反应扩散系统中的模式选择
Pattern selection in reaction diffusion systems
摘要：
图灵的斑图形成理论已被用来描述许多生物、化学和物理系统中自组织周期图案的形成。然而，一般来说，由于我们无法预测从给定的模型参数集获得哪种模式，因此此类模型的使用受到阻碍。虽然在空间不稳定性的开始附近已经知道了很多，但对远离开始的模式选择和动力学的机制却了解得少得多。在这里，我们提供了新的物理洞察这些系统的动态。我们发现，在一个图灵模式的峰值表现为点汇，其中的动力学是由扩散通量到他们。因此，峰朝向使扩散物质的质量最小化的周期性稳态配置移动。我们还表明，在最终的稳定状态的峰的优选数量是这样的，这个质量最小化。我们的工作提出了质量最小化作为一个简单的，可推广的，物理原理理解斑图形成的反应扩散系统远离发病。
英文摘要：
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in general, which pattern is obtained from a given set of model parameters. While much is known near the onset of the spatial instability, the mechanisms underlying pattern selection and dynamics away from onset are much less understood. Here, we provide new physical insight into the dynamics of these systems. We find that peaks in a Turing pattern behave as point sinks, the dynamics of which are determined by the diffusive fluxes into them. As a result, peaks move towards a periodic steady-state configuration that minimizes the mass of the diffusive species. We also show that the preferred number of peaks at the final steady-state is such that this mass is minimised. Our work presents mass minimization as a simple, generalisable, physical principle for understanding pattern formation in reaction diffusion systems far from onset.
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