Effect Of External Periodic Regulations On Thermal Current And Particle Flow

Effect of external periodic regulations on current of a system was investi-gated in this paper. The first chapter mainly introduce the study background, actuality of the heat conduction of nonlinear lattice and the BM’current are respectively summarized.The fundamental theory of nonlinear stochastic dy-namics is introduced in the second chapter. The third chapter study the effect of external periodic regulations on thermal current of a simply model of symmetric Frenkel-Kontorova (FK) lattices with a coupling displacement.Effect of exter-nal periodic regulations on current of a symmetric Brownian motor performing between two temperature sources was investigated in the forth chapter.The last include the conclusion and outlook.Through simplifying the model, we derived analytical expression of ther-mal current of the system in the overdamped case to study effect of external periodic regulations on thermal current. By means of numerical calculations, the results indicate that:(ⅰ) As the coupling displacement d equals to zero, temperature oscillations of the heat baths linked with the lattices can control magnitude and direction of the thermal current; (ⅱ) Whether there is a tem-perature bias or not, the thermal current oscillates periodically with d, whose amplitudes become greater and greater; (ⅲ) As d is not equal to zero, the thermal current monotonically both increases and decreases with temperature oscillation amplitude of the heat baths, dependent on values of d; (ⅳ) The cou-pling displacement also induces nonmonotonic behaviors of the thermal current vs spring constant of the lattice and coupling strength of the lattices; (ⅴ) These dynamical behaviors come from interaction of the coupling displacement with periodic potential of the FK lattices. Our results have the implication that the coupling displacement plays a crucial role in the control of heat current.Studying the effect of external periodic regulations on BM’ current, by means of numerical calculations, we found that the regulations can control magnitude and direction of the motor’s current to a large degree. As one of the motor’s compartments is regulated, the motor’s current can be both inversed and maximized, dependent on amplitude and frequency of the periodic driving force. If two periodic driving forces with identical amplitudes and frequencies are employed to regulate respectively two compartments of the Brownian motor, the current’s magnitude and direction will make periodic oscillations with phase difference between them. In addition, the external periodic regulation can also change direction of thermal rectifier of the system as a switch.