存在有限强度点汇时的Lévy飞行
Lévy flights in the presence of a point sink of finite strength
摘要：
本文研究了在任意强度和位置的点汇存在下，Lévy飞行粒子的吸收问题。这种粒子的运动由一个修正的福克-普朗克方程给出，该方程在拉普拉斯域中的精确解可以用未扰动（不存在汇）格林函数的拉普拉斯变换来描述。这种解决方案的格林函数是一个良好的研究，通用的结果，适用于分数和通常的福克-普朗克方程一样。利用这一结果，得到了自由Lévy飞行和Lévy飞行在含有δ函数汇的线性势和调和势中的传播子和吸收时间分布，并分析了它们对汇强度的依赖性.分析结果提出的吸收时间分布在所有上述三个电位的长时间行为。仿真结果证实了密切与分析结果。
英文摘要：
In this paper, the absorption of a particle undergoing Lévy flight in the presence of a point sink of arbitrary strength and position is studied. The motion of such a particle is given by a modified Fokker-Planck equation whose exact solution in the Laplace domain can be described in terms of the Laplace transform of the unperturbed (absence of the sink) Green's function. This solution for the Green's function is a well-studied, generic result which applies to both fractional and usual Fokker-Planck equations alike. Using this result, the propagator and the absorption time distribution are obtained for free Lévy flight and Lévy flight in linear and harmonic potentials in the presence of a delta function sink, and their dependence on the sink strength is analyzed. Analytical results are presented for the long-time behaviour of the absorption time distribution in all the three above mentioned potentials. Simulation results are found to corroborate closely with the analytical results.
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