Convective instability and boundary driven oscillations in a reaction-diffusion-advection model.
Convective instability and boundary driven oscillations in a reaction-diffusion-advection model.
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DOI：
10.1063/1.4986153
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发表时间：
2017-06
期刊：
影响因子：
2.9
通讯作者：
E. Vidal-Henriquez;V. Zykov;E. Bodenschatz;A. Gholami
中科院分区：
文献类型：
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作者：
E. Vidal-Henriquez;V. Zykov;E. Bodenschatz;A. Gholami
在对流不稳定的反应扩散平流系统中，扰动会产生一个向下游平流并最终离开系统的波列。我们表明，对流不稳定共存的局部绝对不稳定时，上游施加一个固定的边界条件。这种边界引起的不稳定性作为连续波源，在边界附近产生局部周期性激发，从而引发向上和向下游行进的波。为了证实这一点，我们进行了分析和数值模拟的修改后的Martiel-Goldbeter反应扩散模型，增加了一个平流项。我们提供了一个定量描述的波包出现在对流不稳定的制度，我们发现是非常符合数值模拟。我们描述了这种新的不稳定性，并表明，在高平流速度的限制，它被抑制。这种类型的不稳定性可以预期的反应扩散系统，目前既对流不稳定性和可激发的制度。特别是，它可以是相关的，以了解社会阿米巴Dictyosteelium discoideum，可能会遇到流体流在其自然栖息地的信号机制。
In a reaction-diffusion-advection system, with a convectively unstable regime, a perturbation creates a wave train that is advected downstream and eventually leaves the system. We show that the convective instability coexists with a local absolute instability when a fixed boundary condition upstream is imposed. This boundary induced instability acts as a continuous wave source, creating a local periodic excitation near the boundary, which initiates waves travelling both up and downstream. To confirm this, we performed analytical analysis and numerical simulations of a modified Martiel-Goldbeter reaction-diffusion model with the addition of an advection term. We provide a quantitative description of the wave packet appearing in the convectively unstable regime, which we found to be in excellent agreement with the numerical simulations. We characterize this new instability and show that in the limit of high advection speed, it is suppressed. This type of instability can be expected for reaction-diffusion systems that present both a convective instability and an excitable regime. In particular, it can be relevant to understand the signaling mechanism of the social amoeba Dictyostelium discoideum that may experience fluid flows in its natural habitat.