Kolokolnikov Theodore, Sun Hui, Uminsky David, Bertozzi Andrea L
Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 2):015203. doi: 10.1103/PhysRevE.84.015203. Epub 2011 Jul 22.
Pairwise particle interactions arise in diverse physical systems ranging from insect swarms to self-assembly of nanoparticles. In the presence of long-range attraction and short-range repulsion, such systems can exhibit bound states. We use linear stability analysis of a ring equilibrium to classify the morphology of patterns in two dimensions. Conditions are identified that assure the well-posedness of the ring. In addition, weakly nonlinear theory and numerical simulations demonstrate how a ring can bifurcate to more complex equilibria including triangular shapes, annuli, and spot patterns with N-fold symmetry. Many of these patterns have been observed in nature, although a general theory has been lacking, in particular how small changes to the interaction potential can lead to large changes in the self-organized state.
成对粒子相互作用出现在从昆虫群体到纳米粒子自组装等各种物理系统中。在存在长程吸引和短程排斥的情况下，这类系统会呈现束缚态。我们利用环形平衡的线性稳定性分析来对二维图案的形态进行分类。确定了确保环形适定性的条件。此外，弱非线性理论和数值模拟展示了一个环如何分叉到更复杂的平衡态，包括三角形、环形以及具有N重对称性的斑点图案。这些图案中有许多在自然界中都已被观察到，尽管一直缺乏一个通用理论，特别是关于相互作用势的微小变化如何导致自组织状态的巨大变化。
