evaluated at the particle center, is the symmetric part of the velocity-gradient tensor; and are the configuration-dependent resistance matrices that give the hydrodynamic force/torque on the particles due to their motion relative to the fluid () and due to the imposed shear flow (). Note that the subscripts on the matrices indicate the coupling between kinematic () and dynamic () quantities. One of the key features of Stokesian dynamics is its handing of the hydrodynamic interactions, which is fairly accurate without being computationally inhibitive (like boundary integral methods) for a large number of particles. Classical Stokesian dynamics requires operations where N is the number of particles in the system (usually a periodic box). Recent advances have reduced the computational cost to about Brownian force The stochastic or Brownian force arises from the thermal fluctuations in the fluid and is characterized by: The angle brackets denote an ensemble average, is the Boltzmann constant, is the absolute temperature and is the delta function. The amplitude of the correlation between the Brownian forces at time and at time results from the fluctuation-dissipation theorem for the N-body system. See also Immersed boundary method Stochastic Eulerian Lagrangian method References Statistical mechanics Equations Fluid mechanics