Точні аналітичні розв’язки в теорії броунівських моторів і насосів

• Date: 2012
• Author Affiliations: T. Ye. Korochkova — Інститут хімії поверхні ім. О.О. Чуйка Національної академії наук України; N. G. Shkoda — Інститут хімії поверхні ім. О.О. Чуйка Національної академії наук України; A. A. Chernova — Інститут хімії поверхні ім. О.О. Чуйка Національної академії наук України; V. M. Rozenbaum — Інститут хімії поверхні ім. О.О. Чуйка Національної академії наук України
• Keywords: keywords
• Main Authors: Korochkova, T. Ye., Shkoda, N. G., Chernova, A. A., Rozenbaum, V. M.
• Format: Article
• Language: Russian
• Published: Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine 2012
• Online Access: https://surfacezbir.com.ua/index.php/surface/article/view/468
• Journal Title: Surface

We have considered the diffusion dynamics of a Brownian particle, with its potential energy undergoing, in the force field of the environment, dichotomic fluctuations between two potential profiles representing piecewise linear functions.  It is shown that if on some variation interval of these functions the slopes of their linear pieces are equal or opposite in sign, then the general solution of the system of differential equations describing the diffusion dynamics can be written in a simple analytic form. This allows derivation of exact solutions for the average velocity of the particle directed motion induced by potential energy fluctuations, as far as the following cases are concerned: a Brownian motor with extremely asymmetric sawtooth potential fluctuating by half a period, a Brownian pump with two sign-fluctuating linear pieces of the potential, and a reciprocating Brownian motor with a V-shaped potential profile undergoing shift fluctuations. For the situations mentioned, the regularities have been established referring to the dependence of the nanoparticle average velocity on the temperature and potential fluctuation frequency.