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BP: Fachverband Biologische Physik

BP 26: Posters II

BP 26.1: Poster

Thursday, February 28, 2008, 17:00–19:30, Poster A

Fast O(N²) Hydrodynamics for Brownian Dynamics Simulations — •Tihamér Geyer and Uwe Winter — Zentrum für Bioinformatik, Universität des Saarlandes, Saarbrücken, D–66041 Saarbrücken

In Brownian Dynamics (BD) simulations, the solvent molecules are replaced by a continuous solvent, thus greatly reducing the complexity and the required numerical effort. The polarizability of the solvent molecules is thereby taken into account by a shielded Coulomb interactions while the mechanical displacement of the solvent leads to hydrodynamic interactions (HI). Due to the many-body nature of this (effective) interaction, which introduces a correlation into the random motion of the particles, it is more complicated to evaluate. Effectively, HI is calculated from a factorization of the 6N × 6N diffusion matrix, for which the runtime scales as O(N³). This makes it prohibitive to include HI into BD simulations with more than a hundred particles.

Here we report on an approximation to the hydrodynamic interaction, which, at weak coupling, preserves the statistical moments of the correlated random motion of the particles. Due to this approximation, the hydrodynamic corrections to the particle displacements can be evaluated with a runtime ∝ O(N²), i.e., it scales as the evaluation of the direct interactions. With this form it is now possible to include HI into simulations with virtually arbitrarily many particles.

Here we present first test runs that show that the errors introduced through the approximation are negligible compared to the benefit of including the hydrodynamic corrections to the continuum solvent model.