Abad E, Yuste S B, Lindenberg Katja
Departamento de Física Aplicada, Centro Universitario de Mérida, Universidad de Extremadura, E-06800 Mérida, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 1):061120. doi: 10.1103/PhysRevE.86.061120. Epub 2012 Dec 17.
We calculate the survival probability of an immobile target surrounded by a sea of uncorrelated diffusive or subdiffusive evanescent traps (i.e., traps that disappear in the course of their motion). Our calculation is based on a fractional reaction-subdiffusion equation derived from a continuous time random walk model of the system. Contrary to an earlier method valid only in one dimension (d=1), the equation is applicable in any Euclidean dimension d and elucidates the interplay between anomalous subdiffusive transport, the irreversible evanescence reaction, and the dimension in which both the traps and the target are embedded. Explicit results for the survival probability of the target are obtained for a density ρ(t) of traps which decays (i) exponentially and (ii) as a power law. In the former case, the target has a finite asymptotic survival probability in all integer dimensions, whereas in the latter case there are several regimes where the values of the decay exponent for ρ(t) and the anomalous diffusion exponent of the traps determine whether or not the target has a chance of eternal survival in one, two, and three dimensions.
我们计算了一个静止目标被大量不相关的扩散或亚扩散消逝陷阱（即陷阱在其运动过程中消失）包围时的生存概率。我们的计算基于从系统的连续时间随机游走模型推导出来的分数反应 - 亚扩散方程。与仅在一维（d = 1）有效且适用的早期方法不同，该方程适用于任何欧几里得维度d，并阐明了反常亚扩散输运、不可逆消逝反应以及陷阱和目标所嵌入的维度之间的相互作用。对于陷阱密度ρ(t) （i）呈指数衰减和（ii）呈幂律衰减的情况，我们得到了目标生存概率的明确结果。在前一种情况下，目标在所有整数维度中都有一个有限的渐近生存概率，而在后一种情况下，存在几种情况，其中ρ(t) 的衰减指数和陷阱的反常扩散指数的值决定了目标在一维、二维和三维中是否有机会永远存活。
