Alteration in Cross Diffusivities Governs the Nature and Dynamics of Spatiotemporal Pattern Formation.,ChemPhysChem

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Alteration in Cross Diffusivities Governs the Nature and Dynamics of Spatiotemporal Pattern Formation.
ChemPhysChem ( IF 2.3 ) Pub Date : 2020-06-30 , DOI: 10.1002/cphc.202000142
Amitava Giri ₁ , Shreyans Pramod Jain ₁ , Sandip Kar ₁

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Realizing spatiotemporal patterns out of a chemical reaction diffusion system remains an experimental challenge owing to the difficulty in overcoming the stringent condition of diffusion driven instability. Herein, by considering the spatially extended Gray‐Scott model system, we have investigated how the cross diffusivities of the reactants involved influence the nature and dynamics of spatiotemporal patterns. Our study unravels that in absence of diffusion driven instability, spatially inhomogeneous patterns can be obtained for the Gray‐Scott model system, and unstable time dependent patterns can be stabilized just by adjusting cross diffusivities of the reactants. Interestingly, the effect of cross diffusion in presence of the diffusion driven instability can differentially alter the speed of pattern formation, and potentially modify the nature of the spatiotemporal patterns obtained under different parametric conditions. Experimental verification of our findings may allow us to observe spatiotemporal patterns beyond the regime of classical Turing instability.

中文翻译：

交叉扩散率的变化控制着时空模式形成的性质和动力学。

由于难以克服由扩散引起的不稳定的严格条件，因此从化学反应扩散系统中实现时空模式仍然是一项实验挑战。在此，通过考虑空间扩展的Gray-Scott模型系统，我们研究了反应物的交叉扩散如何影响时空模式的性质和动力学。我们的研究表明，在没有扩散驱动的不稳定性的情况下，可以针对Gray-Scott模型系统获得空间上不均匀的模式，并且仅通过调整反应物的交叉扩散性就可以稳定不稳定的时间依赖性模式。有趣的是，在存在扩散驱动的不稳定性的情况下，交叉扩散的影响可以差异地改变图案形成的速度，并可能修改在不同参数条件下获得的时空模式的性质。对我们发现的实验验证可以使我们观察到超越经典图灵不稳定性的时空模式。

更新日期：2020-06-30

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