Administrative Hearings. He has a Ph.D. from West Virginia University and a law degree from University of West Los Angeles. He was licensed to practice as an attorney in California in 1988. His background includes 20 years experience in negotiating and settling civil lawsuits.
Donald Eisner has been a Visiting Professor of Forensic Psychology at Alliant University where he taught courses on law and ethics in mental health Dr. Eisner has also taught courses on forensic psychology assessment and psychopathology. He is currently teaching law and ethics via distance learning. Dr. Eisner is Dean, Eisner Institute for Professional Studies. He has testified in State and Federal court on mental health issues. Dr. Eisner has written an academic textbook entitled The Death of Psychotherapy: From Freud to Alien Abductions. He has published twenty professional articles on forensic issues as well topics on gerontology. The pitfalls of expert witness testimony are examined in an American Journal of Forensic Psychology article.
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Travel Tips
A vibrant city like London has something in store for everyone who comes in touch with it. Attracting droves of people from all over the world, this capital city is one of its kinds. A little planning and hands on knowledge of the place will surely prove worthwhile and a lot more useful for your itinerary, making your visit a grand success. Listed here are those details regarding sightseeing, places to visit with your family, safety, hotels in London, tips to save those extra pennies, and a lot more. Let's have a look at the following:
Tips for Sightseeing in London
With a range of museums, galleries, theatres, castles, for sightseeing and trendy restaurants, pubs and bars for eating and boozing out, travellers are definitely spoilt for choice. Here is a look at the few:
• London city has a lot to offer for your kids. Your children will gather knowledge while playing around. Some of these must visit attractions are London Zoo, The Science Museum, Paddington Bear, The London Aquarium, among many more.
• Oxford Street and Regent Street in London is a shopper's paradise with top of the brands adorning its corners. Travellers can grab some finest deals on their spree. But be careful of the pickpockets especially on Oxford Street.
• Besides these, London Eye, Buckingham Palace, Tower of London, Hyde Park, and Regent Park among many more are some tourist spots, explorers to the city can savour.
• London has a great party and night club scene. With venues for party in every corner, travellers will find something or other to indulge in.
• Somerset House in London offers entertainment to all the age groups of people alike throughout the year, in form of wonderful open air concerts in summer and stunning ice rinks in winter.
• Make a point to visit London Dungeon, a unique tourist attraction in London which uses many special effects, and thrills.
• Comedy clubs in London will make you roll with laughter with downright hilarious acts of seasoned actors in milieu of swankiest clubs of London.
Safety tips in London
London is quite a travel friendly city and is quite safe in comparison to other countries. But it is always better to chart your sojourn and take caution in a foreign country. Some safety tips are:
• Avoid late night out while you are all alone. Always take proper lit main roads.
• Always keep a check on your bags and luggage while on your way to sightseeing or eating out in restaurants
• Never accept food items or drink from a stranger
• Behaving like a tourist will make you more vulnerable to thieves. Be like the locals around.
• Hire legal black cabs for your travel in London
• Mini cabs are illegal, un booked and not safe for moving around the city
• Details regarding marshalled taxi ranks and pick up points are provided by London transport for picking taxis securely by travellers even late at nights.
• Visitors need to take proper precautions while taking out money from ATMs in London
• You can handily and safely drink the clean tap water of London and there is absolutely no need to buy bottled waters.
• Always carry waste bags or bum bags for your requisites
• Headphones can be done away with especially when travelling alone
• Avoid carrying too much cash
• In case your mobile gets stolen or missing, inform the service provider or the cops as soon as possible
Weather of London
London weather can be unpredictable at times. A shade and an umbrella or a raincoat is all you need while packing your travel bag in London. But even if there is a slight change in program, travellers are deluged with so many thrills both indoors and outdoors that not even a fleeting moment of dullness would be observed. Capital city observes a balmy weather in general. Visitors can plan their vacation any time of the year at ease. The maximum temperature in London can be around 30° C observed during the months of August.
In case there is any serious health problem or contingency of any kind, call the number 999 or 112 for medical ambulance, fire and police. These numbers are toll free. But make a point to call them only in case of emergency and not otherwise.
Travellers can save a lot of money while adhering to these aforementioned tips and enjoy lifetime memories with their trip.


