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Diffusion out of a triangle

Published online by Cambridge University Press:  14 July 2016

W. Smith and
G. S. Watson
W. Smith
Affiliation:
The Johns Hopkins University
G. S. Watson
Affiliation:
The Johns Hopkins University
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Abstract

A problem in molecular genetics called for the following result. If a particle is dropped at random on a right-angled isosceles triangle, and thus allowed to execute symmetrical Brownian motion, the chance that it will first leave the triangle via the hypotenuse is 0.41062. An inequality and two methods of deriving this probability are illustrated. The most useful source of solutions to diffusion problems of this kind is the torsion problem of elasticity.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 3 , November 1967, pp. 479 - 488
Copyright
Copyright © Applied Probability Trust 

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References

Abramowitz, M. and Stegun, Irene A. (1965) Handbook of Mathematical Functions. National Bureau of Standards Applied Mathematics Series 55, U.S. Government Printing Office, Washington, D.C. Google Scholar
Copson, E. T. (1935) Theory of Functions of a Complex Variable. Oxford University Press, London.Google Scholar
Courant, R. and Hilbert, D. (1953) Methods of Mathematical Physics. Vol. I. Wiley-Interscience, New York.Google Scholar
Galerkin, B. G. (1919) Torsion of a triangular prism. Izv. Akad. Nauk, SSSR. 111–118.Google Scholar
Kellogg, O. D. (1953) Foundations of Potential Theory. (1st Edition 1929). Reissued by Dover Publications, New York.Google Scholar
Kolossov, G. V. (1924) Sur la torsion des prismes ayant pour base un triangle rectangle. C. R. Acad. Sci. Paris 178, 2057–2060.Google Scholar
Lamb, Horace Sir (1945) Hydrodynamics (6th Edition). Reissued by Dover Publications, New York.Google Scholar
Lévy, P. (1948) Processus Stochastiques et Mouvement Brownien. Gauthier-Villars, Paris.Google Scholar
Love, A. E. H. (1944) A Treatise on the Mathematical Theory of Elasticity (4th Edition). Reissued by Dover Publications, New York.Google Scholar
Mushkelishvili, N. I. (1953) Some Basic Problems of the Mathematical Theory of Elasticity. (Translated Radok, J. R. M.). P. Noordhoff, Groningen.Google Scholar
Watson, G. S., Smith, W. K. and Thomas, C. A. (1966) Recombination of a pool of DNA fragments with complementary single-chain ends. In Progress in Nucleic Acid Research and Molecular Biology, Vol. 5. Academic Press, New York and London.Google Scholar