Ermak-McCammon Brownian dynamics

D. L. Ermak and J. A. McCammon, Brownian dynamics with hydrodynamic interaction, J. Chem. Phys., 69 (1978) 1352-1360. 

Ermak, D. L and McCammon, J. A., Brownian dynamics with hydrodynamic interactions. /. Chem. Phys. 69, 1352 (1978). 

The theory of Brownian motion was developed to describe the dynamics of a massive particle in a medium of small particles. Ermak and McCammon have formulated a Brownian dynamics simulation method suitable for concentrated dispersions. The method follows the traditional deterministic molecular dynamics algorithm used to simulate fluids, except that the set of 3N Newtonian equations is replaced by a set of 3N coupled Langevin equations ... 

The method of Ermak and McCammon is consistent with the Fokker-Planck equation, whose solution yields the complete phase-space distribution function directly. Because the sets of particle velocities v(t) and (t+At) are effectively uncorrelated for At the Brownian dynamics algorithm gives no information about instantaneous velocities (the mean square particle velocity (v (t)) over time intervals At is the equilibrium value, 3kT/m ). 

Ermak DL, McCammon JA (1978) Brownian dynamics with hydrodynamics interactions. J Chem Phys 69(4) 1352-1360... 

As with Newtonian molecular dynamics, a number of different algorithms have been developed to calculate the diffusional trajectories. An efficient algorithm for solving the Brownian equation of motion was introduced by Ermak and McCammon [21]. A detailed survey of this and other algorithms as well as their application can be found in Ref. 2. 

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