From Brownian dynamics to Poisson-Nernst-Planck equations: multi-resolution simulations of ions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912447321866240 |
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| author | Zhang, Jinyuan Erban, Radek |
| author_facet | Zhang, Jinyuan Erban, Radek |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19738 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Brownian dynamics to Poisson-Nernst-Planck equations: multi-resolution simulations of ions Zhang, Jinyuan Erban, Radek Computational Physics Chemical Physics Quantitative Methods 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. |
| title | From Brownian dynamics to Poisson-Nernst-Planck equations: multi-resolution simulations of ions |
| topic | Computational Physics Chemical Physics Quantitative Methods |
| url | https://arxiv.org/abs/2506.19738 |