This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors, and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e. electrostatic) solvation, non-polar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics, and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace–Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson–Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst–Planck (NP) equations for the dynamics of charged solvent species, generalized Navier–Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent–solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent–solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

中文翻译：

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多尺度、多物理场和多域模型 I：基础理论


这项工作将我们早期基于微分几何的多尺度范式的两域公式扩展到多域理论，这使我们能够同时适应水化学、物理和生物系统的多物理描述，例如燃料电池、太阳能电池、纳米流体、离子通道、病毒、RNA 聚合酶、分子马达和大分子复合物。其基本思想是利用表面微分几何理论作为一种自然手段，将溶剂的宏观域与溶质的微观域在几何上分开，并动态耦合连续描述和离散描述。我们的主要策略是构建能量泛函以与多物理场平等，包括极性（即静电）溶剂化、非极性溶剂化、化学势、量子力学、流体力学、分子力学、粗粒动力学和弹性动力学。将变分原理应用于能量泛函，以导出理想的控制方程，例如用于大分子形态的多域拉普拉斯 - 贝尔特拉米 (LB) 方程、用于静电势的多域泊松 - 玻尔兹曼 (PB) 方程或泊松方程、广义能斯特 - 普朗克 (NP) ) 带电溶剂物种动力学方程、流体动力学广义纳维-斯托克斯 (NS) 方程、分子动力学 (MD) 或粗粒动力学广义牛顿方程以及弹性动力学运动方程。与经典的 PB 方程不同，我们的 PB 方程是由于溶剂-溶质相互作用而形成的积分微分方程。 为了说明所提出的形式，我们明确构建了三个模型：多域溶剂化模型、多域电荷传输模型和多域化学电流体MD弹性模型。每个溶质域都具有不同的表面张力、压力、介电函数和电荷密度分布。除了长程库仑相互作用之外，本模型还考虑了各种非静电溶剂-溶质相互作用。我们通过展示非平衡电荷传输模型和平衡溶剂化模型在平衡时系统地还原为后者来证明非平衡电荷传输模型和平衡溶剂化模型之间的一致性。本文还对该领域进行了简要回顾。