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From Brownian dynamics to Poisson-Nernst-Planck equations: multi-resolution simulations of ions (2506.19738v1)

Published 24 Jun 2025 in physics.comp-ph, physics.chem-ph, and q-bio.QM

Abstract: Starting with a microscopic (individual-based) Brownian dynamics model of charged particles (ions), its macroscopic description is derived as a system of partial differential equations that govern the evolution of ion concentrations in space and time. The macroscopic equations are obtained in the form of the Poisson-Nernst-Planck system. A multi-resolution method for simulating charged particles is then developed, combining the detailed Brownian dynamics model in a part of the computational domain with coarser macroscopic equations in the remainder. The strengths, limitations, and applicability of microscopic, macroscopic, and multi-resolution simulation approaches are demonstrated through an illustrative model comprising a system of Na$+$ and Cl$-$ ions.

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