On the free path length distribution for linear motion in an n-dimensional box
(English)Manuscript (preprint) (Other academic)
We consider the distribution of free path lengths, or the distance betweenconsecutive bounces of random particles, in an n-dimensional rectangular box.If each particle travels a distance R, then, as R → ∞ the free path lengthscoincides with the distribution of the length of the intersection of a randomline with the box (for a natural ensemble of random lines) and we determinethe mean value of the path lengths. Moreover, we give an explicit formula(piecewise real analytic) for the probability density function in dimension twoand three.In dimension two we also consider a closely related model where eachparticle is allowed to bounce N times, as N → ∞, and give an explicit (againpiecewise real analytic) formula for its probability density function.Further, in both models we can recover the side lengths of the box fromthe location of the discontinuities of the probability density functions.
free path lengths
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-177289OAI: oai:DiVA.org:kth-177289DiVA: diva2:872110
QS 20152015-11-172015-11-172015-12-04Bibliographically approved