Iomin A, Méndez V
Department of Physics, Technion, Haifa 32000, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012706. doi: 10.1103/PhysRevE.88.012706. Epub 2013 Jul 8.
Fractional reaction-diffusion equations are derived by exploiting the geometrical similarities between a comb structure and a spiny dendrite. In the framework of the obtained equations, two scenarios of reaction transport in spiny dendrites are explored, where both a linear reaction in spines and nonlinear Fisher-Kolmogorov-Petrovskii-Piskunov reactions along dendrites are considered. In the framework of fractional subdiffusive comb model, we develop a Hamilton-Jacobi approach to estimate the overall velocity of the reaction front propagation. One of the main effects observed is the failure of the front propagation for both scenarios due to either the reaction inside the spines or the interaction of the reaction with the spines. In the first case the spines are the source of reactions, while in the latter case, the spines are a source of a damping mechanism.
通过利用梳状结构与多刺树突之间的几何相似性，推导出了分数阶反应扩散方程。在所得到的方程框架内，探索了多刺树突中反应传输的两种情况，其中既考虑了树突棘中的线性反应，也考虑了沿树突的非线性Fisher-Kolmogorov-Petrovskii-Piskunov反应。在分数阶次扩散梳状模型框架下，我们开发了一种哈密顿-雅可比方法来估计反应前沿传播的整体速度。观察到的一个主要效应是，由于树突棘内部的反应或反应与树突棘的相互作用，两种情况下的前沿传播都会失败。在第一种情况下，树突棘是反应的来源，而在后一种情况下，树突棘是一种阻尼机制的来源。
