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arXiv 1906.04073cond-mat.softcond-mat.mes-hallcond-mat.stat-mechphysics.flu-dyn
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作为软condensed matter不连续行为源的几何演化

Geometric evolution as a source of discontinuous behavior in soft condensed matter

James E. McClure, Steffen Berg, Ryan T. Armstrong

摘要:

几何演化是许多物理现象的基本方面。在本文中,我们考虑的几何结构,经历拓扑变化的演变。拓扑变化发生在物体的形状演变时,它要么分裂,要么收敛到自身形成一个环。对象拓扑的更改基本上是离散事件。我们考虑如何在几何演化过程中出现的不连续性,通过表征可能的拓扑事件和分析相关的源项的基础上的几何不变量的演化方程。我们表明,离散性质的拓扑变化导致不连续的源项,传播到物理变量。

英文摘要:

Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves such that it either breaks apart or converges back into itself to form a loop. Changes to the topology of an object are fundamentally discrete events. We consider how discontinuities arise during geometric evolution processes by characterizing the possible topological events and analyzing the associated source terms based on evolution equations for geometric invariants. We show that the discrete nature of a topological change leads to discontinuous source terms that propagate to physical variables.

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