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복잡계 이론물리 연구단
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Surprising variants of Cauchy’s formula for mean chord length

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Title
Surprising variants of Cauchy’s formula for mean chord length
Author(s)
Prabodh Shukla; Diana Thongjaomayum
Publication Date
2019-11
Journal
PHYSICAL REVIEW E, v.100, no.5, pp.050103 -
Publisher
AMERICAN PHYSICAL SOCIETY
Abstract
We examine isotropic and anisotropic random walks which begin on the surface of linear (N ), square (N × N ), or cubic (N × N × N) lattices and end upon encountering the surface again. The mean length of walks is equal to N and the distribution of lengths n generally scales as n−1.5 for large n. Our results are interesting in the context of an old formula due to Cauchy that the mean length of a chord through a convex body of volume V and surface S is proportional to V/S. It has been realized in recent years that Cauchy’s formula holds surprisingly even if chords are replaced by irregular insect paths or trajectories of colliding gas molecules. The random walk on a lattice offers a simple and transparent understanding of this result in comparison to other formulations based on Boltzmann’s transport equation in continuum. ©2019 American Physical Society
URI
https://pr.ibs.re.kr/handle/8788114/6762
ISSN
2470-0045
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > Journal Papers (저널논문)
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