Abstract
A generalized approach has been proposed to describe the diffusive transport of inertial particles at which the known inertialess relations (in particular, between the concentration of particles and the corresponding flux) are supplemented by a factor allowing the calculation of inertial effects in terms of the matrix continued fraction method. The advantage of this approach, which is in the analytical representation of the results, is illustrated by solving the problem of the determination of the effective diffusion coefficient of an inertial particle in a sawtooth potential and the average velocity of the adiabatic inertial ratchet. The character of the nonanalytic behavior of these quantities in the presence of large gradients of the potential has been established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. von Smoluchowski, Ann. Phys. 48, 1103 (1915).
H. Riskin, The Fokker–Plank Equation. Methods of Solution and Applications (Springer, Berlin, 1989).
O. Klein, Ark. Mat., Astron. Fys. 16 (5), 1 (1922).
H. A. Kramers, Physica 7, 284 (1940).
V. I. Mel’nikov and S. V. Meshkov, J. Chem. Phys. 85, 1018 (1986).
P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
V. I. Mel’nikov, Phys. Rep. 209, 1 (1991).
V. I. Mel’nikov, JETP Lett. 40, 787 (1984).
W. T. Coffey and Yu. P. Kalmykov, The Langevin Equation, 3rd ed. (World Scientific, Singapore, 2012), Chap. 12
W. L. Reenbohn and M. C. Mahato, J. Stat. Mech.: Theor. Exp., P03011 (2009).
S. Saikia and M. C. Mahato, Phys. Rev. E 80, 062102 (2009).
W. T. Coffey, Y. P. Kalmykov, and S. V. Titov, Eur. Phys. J. Spec. Top. 222, 1847 (2013).
R. L. Stratonovich, Radiotekh. Elektron. 4, 497 (1958).
J. M. R. Parrondo, Phys. Rev. E 57, 7297 (1998).
V. M. Rozenbaum, I. V. Shapochkina, and T. E. Korochkova, JETP Lett. 98, 568 (2013).
V. M. Rozenbaum, Yu. A. Makhnovskii, I. V. Shapochkina, S.-Y. Sheu, D.-Y. Yang, and S. H. Lin, Phys. Rev. E 89, 052131 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.M. Rozenbaum, I.V. Shapochkina, 2015, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheckoi Fiziki, 2015, Vol. 102, No. 4, pp. 275–280.
Rights and permissions
About this article
Cite this article
Rozenbaum, V.M., Shapochkina, I.V. Analytical representation of the relations of inertial diffusion transport. Jetp Lett. 102, 248–253 (2015). https://doi.org/10.1134/S0021364015160110
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364015160110