Motion reversal modeling for a Brownian particle affected by nonequilibrium fluctuations

Modeling the Jump-like Diffusion Motion of a Brownian Motor by a Game- Theory Approach: Deterministic and Stochastic Models

“…Figures 2a and 2b are related to the lifetimes values τ A = τ B = 2 and τ A = τ B = 5 (for deterministic dependencies) and the corresponding frequencies γ A = γ B = 1/2 and γ A = γ B = 1/5 (for stochastic dependencies); below we will indicate these sets of the time parameters as [2; 2] and [5; 5]. The obtained graphical results supplement the known deterministic results [21] with dependencies characteristic of ratchets with the stochastic alternating the states. In both figures, the upper pairs of the trajectories (calculated with the set (a) of the probability values and marked with open markers) demonstrate the increase in capital, or, in terms of the theory of Brownian motors, a rightward shift of particles.…”

“…In this work, we have continued and expanded the results of Refs. [20,21] devoted to the application of game-theory models to study the nonequilibrium nanoparticle transport arising due to the ratchet effect. Using the technique proposed in Refs.…”

“…For an on-off ratchet, one of the ways to affect the ratchet motion direction is to use a double-well potential, its minima being located at different distances from the location its highest barrier [27]. Parametrization of such a potential in terms of probabilities of transitions between the potential wells was performed in [21] (using the Arrhenius law, the values of transition probabilities are assign to the values of minima and maxima of the potential profile), the results of [21] were used here to construct the computational model. In the state B, which describes the free diffusion, the geometric arrangement of nodes 1 and 2 (determining motion direction) is characterized by different probabilities of the jump of particles from these nodes (in Eq.…”

“…Let us denote by (a) and (b) the sets of parameter values associated, respectively, with the low-temperature (β∆V = 2) and high-temperature (β∆V = 0.5) ratchet operation modes. Then, according to [21], the parameterization of the corresponding potential profiles makes it possible to operate in the hopping model with the following sets of transition probabilities: (a) 2 shows the averaged, over 3 million realizations (experiments), trajectories of capital accumulation for the deterministic (the solid curves with square markers) and stochastic (the dotted curves with round markers) dichotomous process. Figures 2a and 2b are related to the lifetimes values τ A = τ B = 2 and τ A = τ B = 5 (for deterministic dependencies) and the corresponding frequencies γ A = γ B = 1/2 and γ A = γ B = 1/5 (for stochastic dependencies); below we will indicate these sets of the time parameters as [2; 2] and [5; 5].…”

“…Consideration of the high-temperature ratchets [19] showed that, all other things being equal, the manner in which the potentials are switched significantly affects the characteristics of the ratchet effect: Its intensity (the maximum motor velocity) is higher for deterministic ratchet systems, while for stochastic ratchet systems, the fluctuation frequency range is wider, allowing, obviously, more degree of freedom in controlling the motor motion. In previous works [20,21], we used the game-theory techniques to construct hopping models of deterministic Brownian motors with a double-well potential profile.…”