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Topological singularities of domains in globally constrained bistable reaction-diffusion systems

机译:全局约束双稳态反应扩散系统中域的拓扑奇异性

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摘要

A general (nonvariational) globally constrained reaction-diffusion equation (GCRDE) with bistability is employed for studying the dynamics of two-dimensional non-single-connected domains: circular spots of one phase with inclusions of another phase. In the sharp-interface approximation, the dynamics is describable by a set of coupled ordinary differential equations which have a universal form. It is shown that domains with a single inclusion always develop topological singularity in a finite time: the inclusion either shrinks to zero, or breaks out. The results are supported by numerical simulations with the full GCRDE.
机译:一个具有双稳态的通用(非变分)全局约束反应扩散方程(GCRDE)被用于研究二维非单连接域的动力学:一相的圆形斑点与另一相的夹杂物。在尖锐界面近似中,动力学是由一组具有通用形式的耦合常微分方程描述的。结果表明,包含单个包含物的域总是在有限的时间内发展出拓扑奇异性:包含物缩小为零或破裂。使用完整的GCRDE进行数值模拟可为结果提供支持。

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