机电系统极化响应的变分原理
On variational principles for polarization responses in electromechanical systems
摘要：
经典电动力学使用介电常数来描述机电系统对电场变化的极化响应。我们概括的描述，包括各种各样的反应，在电场的变化，发现在大多数系统和应用。机电系统可以在许多物理和生物应用中找到，例如膜，电池和介电弹性体中的离子传输。我们提出了一个统一的，一致的，变分的框架建模机电系统，因为它们响应于电场的变化，也就是说，因为它们的振动。这个框架的动机和开发使用经典的能量变分方法（EnVarA）。系统的电部分和化学机械部分之间的耦合由拉格朗日乘子或各种能量弛豫来描述。经典极化及其介电常数和介电常数作为该分析的输出出现。然后，麦克斯韦方程组成为电荷和电流的普遍守恒定律，并结合了极化的机电描述。极化描述了对电场变化的整个机电响应，有时可以近似为介电常数或介电色散。
英文摘要：
Classical electrodynamics uses a dielectric constant to describe the polarization response of electromechanical systems to changes in an electric field. We generalize that description to include a wide variety of responses to changes in the electric field, as found in most systems and applications. Electromechanical systems can be found in many physical and biological applications, such as ion transport in membranes, batteries, and dielectric elastomers. We present a unified, thermodynamically consistent, variational framework for modeling electromechanical systems as they respond to changes in the electric field; that is to say, as they polarize. This framework is motivated and developed using the classical energetic variational approach (EnVarA). The coupling between the electric part and the chemo-mechanical parts of the system is described either by Lagrange multipliers or various energy relaxations. The classical polarization and its dielectrics and dielectric constants appear as outputs of this analysis. The Maxwell equations then become universal conservation laws of charge and current, conjoined to an electromechanical description of polarization. Polarization describes the entire electromechanical response to changes in the electric field and can sometimes be approximated as a dielectric constant or dielectric dispersion.
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