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2004-03-17 at 9:09:00 am #6596
Canon Likely To Post Record Group Net Profit For Jan-March Canon Inc. said Tuesday it expects to post a record high group net profit for the January-March quarter thanks to its strong performance in the first two months of the year. "The January and February figures were quite good. So we think we can expect ( earnings) figures close to" those reported in the Nihon Keizai Shimbun, a company spokesman said.
The Nihon Keizai Shimbun reported in its Tuesday morning edition that Canon's group net profit for the January-March period is likely to rise 26% on year to Y90 billion. That's much stronger than a Y73 billion profit the company had projected earlier and represents a record high amount.
Continued strong sales of digital cameras and office equipment, as well as its aggressive cost- cutting program, will likely contribute to the higher earnings. Group sales for the January-March quarter are expected to edge up 5% to Y770 billion, the Nikkei reported.
The major Japanese maker of cameras, printers and copiers has been enjoying solid earnings results in recent years thanks to brisk sales of multifunction copiers and digital cameras.
Canon's group net profit soared 45% to Y275.73 billion in 2003 from Y190.74 billion in 2002, marking a record for the fourth year running. Its group operating profit jumped 31% to Y454.42 billion, while group revenue rose 4.1% to Y3.198 trillion.
In reporting its results for last fiscal year, Canon also forecast its group net profit would rise 3.7% to another record high of Y286 billion this year.
Canon is slated to report its January-March results in late April


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Balloon Decorations
Click through to our Facebook and "like"us to see our very latest designs and inspiration.
Delivering "MAD Balloons" to parties, special events & launches all over Sydney, NSW and across the nation, 7 days a week.
Go to our "Prices" page to see our most popular designs, a description and the price! Then you can also browse through our galleries to see many more inspiring creations.
Balloons are the most cost effective and best way to transform any space, and we hope that this website will get your creative juices flowing and give you lots of ideas for your next event.
For more theme ideas please check out the MAD Blog and Facebook, as we put pics up there of recent events, and other fun stuff all the time.
To discuss your ideas or place your order you can email us from this website. Or feel free to call and speak to our friendly staff.


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A man in Russia murdered two of his nearest individuals — his wife and closest companion – The twosome was having intercourse when Vladimir Sidorov got them amidst the procedure – The chafed man cut out his buddy's penis and wounded his better half to death Vladimir Sidorov, 35, ended up in the most noticeably bad comprehensible circumstance as he unearthed on his better half, 31, and closest companion, 32, having hot sex.
House in Tatarstan district where the twofold murder occurred The bizzare circumstance transformed into dramatization after the cuckold hauled out a blade, cut his companion's privates and over and again wounded his swindling spouse to death. Both significant others kicked the bucket at the scene and Sidorov called the police to admit to the killings. The bleeding show took plcae in Shama town, the Russian locale of Tatarstan, where every one of them three lived. As indicated by an announcement discharged by the investigative council, Sidorov had been home with the couple's youngsters while his better half professedly went to see a female companion.
However when the man found out his spouse actually had not visited her friend, he headed to his own friend who was supposed to have driven her to the meeting, but was not answering the phone. The statement reads in part: "Sidorov walked to the house of his friend who was supposed to have driven his wife – and there he found both of them in an intimate situation.
The suspect took out his knife, stabbed the male victim several times. He then cut off his genitals. As a result of the injuries both victims died at the scene of the crime. Having committed his crime, Sidorov called the local police office and reported the crime." Sidorov, who works as a veterinarian at a local farm, was later detained and taken to police station. He is now awaiting trial.
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Photo: Getty Images
Finding peace
Small changes in your routine can make you feel much more at peace.
Try these strategies from Deepak Chopra, MD, author of The Ultimate Happiness Prescription: 7 Keys to Joy and Enlightenment.
Photo: Getty Images
Tune in to your body
Whenever you feel any pain, fatigue, or anxiety, figure out what's causing it.
In order to be happy, you need to feel good physically, Dr. Chopra says.
So if you're exhausted, say, ask your husband to help so you can take a break.
Photo: Corbis
Be Switzerland
"You can save 99% of your psychological energyand feel happierif you can stop defending your point of view," says Dr. Chopra.
Instead of always pushing your way of thinking and setting up a tense win-or-lose situation, say, "I see your point of view."
Listening to other sides will improve your relationships and make you feel calmer and sunnier, too.
Photo: Corbis
Give yourself a pep talk
Try this instant confidence builder: Look in the mirror and say out loud or to yourself, "I am immune to criticism, I am beneath no one, I am fearless."
It may make you giggle, but repeating this mantra helps people stand taller, according to Dr. Chopra.
Photo: Corbis
Embrace the right now
We know you've heard it before, but enjoying the moment rather than dwelling on future worries is a lasting mood booster.
If you start to drift, say to yourself, "Focus on the present."
That will help snap you back to the good stuff in front of you.


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Meaning and Origin of: Hasan
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Boy name origins & meanings:
- Arabic : Good-looking
Family name origins & meanings:
- Muslim : from the Arabic personal name ̣Hasān 'good', 'handsome'. Hasan (c.625–669) and his brother Husain were sons of the khalif 'Alī ibn Abī ̣Tālib (see Ali) and, through their mother Fatima, grandsons of the Prophet Muhammad. Shiite Muslims regard Hasan and his brother Husain as the true successors of Muhammad. The name is popular among Sunni Muslims as well as Shiites.
- Jewish : variant of Hazan.