发表机构
Virginia Polytechnic Institute and State University（弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种从第一性原理推导的粗粒化几何理论，用于描述刚性曲面上的一维弹性曲线，该理论明确包含拉伸、弯曲和扭转，并用于确定不同高斯曲率表面上的平衡构象。
AI 中文摘要
细长弹性物体被约束在弯曲表面上在软物质系统中普遍存在，其例子包括DNA缠绕组蛋白，以及细胞分裂过程中肌动蛋白丝在细胞膜上形成收缩环。在连续极限下，这些有效一维（1D）物体的构象由嵌入表面的几何和力学性质以及物体本身的弹性共同决定。现有的唯象理论通常通过包含弯曲和扭转的弹性能量最小化来描述此类行为，但忽略了拉伸效应，而拉伸对于具有有限横截面或与底层表面高度不兼容的细丝可能很重要。在此，我们提出一种从第一性原理推导的、约束在刚性表面上的1D弹性曲线的粗粒化几何理论。对于各向同性材料，我们的模型自然地以杨氏模量、泊松比和面积惯性矩的形式出现。所得的有效能量泛函明确包含了拉伸以及弯曲和扭转。我们对其最小化以确定在不同零、正或负高斯刚性表面上的平衡曲线构象。我们的理论为分析生物和物理相关环境中表面结合弹性曲线的平衡构型提供了一个通用框架。
英文摘要
Slender elastic objects constrained to curved surfaces are ubiquitous in soft systems, with examples ranging from DNA wrapping around histones to actin filaments forming contractile rings on the cell membrane during cytokinesis. In the continuum limit, the conformation of these effectively one-dimensional (1D) objects is governed by both the geometry and mechanics of the embedding surface, and the elasticity of the object. Existing phenomenological typically describe such behavior through elastic energy minimization that incorporates bending and twisting, but neglect stretching that may be important for filaments with finite cross-section or are highly incompatible with the underlying surface. Here we present a coarse-grained geometric theory of 1D elastic curves constrained on rigid surfaces, derived from the first principles. For an isotropic material, our model emerges naturally in terms of the Young's modulus, Poisson's ratio, and area moments of inertia. The resulting effective energy functional explicitly includes stretching in addition to bending and twisting. We minimize it to determine the equilibrium curve conformations on different zero, positive, or negative Gaussian rigid surfaces. Our theory provides a general framework for analyzing the equilibrium configurations of surface-bound elastic curves in biologically and physically relevant settings.
Comments22 pages, 13 figures
