Computer simulations of Brownian motion of complex systems

Abstract

Care is needed with algorithms for computer simulations of the Brownian motion of complex systems, such as colloidal and macromolecular systems which have internal degrees of freedom describing changes in configuration. Problems can arise when the diffusivity or the inertia changes with the configuration of the system. There are some problems in replacing very stiff bonds by rigid constraints. These problems and their resolution are illustrated by some artificial models; firstly in one dimension, then in the neighbourhood of an ellipse in two dimensions and finally for the trimer polymer molecule.

Evaluation of the Kirkwood approximation for the diffusivity of channel-confined DNA chains in the de Gennes regime

“…[40][41][42] However, we do not use matrix-free approaches here because there is no computational advantage -we need to store the diffusion tensor to calculate the Kirkwood diffusivity, so we can also use it in the integration of Eq. (7).…”

“…43 The divergence term is not calculated explicitly but handled using midpoint algorithm. 40,42 The CPU time of the resulting algorithm scales as OðN 2:25 b Þ. This algorithm is useful for relatively small systems and has a favorable prefactor, but the N b scaling eventually becomes unfavorable for a large number of beads.…”

Accelerated Stokesian dynamics: Brownian motion

“…Replacing it by any higher order scheme, such as a mid-point or end-point algorithm, leads to an evolution equation without a mean drift term. 14 In this way, the explicit computation of ""R FU Ϫ1 , of order O(N 3 ), may be completely avoided. However, the price for this is that one has to compute two velocities by iteratively inverting R FU at each time step.…”

Influence of shear on globule formation in dilute solutions of flexible polymers

“…[3][4][5][6]39,40 In BD simulations, the particles obey Newton's laws of motion in an implicit solvent. The force balance on any particle is given by…”