We present fast simulation methods for the self-assembly of complex shapes in two dimensions. The shapes are modeled via a general boundary curve and interact via a standard volume term promoting overlap and an interpenetration penalty. To efficiently realize the Gibbs measure on the space of possible configurations we employ the hybrid Monte Carlo algorithm together with a careful use of signed distance functions for energy evaluation. Motivated by the self-assembly of identical coat proteins of the tobacco mosaic virus which assemble into a helical shell, we design a particular nonconvex 2D model shape and demonstrate its robust self-assembly into a unique final state. Our numerical experiments reveal two essential prerequisites for this self-assembly process: blocking and matching (i.e., local repulsion and attraction) of different parts of the boundary; and nonconvexity and handedness of the shape.

翻译：我们提出了复杂二维形状自组装的快速模拟方法。这些形状通过通用边界曲线建模，并借助促进重叠的标准体积项与互渗透罚函数相互作用。为高效实现可能构型空间上的吉布斯测度，我们采用混合蒙特卡洛算法，并结合符号距离函数进行能量评估。受烟草花叶病毒相同衣壳蛋白自组装形成螺旋壳结构的启发，我们设计了一种特定的二维非凸模型形状，并证明了其能够鲁棒地自组装为唯一的最终状态。数值实验揭示了该自组装过程的两个关键前提：边界不同部分的阻断与匹配（即局部排斥与吸引），以及形状的非凸性与手性。