具有静态陷阱随机分布的扩散。
Diffusion with random distribution of static traps.
作者信息
Barkema G T, Biswas P, van Beijeren H
机构信息
Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands.
出版信息
Phys Rev Lett. 2001 Oct 22;87(17):170601. doi: 10.1103/PhysRevLett.87.170601. Epub 2001 Oct 5.
The survival probability P(c,t) of a random walk of t steps with static traps at concentration c is studied in two and three dimensions by an efficient Monte Carlo method based on a mapping onto a polymer model. On the basis of the theoretical work of Donsker and Varadhan [Commun. Pure Appl. Math. 28, 525 (1975); 32, 721 (1979)] and of Rosenstock [J. Math. Phys. (N.Y.) 11, 487 (1970)] one expects a data collapse for -ln[P(c,t)]/ln(t) plotted vs square root of [lambda t]/ln(t) [with lambda = -ln(1-c)], in two dimensions, and for -t(-1/3)ln[P(c,t)] vs t(2/3)lambda in three dimensions. These predictions are well supported by the Monte Carlo results.
通过基于聚合物模型映射的高效蒙特卡罗方法，研究了在二维和三维空间中，浓度为(c)的静态陷阱情况下，(t)步随机游走的生存概率(P(c,t))。基于唐斯克和瓦拉丹[《纯粹与应用数学通讯》28, 525 (1975); 32, 721 (1979)]以及罗森斯托克[《数学物理杂志》(纽约)11, 487 (1970)]的理论工作，人们预期在二维中，将(-\ln[P(c,t)] / \ln(t))与([\lambda t] / \ln(t))的平方根（其中(\lambda = -\ln(1 - c))）作图时会出现数据塌缩；在三维中，(-t^{(-1/3)}\ln[P(c,t)])与(t^{(2/3)}\lambda)作图时会出现数据塌缩。这些预测得到了蒙特卡罗结果的有力支持。
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