电磁场中的运动流形
Moving Manifolds in Electromagnetic Fields
摘要：
建立了电磁场中运动物体的非线性动力学方程。场由具有表面边界的物质体感生。相应地，由边界处的场确定的势能，可以写成四个势乘以四个流对电磁张量的收缩的加法。将最小作用量原理适当地应用于系统拉格朗日，得到电磁场中三维运动流形的动力学非线性方程。这些方程在不同条件下可简化为无质量三曲面的麦克斯韦方程组、动力学流体的欧拉方程、磁流体动力学方程和Poisson-Boltzmann方程。为了说明运动方程的有效性，我们应用形式主义来分析大分子和膜的动力学。
英文摘要：
We propose dynamic non-linear equations for moving surfaces in electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary, can be written as an addition of four-potential times four-current to a contraction of electromagnetic tensor. Proper application of minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations, in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for dynamic fluid, to magneto-hydrodynamic equations and to Poisson-Boltzmann equation. To illustrate effectiveness of the equations of motion we apply the formalism to analyze dynamics of macro-molecules and membranes.
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