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Simulations of Polymers with Brownian Dynamics
Hájková, Alexandra ; Uhlík, Filip (advisor) ; Posel, Zbyšek (referee)
Title: Simulations of Polymers with Brownian Dynamics Author: Alexandra Hájková Supervisor: RNDr. Filip Uhlík, Ph.D. Department of Physical and Macromolecular Chemistry Abstract: This work presents Brownian Dynamics simulations of macromolecules. A com- mon approaches to hydrodynamic interactions employes the Rotne-Prager-Yamakawa (RPY) tensor. In such cases simple simulation step takes time proportional to O(N3) when Cholesky decomposition of RPY tensor is used. This makes the simulation too much time-consuming. This work proposes a new method for approximation of hydrodynamic interactions with a Toeplitz matrix. Decomposition of this matrix can be performed in O(N2) time, which considerably speeds up the simulations. In this work the new method was implemented, thoroughly tested, compared to a reference RPY approximation and applied to linear, cyclic and star macromolecules. Keywords: Brownian dynamics, macromolecules, hydrodynamic interactions, Rotne-Prager- Yamakawa tensor, Toeplitz matrix, Cholesky decomposition 1
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