Search

A relevant and important question in studying the transport of nanoparticles is the possibility and methods of controlling the generated currents. One of the possibilities is to use the ratchet effect, i.e. the occurrence of directed motion as a result of the influence of nonequilibrium fluctuations of various nature when one or more symmetries in the system are broken. To implement the ratchet effect, a deterministic dichotomous process is often used, which can be modeled by two alternating states that have constant characteristics. Usually, the main factor determining the direction of motion of a Brownian motor is the spatial asymmetry of the potential profile. In certain cases, for example, for a double-well potential profile, one can relatively easily investigate the conditions for reversal of the direction of motor motion. In this paper, using the idea of Parrondo’s paradox games consisting of alternating strategies of a game that provides an average winning, we simulated the ratchet effect for a diffusion hopping model of an adiabatic Brownian motor with an asymmetric double-well on-off potential. The conditions affecting the direction of nanoparticle motion are investigated, the possibility of temperature control of the motion direction is shown, and an estimate of the generated average velocity of the Brownian motor in the adiabatic approximation is obtained. The motor functioning is simulated in terms of the game theory and the average trajectories of capital accumulation are obtained, which correspond to the trajectories of the average displacement of a Brownian particle due to the ratchet effect. For the chosen model, it is shown that, at low temperatures, a particle moves to the right in accordance with the simplest on-off ratchet model, while, at high temperatures, the motion reverses. A comparison of the simulation results with the values of the ratchet velocity obtained within the adiabatic approximation shows that this approximation becomes valid at sufficiently large values of the lifetimes of the states of the dichotomous process, and it turns out to be much more accurate in the high-temperature region than in the low-temperature one. [ABSTRACT FROM AUTHOR]

In this paper heterogeneous subjects are investigated, namely laminated nanoparticles and flat-layered media. Common feature of objects under consideration is presence of surfaces divided into slabs with different physical characteristics. The aim of the work is to demonstrate large possibilities and certain preferences of transfer matrices method for solution different problems of applied physics and generalization of the results taken out by author early. The method is especially convenient for analysis of such systems under action of different external physical fields. The method makes possible to transfer boundary conditions from slab to slab, to avoid the necessity of consideration of high order algebraical systems and matrices inversion problem is reduced to theirs simple multiplication. We presented a general scheme of building transfer matrices based on conversion of partial differential equations to ordinary differential equations with using expansion by a system of orthogonal functions. In addition to known results, the transfer matrices for inhomogeneous differential equations are constructed, i.e. those for physical systems with internal energy sources. Transfer matrix method has been used to solve some applied problems, especially problems of electromagnetic scattering on ellipsoidal nanoparticles (electrostatic approximation), spherical particles (electrostatic and wave approximations), expressions for calculations of electrical energy in slabs are found. Solution of Eigen value problems for multilayer panels is constructed, design formulas for determination of oscillation Eigen frequencies of multilayer panel with using three-dimensional elasticity theory are also obtained. Design formulas and some typical artwork are presented. [ABSTRACT FROM AUTHOR]