介电弹性体中的机电畴壁传播：基于共形映射的精确几何求解
Electromechanical Domain Wall Propagation in Dielectric Elastomers: An Exact Geometric Resolution via Conformal Mapping
- Tianjin University（天津大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对介电弹性体机电相变的畴壁传播问题，提出基于共形映射的渐近精确几何框架，结合Gent模型与BPS分析得到精确标度关系，为活性软物质几何不稳定性提供确定性范式。
AI中文摘要：
介电弹性体中的局域机电相变涉及由高曲率界面驱动的复杂运动边界与严重的静电 fringe 场（边缘场）。传统现象学模型因完全忽略面内电场分量和几何奇点，从根本上低估了构型力。本文提出一种渐近精确的几何框架以求解畴壁传播：通过共形映射将高度变形的当前构型映射为规则参数带，代数地消除场奇点；精确分部积分将高阶几何度量直接转化为严格的拓扑质量项，将全局共形静电学投影为非线性σ-模型拉格朗日密度；结合Gent 应变硬化模型，连续平移对称性给出哈密顿首次积分；本征值分析与Bogomol'nyi-Prasad-Sommerfield（BPS）界计算证明，畴壁严格表现为连接两个鞍点的非对称异宿轨道。该几何求解为局域界面能、畴壁厚度与渐近衰减长度提供了精确的标度关系，消除了所有现象学参数，为活性软物质中的几何不稳定性提供了确定性范式。
英文摘要：
The localized electromechanical phase transition in dielectric elastomers involves complex moving boundaries and severe electrostatic fringe fields driven by high-curvature interfaces. Traditional phenomenological models fundamentally underestimate the configurational forces by completely ignoring the in-plane electric field components and geometric singularities. Here, we present a asymptotically exact geometric framework to resolve the domain wall propagation. By mapping the highly deformed current configuration to a regular parametric strip via conformal mapping, the field singularities are algebraically eliminated. An exact integration by parts directly translates the higher-order geometric metric into a rigorous topological mass term, projecting the global conformal electrostatics into a non-linear $σ$-model Lagrangian density. Incorporating the Gent strain-stiffening model, the continuous translation symmetry yields a Hamiltonian first integral. Eigenvalue analysis and Bogomol'nyi-Prasad-Sommerfield (BPS) bound calculations prove that the domain wall emerges strictly as an asymmetric heteroclinic orbit connecting two saddle points. This geometric resolution provides exact analytical scalings for the localized interface energy, domain wall thickness, and asymptotic decay lengths, eliminating all phenomenological parameters and offering a deterministic paradigm for geometric instabilities in active soft matter.
