In physics, Brownian dynamics is a mathematical approach for describing the dynamics of molecular systems in the diffusive regime.
It is a simplified version of Langevin dynamics and corresponds to the limit where no average acceleration takes place.
This approximation is also known as overdamped Langevin dynamics or as Langevin dynamics without inertia.
In Brownian dynamics, the following equation of motion is used to describe the dynamics of a stochastic system with coordinates
:[1][2][3] where: In Langevin dynamics, the equation of motion using the same notation as above is as follows:[1][2][3]
In Brownian dynamics, the inertial force term
is so much smaller than the other three that it is considered negligible.
In this case, the equation is approximately[1] For spherical particles of radius
in the limit of low Reynolds number, we can use the Stokes–Einstein relation.
, and the equation reads: For example, when the magnitude of the friction tensor
increases, the damping effect of the viscous force becomes dominant relative to the inertial force.
Consequently, the system transitions from the inertial to the diffusive (Brownian) regime.
In 1978, Ermak and McCammon suggested an algorithm for efficiently computing Brownian dynamics with hydrodynamic interactions.
[2] Hydrodynamic interactions occur when the particles interact indirectly by generating and reacting to local velocities in the solvent.
three-dimensional particle diffusing subject to a force vector F(X), the derived Brownian dynamics scheme becomes:[1] where
is a diffusion matrix specifying hydrodynamic interactions, Oseen tensor[4] for example, in non-diagonal entries interacting between the target particle
is a Gaussian noise vector with zero mean and a standard deviation of
refers to the total number of particles.
This equation works for the dilute system where the near-field effect is ignored.
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