三维波纹状反应扩散介质中的波前传播
Front propagation in three-dimensional corrugated reaction-diffusion media
摘要：
以Schlögl模型为代表，研究了三维空间调制截面反应扩散介质中行波波前的传播。应用适当的扰动技术，首先导致降维的空间相关的诺依曼边界条件转化为边界诱导的平流项，其次，到一个运动方程的行波位置在弱波纹约束。与数值模拟的比较表明，我们的分析结果正确地预测的非线性依赖的传播速度的限制的固有宽度的前的空间周期的比率，包括传播失败的特性。基于程函方程，我们得到了传播失效的有限区间的解析估计。最后，我们证明了前的速度是由抑制扩散的反应物，如果前的固有宽度是远远大于介质的空间变化。
英文摘要：
Propagation of traveling fronts in three-dimensional reaction-diffusion media with spatially modulated cross-section is studied using the Schlögl model as a representative example. Applying appropriate perturbation techniques leads first to a reduction of dimensionality in which the spatially dependent Neumann boundary condition translate into a boundary-induced advection term and, secondly, to an equation of motion for the traveling wave position in weakly corrugated confinements. Comparisons with numerical simulations demonstrate that our analytical results properly predicts the nonlinear dependence of the propagation velocity on ratio of the spatial period of the confinement to the intrinsic width of the front; including the peculiarity of propagation failure. Based on the eikonal equation, we obtain an analytical estimate for the finite interval of propagation failure. Lastly, we demonstrate that the front velocity is determined by the suppressed diffusivity of the reactants if the intrinsic width of the front is much larger than the spatial variation of the medium.
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