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Brownian motors belong to the class of nanoscale devices that use the thermal noise of the environment as one of the necessary components in the mechanism of their operation. Today, there are a lot of practical implementations of such nanomachines, both inorganic, fairly simple mechanisms produced artificially, and more complex ones created from separate biological components available at the cellular level. One of the options for implementing the mechanism of straightening the chaotic thermal noise of the environment into unidirectional motion is the presence of a motor particle in the field of action of an asymmetric periodic stationary potential, which undergoes certain small disturbances (fluctuations) periodically over time. To describe such asymmetric one-dimensional structures (for example, dipole chains or fibers of the cytoskeleton) in the theory of Brownian motors, two model potentials are most often used: piecewise linear sawtooth and double sinusoidal. In this work, within the framework of the approximation of small fluctuations, a model of a pulsating Brownian motor with a stationary double sinusoidal potential and a disturbing small harmonic signal is considered. A new method of parametrization of such a problem is proposed, which allows to separate the contributions from various factors affecting the operation of the ratchet, and the numerical procedure for calculating the average speed of the directional movement of nanoparticles for the selected type of model potentials is specified. A number of numerical dependences of the average speed on the main parameters of the system were obtained. Peculiarities of the behavior of the motor as dependent on the parameter responsible for asymmetry and the number of potential wells on the spatial period of the stationary potential have been investigated. It is shown that the direction of the generated flux of nanoparticles depends not only on the phase shift between the stationary and fluctuating components of the potential, but also on the temperature of the system and the frequency of fluctuations, i.e., a possibility of temperature-frequency control of the direction of movement in the considered model has been found. Diagrams have been constructed that allow you to choose the ratio between the parameters of the nanomotor to create a flux of particles in the desired direction. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]