Compounded random walk for space-fractional diffusion on finite domains.

IF 2.2 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS
Christopher N Angstmann, Daniel S Han, Bruce I Henry, Boris Z Huang, Zhuang Xu
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引用次数: 0

Abstract

We formulate a compounded random walk that is physically well defined on both finite and infinite domains, and samples space-dependent forces throughout jumps. The governing evolution equation for the walk limits to a space-fractional Fokker-Planck equation valid on bounded domains, and recovers the well known superdiffusive space-fractional diffusion equation on infinite domains. We describe methods for numerical approximation and Monte Carlo simulations and demonstrate excellent correspondence with analytical solutions. This compounded random walk, and its associated fractional Fokker-Planck equation, provides a major advance for modeling space-fractional diffusion through potential fields and on finite domains.

有限域上空间-分数扩散的复合随机漫步。
我们制定了一个复合随机漫步,它在有限和无限域上都有很好的物理定义,并在跳跃过程中采样与空间相关的力。将游动的控制演化方程限制为在有界域上有效的空间分数型Fokker-Planck方程,并在无限域上恢复了众所周知的超扩散空间分数型扩散方程。我们描述了数值逼近和蒙特卡罗模拟的方法,并证明了与解析解的良好对应关系。这种复合随机漫步及其相关的分数Fokker-Planck方程,为通过势场和有限域的空间分数扩散建模提供了重大进展。
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来源期刊
Physical Review E
Physical Review E PHYSICS, FLUIDS & PLASMASPHYSICS, MATHEMAT-PHYSICS, MATHEMATICAL
CiteScore
4.50
自引率
16.70%
发文量
2110
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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