Abstract
The problem of Wang and Uhlenbeck on the imposition of boundary conditions for space in the Fokker-Planck-Kramers equation is solved for Brownian motion under uniform and gravitational potentials. These cases with the full consideration of inertial effects lead to a modified diffusion equation with time-dependent diffusion coefficients determined by the initial condition of the velocity distribution. Moreover, the former case is applied to the rate theory for the diffusion limited reaction in liquids and new results have been obtained especially for the short time behavior where inertial effects play an important role.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Crank,The Mathematics of Diffusion (Clarendon Press, Oxford, 1975).
H.S. Carslaw and J.C. Jaeger,Conduction of Heat in Solids (Clarendon Press, Oxford, 1959).
M.C. Wang and G.E. Ulenbeck, Rev. Mod. Phys. 17 (1945) 323.
D.F. Calef and J.M. Deutch, Ann. Rev. Phys. Chem. 34 (1983) 493.
S. Harris, J. Chem. Phys. 78 (1983) 4698, where other references can be found.
A. Morita, J. Chem. Phys. 96 (1992) 3678.
S.A. Rice,Diffusion-Limited-Reactions (Elsevier, Amsterdam, 1985).
S. Chandrasekhar, Rev. Mod. Phys. 15 (1943) 1.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Morita, A. Diffusion processes with inertial effects and with boundary conditions — A solution to the Wang and Uhlenbeck problem. J Math Chem 16, 49–60 (1994). https://doi.org/10.1007/BF01169195
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01169195