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On the free path length distribution for linear motion in an n-dimensional box
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
KTH, School of Electrical Engineering and Computer Science (EECS), Electromagnetic Engineering.ORCID iD: 0000-0003-4740-1832
2018 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, no 46, article id 465201Article in journal (Refereed) Published
Abstract [en]

We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R -> infinity the free path length coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we give an explicit formula (piecewise real analytic) for the probability density function in dimension two and three. In dimension two we also consider a closely related model where each particle is allowed to bounce N times, as N -> infinity, and give an explicit (again piecewise real analytic) formula for its probability density function. Further, in both models we can recover the side lengths of the box from the location of the discontinuities of the probability density functions.

Place, publisher, year, edition, pages
IOP PUBLISHING LTD , 2018. Vol. 51, no 46, article id 465201
Keywords [en]
free, path, length, distribution
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-246299DOI: 10.1088/1751-8121/aae5eeISI: 000460029900001Scopus ID: 2-s2.0-85055489270OAI: oai:DiVA.org:kth-246299DiVA, id: diva2:1298288
Note

QC 20190321

Available from: 2019-03-22 Created: 2019-03-22 Last updated: 2019-05-13Bibliographically approved

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Holmin, SamuelKurlberg, PärMånsson, Daniel

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