Ratchet effect modeling by method of paradoxical games for stochastic fluctuations of double-well potential

Abstract

The ratchet effect is a directed nanoparticle flux phenomenon induced by nonequilibrium fluctuations in a system with spatial and (or) temporal asymmetry. One is used as the way to create a controlled nanotransport and is the basis of the theory of Brownian motors. Fluctuation motion simulation is a promising way to calculate the main characteristics of Brownian motors, it avoids complex calculations and quickly obtains predictions about the appearance or absence of generated directional motion in a specific model. Nonequilibrium fluctuations are usually introduced into the system by a dichotomous process that switches two periodic asymmetric potential profiles at certain fixed intervals (deterministic process), or randomly with average potential lifetimes (stochastic process). We investigate the modeling of the process of the ratchet effect in the framework of the Brownian motor jump-like model by the method of Parrondo’s paradoxical game for the stochastic dichotomous process and compare results with a similar deterministic process. A calculus method for the main characteristics obtaining of the motor with stochastic dichotomous process is proposed, it is shown correspondence to the analytical description of this model in extreme cases. It is shown that the stochasticity of the process directly affects the characteristics of the ratchet effect: the trajectories of the average displacements of nanoparticles fundamentally differs in the deterministic description, and a gradual difference in these processes is observed at low values. The study of asymmetric dichotomous processes for different temperature modes of motor operation is carried out. The model allows one to analyze the peculiarities of the directional motion starting at the level of single jumps, as well as to formulate recommendations for possible improvement of motor efficiency for different temperatures. For high-temperature mode, it is advisable to reduce the lifetime of the state with the active potential, and for low-temperature mode, arbitrary, it should be increased.