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J Chem Phys. 2016 Apr 28;144(16):164107. doi: 10.1063/1.4947086.

Hybrid finite element and Brownian dynamics method for charged particles.

Author information

1
Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365, USA.
2
Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu, China.
3
Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112, USA.
4
Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093, USA.

Abstract

Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.

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