Kneer Frederike, Obermayer Klaus, Dahlem Markus A
Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, Ernst-Reuter-Platz 7, D-10587, Berlin, Germany,
Eur Phys J E Soft Matter. 2015 Feb;38(2):95. doi: 10.1140/epje/i2015-15010-y. Epub 2015 Feb 25.
The effect of advection on the propagation and in particular on the critical minimal speed of traveling waves in a reaction-diffusion model is studied. Previous theoretical studies estimated this effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below which propagating waves are not supported anymore. In this paper, an analytical expression for the advection-velocity relation of the unstable slow wave is derived. In addition, the critical advection strength is calculated taking into account the unstable slow wave solution. We also analyze a two-variable reaction-diffusion-advection model numerically in a wide parameter range. Due to the new control parameter (advection) we can find stable wave propagation in the otherwise non-excitable parameter regime, if the advection strength exceeds a critical value. Comparing theoretical predictions to numerical results, we find that they are in good agreement. Theory provides an explanation for the observed behaviour.
研究了平流对反应扩散模型中波传播的影响,特别是对行波临界最小速度的影响。先前的理论研究估计了这种对稳定快波速度的影响,并预测存在一个临界平流强度,低于该强度时行波不再被支持。本文推导了不稳定慢波的平流-速度关系的解析表达式。此外,考虑不稳定慢波解计算了临界平流强度。我们还在很宽的参数范围内对一个双变量反应扩散-平流模型进行了数值分析。由于新的控制参数(平流),如果平流强度超过临界值,我们可以在原本不可激发的参数区域中找到稳定的波传播。将理论预测与数值结果进行比较,我们发现它们吻合得很好。理论为观察到的行为提供了解释。