反应扩散方程的区域增长混合方法
Incorporating domain growth into hybrid methods for reaction-diffusion systems
摘要：
反应-扩散机制是一个强大的范例，可以用来表示许多生物和物理现象在多个空间尺度。应用包括细胞内动力学、细胞迁移和半干旱景观中植被形成的模式。此外，畴生长是胚胎生长和伤口愈合的重要过程。有许多数值模拟框架能够在不断增长的领域中模拟这种系统，但是其中每一个都可能非常适合不同的空间尺度和粒子数量。最近，空间扩展的静态域的混合方法已经产生，以弥合这些不同的建模范式之间的差距，以代表多尺度现象。然而，这些方法并没有考虑到域增长而开发。在本文中，我们开发了三个混合方法的增长域，扩展了三个突出的静态域混合方法。我们还提供了详细的算法，以允许其他人使用它们。我们证明，该方法能够准确地模拟三个代表性的反应扩散系统准确，没有偏见。
英文摘要：
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns formed by vegetation in semi-arid landscapes. Moreover, domain growth is an important process for embryonic growth and wound healing. There are many numerical modelling frameworks capable of simulating such systems on growing domains, however each of these may be well suited to different spatial scales and particle numbers. Recently, spatially extended hybrid methods on static domains have been produced in order to bridge the gap between these different modelling paradigms in order to represent multiscale phenomena. However, such methods have not been developed with domain growth in mind. In this paper, we develop three hybrid methods on growing domains, extending three of the prominent static domain hybrid methods. We also provide detailed algorithms to allow others to employ them. We demonstrate that the methods are able to accurately model three representative reaction-diffusion systems accurately and without bias.
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