标题： 弹性网络在无旋转对称性情况下的任意曲面一般解 显示英文标题

标题： General Solution for Elastic Networks on Arbitrary Curved Surfaces in the Absence of Rotational Symmetry

摘要： 理解在任意曲面和任意边界上的晶体生长是一个严峻的挑战，这源于使用几何不变量来表述非线性弹性力学的复杂性。 解决方案通常局限于具有旋转对称性的系统。 在本文中，我们引入了一个框架来解决这些挑战，通过数值求解这些方程而不依赖于固有的对称性。 我们通过计算包含位错的弹性网络在任何点所需的最小能量，并研究缺乏旋转对称性的表面来说明我们的方法。 我们的发现表明，从无缺陷结构到具有单个五重或七重位错的稳定状态的转变强烈依赖于区域的形状，强调了边缘几何形状的深远影响。 我们讨论了这些结果对一般实验系统的意义，特别是在阐明病毒衣壳的组装路径方面。 这项研究增强了我们对复杂表面上晶体生长的理解，并扩展了其在多个科学领域的应用。 显示英文摘要

摘要： Understanding crystal growth over arbitrary curved surfaces with arbitrary boundaries is a formidable challenge, stemming from the complexity of formulating non-linear elasticity using geometric invariant quantities. Solutions are generally confined to systems exhibiting rotational symmetry. In this paper, we introduce a framework to address these challenges by numerically solving these equations without relying on inherent symmetries. We illustrate our approach by computing the minimum energy required for an elastic network containing a disclination at any point and by investigating surfaces that lack rotational symmetry. Our findings reveal that the transition from a defect-free structure to a stable state with a single 5-fold or 7-fold disclination strongly depends on the shape of the domain, emphasizing the profound influence of edge geometry. We discuss the implications of our results for general experimental systems, particularly in elucidating the assembly pathways of virus capsids. This research enhances our understanding of crystal growth on complex surfaces and expands its applications across diverse scientific domains.