基于能量最小化的空间变结构静电场的严格处理
Rigorous treatment of electrostatics for spatially varying dielectrics based on energy minimization
摘要：
提出了一种新的能量最小化静电公式，它允许在具有任意介电特性的系统中计算静电能量和力到任何期望的精度。从极化矢量场的能量泛函出发，导出标量电荷密度的积分方程。该能量泛函表示系统即使在非平衡态下的真实能量。通过求解电荷密度的积分方程，可以获得任意的精度，该积分方程是通过方程的核心进行级数展开的，这只取决于电荷密度的几何形状。流线型的形式主义只与体积电荷分布，而不是诉诸引入表面电荷的手。因此，它可以适用于任何空间变化的介电磁化率，这是特别重要的应用程序中的生物分子系统。的形式主义的应用程序的简单性，以实际问题的分析和数值例子。
英文摘要：
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the scalar charge density is derived from an energy functional of the polarization vector field. This energy functional represents the true energy of the system even in non-equilibrium states. Arbitrary accuracy is achieved by solving the integral equation for the charge density via a series expansion in terms of the equation's kernel, which depends only on the geometry of the dielectrics. The streamlined formalism operates with volume charge distributions only, not resorting to introducing surface charges by hand. Therefore, it can be applied to any spatial variation of the dielectric susceptibility, which is of particular importance in applications to biomolecular systems. The simplicity of application of the formalism to real problems is shown with analytical and numerical examples.
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