Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks
Reaction-subdiffusion and reaction-superdiffusion equations for evanescent particles performing continuous-time random walks
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DOI：
10.1103/physreve.81.031115
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发表时间：
2010-03-01
影响因子：
2.4
通讯作者：
Lindenberg, Katja
中科院分区：
文献类型：
--
作者：
Abad, E.;Yuste, S. B.;Lindenberg, Katja
从一个连续时间随机行走（CTRW）模型的粒子，可能会消失，因为他们走，我们的目标是到达宏观积分微分方程的概率密度为一个粒子被发现在点r在时间t给定它开始其步行从r（0）在时间t=0。从CTRW到积分微分方程的通道是很好理解时，粒子是不是渐逝。根据步进时间和距离的分布，可以得到标准的宏观方程，这些方程可以是“正常”的（扩散）或“异常”的（亚扩散和/或超扩散）。如果粒子在行走过程中会死亡，那么宏观描述就变得相当复杂，而且不那么直观。虽然这样的方程是针对特定情况导出的，例如，对于位置无关的指数倏逝，我们提出了一个更一般的推导有效的约束条件下较不严格的比那些发现在目前的文献。
Starting from a continuous-time random-walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integrodifferential equations for the probability density for a particle to be found at point r at time t given that it started its walk from r(0) at time t=0. The passage from the CTRW to an integrodifferential equation is well understood when the particles are not evanescent. Depending on the distribution of stepping times and distances, one arrives at standard macroscopic equations that may be "normal" (diffusion) or "anomalous" (subdiffusion and/or superdiffusion). The macroscopic description becomes considerably more complicated and not particularly intuitive if the particles can die during their walk. While such equations have been derived for specific cases, e.g., for location-independent exponential evanescence, we present a more general derivation valid under less stringent constraints than those found in the current literature.