含多体效应的电荷输运方程的分析和计算.

The understanding of electrostatic correlations has been considered as essential for physical properties of many soft matter and biophysical systems and electrochemical energy devices, and is a topic with great challenging. Equilibrium charged systems are often described by the Poisson-Boltzmann theory, while the quasi-equilibrium dynamics of these systems can be described by the Poisson-Nernst-Planck equations. In order to include the contributions of electrostatic correlation, variable dielectric environments, and ionic excluded-volume effects to free energy, we should correct the approximation of the potential of mean force in the system. The theory with self-energy modification introduces the difficulties of solving a Green’s function equation and complicated interface conditions. The objectives of this project are to study this self-energy modified charge dynamics equations, analyze the asymptotic properties of the equations, and develop fast algorithms for the Green’s function equation with nonlinear coefficients and numerical schemes for dynamics equations. In particular, efficient numerical methods for complicated interface environments and for satisfying specific physical properties will be designed. By the developed methods, the project will study the dynamic properties of strong-correlated systems appearing in different applications.

静电多体效应的理解是研究软物质和生物系统的物理性质和设计新型电化学能源系统的核心问题，并且是非常具有挑战性的课题。平衡态带电体系的连续介质描述通常采用Poisson-Boltzmann理论，对于近平衡输运过程则可以通过Poisson-Nernst-Planck方程组描述。这些平均场理论没有包含关联效应。为了引入静电关联﹑空间介电环境改变和离子体积排空作用对自由能的贡献，需修正方程中的平均力静电能。自能修正的理论包含格林函数方程求解和复杂界面条件的难题。本项目研究自能修正的电荷输运方程，分析方程的渐近性质，发展具有非线性系数的格林函数方程的快速算法求解自能和方程组的数值方法。尤其针对复杂界面环境设计高效的计算方法以及满足物理特性的数值格式。同时利用所设计的方法研究软物质，生物物理和能源领域中的强关联系统的动力学性质。

库仑多体效应是研究软物质、生物系统的物理性质和设计新型电化学能源系统的核心问题，由于长程性质，它的理论研究具有非常大的挑战性。本项目开展多体系统的连续介质理论、渐近分析、数值算法和计算机模拟等研究。通过引入静电关联和离子排空体积作用等对自由能的贡献，发展了修正的Poisson-Nernst-Planck方程。基于该方程，项目分析方程的渐近性质，发现了边界层问题的双层结构性质。项目也研究了核壳结构的界面问题的快速算法，并应用于研究超级电容问题中离子-界面电子关联对电容的影响。本项目利用所设计的方法研究软物质和电化学能源等领域中的强关联系统的动力学性质。