二维和三维首次通过时间分布和命中分布的分析表达式

IF 0.8 4区 教育学 Q3 EDUCATION, SCIENTIFIC DISCIPLINES
Alexander Clarkson, Chi-Hang Lam, Hai-Yao Deng
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引用次数: 0

摘要

随机变量首次达到临界值之前的时间分布,称为首次通过时间(FPT)分布,是随机过程的一个基本特征。在这里,通过求解标准宏观扩散方程,我们推导出了扩散粒子在二维(2D)和三维(3D)空间无限制扩散过程中撞击球形物体的 FPT 分布的解析表达式。此外,我们还分析计算了 FPT 的角度依赖性,即所谓的撞击分布。我们还将分析结果与离散晶格上随机行走者的运动模拟进行了比较。由于 FPT 不仅在物理学中非常重要,在化学、生物学、医学、农业、工程学和金融学中也非常重要,因此本课题在教学上具有广泛的意义。此外,物理和工程中经常出现的中心方程只有微不足道的变化,这使得求解技术具有广泛的适用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Analytical expressions for the first passage time distribution and hit distribution in two and three dimensions
The distribution of the time elapsed before a random variable reaches a threshold value for the first time, called the first passage time (FPT) distribution, is a fundamental characteristic of stochastic processes. Here, by solving the standard macroscopic diffusion equation, we derive analytical expressions for the FPT distribution of a diffusing particle hitting a spherical object in two dimensions (2D) and three dimensions (3D) in the course of unrestricted diffusion in open space. In addition, we calculate, analytically, the angular dependence of the FPT, known as the hit distribution. The analytical results are also compared to simulations of the motions of a random walker on a discrete lattice. This topic could be of wide pedagogical interest because the FPT is important not only in physics but also in chemistry, biology, medicine, agriculture, engineering, and finance. Additionally, the central equations often appear in physics and engineering with only trivial variations, making the solution techniques widely applicable.
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来源期刊
American Journal of Physics
American Journal of Physics 物理-物理:综合
CiteScore
1.80
自引率
11.10%
发文量
146
审稿时长
3 months
期刊介绍: The mission of the American Journal of Physics (AJP) is to publish articles on the educational and cultural aspects of physics that are useful, interesting, and accessible to a diverse audience of physics students, educators, and researchers. Our audience generally reads outside their specialties to broaden their understanding of physics and to expand and enhance their pedagogical toolkits at the undergraduate and graduate levels.
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