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Mean free paths in a convex reflecting region

Published online by Cambridge University Press:  14 July 2016

J. F. C. Kingman
J. F. C. Kingman*
Affiliation:
University of Sussex
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Extract

Kendall and Moran ([4], §3.41) consider the following problem, which first arose in connexion with the acoustical design of auditoria. Imagine a convex room with perfectly reflecting walls, and suppose that a particle is projected from a point inside the room. Then it will bounce around the room, and its trajectory will consist of a large number of straight segments. The average length of these segments is the mean free path of the particle.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 1 , June 1965, pp. 162 - 168
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Bate, A. E. and Pillow, M. E. (1947) Mean free path of sound in an auditorium. Proc. Phys. Soc. 59, 535–541.CrossRefGoogle Scholar
[2] Doob, J. L. (1953) Stochastic Processes. John Wiley, New York.Google Scholar
[3] Jäger, G. (1911) Zur theorie des nachhalls. Sitzungsebr. Wiener Akad. Math. Naturw. Kl. 120, IIa, 613–634.Google Scholar
[4] Kendall, M.G. and Moran, P. A. P. (1963) Geometric Probability. Griffin, London.Google Scholar
[5] Reidemeister, K. (1921) Über die singulären Randpunkte eines konvexen Körper. Math. Ann. 83, 116–118.Google Scholar
[6] Zaanen, A. C. (1958) An Introduction to the Theory of Integration. North-Holland.Google Scholar