BINARY RANDOM WAI KS: AIIDENDL‘M
71
It is expected that thc solution to Eq. (36) should exhibit behavior similar to
Eq. (37). although only rough estimates of the effect of integrating FPBr over
its past history have been made.
ACKNOWLEDGEMENTS
The author wishes to thank S. Corrsin for his encouragement and persistence. This work was
supported by the ORicc of Naval Research, Contract NONR 4010 (5). and a portion by the
Sloan Foundation.
REFERENCFS
Chiindrasekhar, S. (1943). Stochastic probkms in physics and astronomy. Reu. Mad. Phys. IS,
1.
Einstein, A. (1905). [Jber die von der mokkularkinetischen Yheorie der W H m geforderte
fkwegung von in ruhenden Fliissipkeilen suspendierten Teilchen. Ann. Phys. (Leipzig) 17.
549.
Feller. W. (1957). “An Introduction to Probability Theory and Its Applications,” 2nd Ed. Wiley.
New Yorli.
(ioldstein. S. ( 1 9 5 I). O n diffusion hy discontinuous movements. and on the telegraph equation.
Quurt. .I Medt. Appl. Maih. 4. Part 2, 129.
Kampk de Ferict, J. (1959). Statistical mechanics and theoretical models ofdiiTusion processes.
.4dUUIl. Geophys. 6, 139.
Lumley. 1. 1.. (1961). Distribution and dispersion in the Euler-Lagrange random walk. Appl.
Sci. Rrs.. Sec. A 10, 153.
Lumley. J. L.. and Corrsin, S. (1959). A random walk with both Lagrangion and Eukrian
statistics. .4di:cin. Gc.ophys. 6. 17Y.
Paticrson, G . S.. Jr. (1966). Walks on a random binary velocity field. Ph.D. Thesis, Johns
fbpkins L‘niv., Baltimore, Maryland.
Patterson, G . S.. Jr.. and Corrsin. S. (1966). Computer experiments on random walks with both
Eulcriiin and Lagangian hlatistics. In “Dynamics of Fluids and Plasmas” (S. I. Pai, ed.).
pp. 275 307. Academic Press. New York.
Hayleigh, Lord (1880). On the resultant o l a larp number of vibrations of the same pitch and of
arbitrary pha\e. Phil. Mug. 10. 73. [Also Sci. Pup. 1, 491.1
Riley. J J.. :ind Patterson. G. S.. Jr. (1974). Turbulent diffusion on numerically integrated
velocity lields. P h p . f/rticl\ (10 be published).
v o i i hrnoluchou~ki. (1916). Drei Vortrage iiber Dithion, Brownsche Bcwegung und K u ~ -
guliitiori \on Kolloidteilchcn. P/i~..v. Z . 17, 557.
71
It is expected that thc solution to Eq. (36) should exhibit behavior similar to
Eq. (37). although only rough estimates of the effect of integrating FPBr over
its past history have been made.
ACKNOWLEDGEMENTS
The author wishes to thank S. Corrsin for his encouragement and persistence. This work was
supported by the ORicc of Naval Research, Contract NONR 4010 (5). and a portion by the
Sloan Foundation.
REFERENCFS
Chiindrasekhar, S. (1943). Stochastic probkms in physics and astronomy. Reu. Mad. Phys. IS,
1.
Einstein, A. (1905). [Jber die von der mokkularkinetischen Yheorie der W H m geforderte
fkwegung von in ruhenden Fliissipkeilen suspendierten Teilchen. Ann. Phys. (Leipzig) 17.
549.
Feller. W. (1957). “An Introduction to Probability Theory and Its Applications,” 2nd Ed. Wiley.
New Yorli.
(ioldstein. S. ( 1 9 5 I). O n diffusion hy discontinuous movements. and on the telegraph equation.
Quurt. .I Medt. Appl. Maih. 4. Part 2, 129.
Kampk de Ferict, J. (1959). Statistical mechanics and theoretical models ofdiiTusion processes.
.4dUUIl. Geophys. 6, 139.
Lumley. 1. 1.. (1961). Distribution and dispersion in the Euler-Lagrange random walk. Appl.
Sci. Rrs.. Sec. A 10, 153.
Lumley. J. L.. and Corrsin, S. (1959). A random walk with both Lagrangion and Eukrian
statistics. .4di:cin. Gc.ophys. 6. 17Y.
Paticrson, G . S.. Jr. (1966). Walks on a random binary velocity field. Ph.D. Thesis, Johns
fbpkins L‘niv., Baltimore, Maryland.
Patterson, G . S.. Jr.. and Corrsin. S. (1966). Computer experiments on random walks with both
Eulcriiin and Lagangian hlatistics. In “Dynamics of Fluids and Plasmas” (S. I. Pai, ed.).
pp. 275 307. Academic Press. New York.
Hayleigh, Lord (1880). On the resultant o l a larp number of vibrations of the same pitch and of
arbitrary pha\e. Phil. Mug. 10. 73. [Also Sci. Pup. 1, 491.1
Riley. J J.. :ind Patterson. G. S.. Jr. (1974). Turbulent diffusion on numerically integrated
velocity lields. P h p . f/rticl\ (10 be published).
v o i i hrnoluchou~ki. (1916). Drei Vortrage iiber Dithion, Brownsche Bcwegung und K u ~ -
guliitiori \on Kolloidteilchcn. P/i~..v. Z . 17, 557.