用于电荷动力学建模的Maxwell-Ampère Nernst-Planck框架
A Maxwell-Ampère Nernst-Planck Framework for Modeling Charge Dynamics
AI总结：
本文提出Maxwell-Ampère Nernst-Planck（MANP）框架用于电荷动力学建模，证明其能量耗散性及与Poisson-Nernst-Planck模型的等价性，并开发了保持离散Gauss定律的局部无旋松弛算法，可高效处理空间依赖介电常数和超越平均场的多体效应。
摘要：
理解电荷动力学的性质对许多实际应用至关重要，例如电化学能源器件和跨膜离子通道。本工作提出了一个用于描述电荷动力学的Maxwell-Ampère Nernst-Planck（MANP）框架。研究表明，在电位移满足无旋条件下，MANP模型关于一个凸自由能泛函是能量耗散的，并且证明了该模型等价于Poisson-Nernst-Planck模型。根据能量耗散定律，MANP模型的稳态再现了电荷守恒的Poisson-Boltzmann（PB）理论，为研究PB理论提供了一种替代的能量稳定方法。为了实现无旋条件，本文为MANP模型开发了一个伴随的局部无旋松弛算法，该算法被证明能自然保持离散Gauss定律，并具有线性计算复杂度且收敛稳健。我们这一发展的主要优势之一是能够高效处理空间依赖的介电常数，而无需求解变系数Poisson方程。多体效应（如离子位阻效应和Coulomb关联）可以纳入MANP框架中，以推导出适用于平均场近似失效问题的修正MANP模型。本文给出了在非均匀介电环境中具有此类超越平均场效应的电荷动力学的数值结果，以展示MANP模型在描述电荷动力学方面的性能，说明所提出的MANP模型为电荷动力学建模提供了一个通用框架。
英文摘要：
Understanding the properties of charge dynamics is crucial to many practical applications, such as electrochemical energy devices and transmembrane ion channels. This work proposes a Maxwell-Ampère Nernst-Planck (MANP) framework for the description of charge dynamics. The MANP model with a curl-free condition on the electric displacement is shown to be energy dissipative with respect to a convex free-energy functional, and demonstrated to be equivalent to the Poisson-Nernst-Planck model. By the energy dissipation law, the steady state of the MANP model reproduces the charge conserving Poisson--Boltzmann (PB) theory, providing an alternative energy stable approach to study the PB theory. In order to achieve the curl-free condition, a companion local curl-free relaxation algorithm, which is shown to naturally preserve the discrete Gauss's law and converge robustly with linear computational complexity, is developed for the MANP model. One of the main advantages of our development is that it can efficiently deal with space-dependent permittivity instead of solving the variable-coefficient Poisson's equation. Many-body effects such as ionic steric effects and Coulomb correlations can be incorporated within the MANP framework to derive modified MANP models for problems in which the mean-field approximation fails. Numerical results on the charge dynamics with such beyond mean-field effects in inhomogeneous dielectric environments are presented to demonstrate the performance of the MANP models in the description of charge dynamics, illustrating that the proposed MANP model provides a general framework for modeling charge dynamics.
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