Brownian dynamics

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Brownian dynamics (BD) can be used to describe the motion of molecules in molecular simulation. It is a simplified version of Langevin dynamics and corresponds to the limit where no average acceleration takes place during the simulation run. This approximation can also be described as 'overdamped' Langevin dynamics, or as Langevin dynamics without inertia.

The equation of motion is

$0 \approx - \nabla \bar{U}(X)- \gamma M \dot{\bar{X}}+ \bar{R}(t),$

where $\nabla \bar{U}(X)$ describes the force as calculated from the particle interaction potentials; $\gamma M \dot{\bar{X}}$ describes the velocity-dependent friction; and $\bar{R}(t)$ is a random noise term. As on average no acceleration is assumed to take place, the sum of these terms is zero.