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Total reflection of a plane wave by a semi-infinite random medium

Published online by Cambridge University Press:  13 March 2009

P. L. Sulem
Affiliation:
Observatoire de Nice, 06 Nice, France
U. Frisch
Affiliation:
Observatoire de Nice, 06 Nice, France

Abstract

An exact result in the theory of wave propagation in random media is presented. Using the ergodic theory of dynamical systems, it is shown that a semi-infinite, one-dimensional random medium is totally reflecting. A direct numerical study shows that the mean reflection coefficient converges exponentially to one.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1972

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References

REFERENCES

Arnold, U. I. & Avez, A. 1967 Problèmes Ergodiques de la Mécanique Classique Gautbier–Villars.Google Scholar
Barn, M. & Wolf, E. 1964 Principles of Optics (2nd edn.). Pergamon.Google Scholar
Bourret, R. 1962 Nuovo Cimento, 26, 1.CrossRefGoogle Scholar
Brown, W.P. 1972 J. Opt. Soc. Am. 62, 45.Google Scholar
Frisch, U. 1968 Wave propagation in random media. Probabilistic Methods in Applied Mathematics (ed. Bharucha–Reid, A. T.). Academic.Google Scholar
Furstenberg, H. 1963 Trans. Am. Math. Soc. 108, 377.CrossRefGoogle Scholar
Gazaryan, Y. L. 1969 Soviet Phys. JETP, 29, 996.Google Scholar
Halmos, P. R. 1956 Lectures on Ergodic Theory. Chelsea.Google Scholar
Halmos, P. R. 1961 Bull. Am. Math. Soc. 67, 70.Google Scholar
Keller, J. 1964 Amer. Math. Soc. Proc. Symp. Appl. Math. 16, 145.Google Scholar
Lau, C. & Watson, K. M. 1970 J. Math. Phys. 11, 3125.Google Scholar
Klyatskin, V. I. 1971 Soviet Phys. JETP, 33, 703.Google Scholar
Klyatskin, V. I. & Tatarski, V. I. 1970 Soviet Phys. JETP, 31, 335.Google Scholar
Mckenna, J. & Morrison, J. A. 1970 J. Math. Phys. 11, 2348.Google Scholar
Morisson, J. A. & McKenna, J. 1970 J. Math. Phys. 11, 2361.CrossRefGoogle Scholar
Morisson, J. A., Papanicolaou, G. C. & Keller, J. B. 1971 Comm. Pure Appl. Math. 24, 473.Google Scholar
Papanicolaou, G. C. 1971 Siam J. Appl. Math. 21, 13.Google Scholar
Papaniculaou, G. C. & Keller, J. 1971 Siam J. Appl. Math. 21, 287.Google Scholar
Peacher, J. L. & Watson, K. M. 1970 J. Math. Phys. 11, 1496.Google Scholar
Pitt, H. R. 1942 Proc. Camb. Phil. Soc. 38, 325.Google Scholar
Sinai, I. G. 1971 Actes du Congrès International des Mathématiciens, de Nice, vol. 2, p. 929. Gauthier–Vilars.Google Scholar
Sobolev, V. V. 1963 A Treatise on Radiative Transfer. Van Nostrand.Google Scholar
Tatarski, V. I. 1961 Wave Propagation in a Turbulent Medium. McGraw-Hill.Google Scholar
Tortrat, A. 1971 Calcul des Probabilités. Masson.Google Scholar
Tutubalin, V. N. 1965 Theor. Probability Appl. 10, 15.Google Scholar
Uhlenbeck, G. E. & Ford, G. W. 1963 Lectures in Statistical Mechanics. American Mathematical Society.Google Scholar
Ulam, S. & Neumann, J. Von 1945 Bull. Am. Math. Soc. 51, 600.Google Scholar
Watson, K. M. 1969 J. Math. Phys. 10, 688.Google Scholar
Watson, K. M. 1970 Phys. Fluids, 13, 2514.Google Scholar