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Probability of random paths across elementary geometrical shapes

Published online by Cambridge University Press:  14 July 2016

Maurice Horowitz
Maurice Horowitz*
Affiliation:
The Magnavox Company, Fort Wayne, Indiana
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Extract

There are several practical situations where one requires the statistical properties of the straight path length l across a specified geometrical shape. Typical examples are the length of the path of a gamma-ray to the wall of a nuclear reactor (Primak (1956)), the length of a sound ray in a room from one reflection to the next (Kosten (1960)), or the length of a straight path across a square (Horowitz (1964)).

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 1 , June 1965 , pp. 169 - 177
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Groenewoud, Cornelius (1964) Private communication.Google Scholar
[2] Horowitz, M. (1964) Mean random path across a square. Notices Amer. Math. Soc. 11, 55 (Abstract 608–6).Google Scholar
[3] Jäger, G. (1911) Zur theorie des nachhalls. Wiener Akad. Ber., Math-naturw. Klasse. Bd. 120, Abt. IIa.Google Scholar
[4] Kendall, D.G. and Moran, P. A. P. (1963) Geometrical Probability. Hafner Publishing Company, New York.Google Scholar
[5] Kosten, C. W. (1960) The mean free path in room acoustics. Acustica 10, 245–250.Google Scholar
[6] Primak, W. (1956) Gamma-ray dosage in inhomogeneous nuclear reactors. J. Appl. Physics 27, 56.CrossRefGoogle Scholar