Symmetric Brownian Motor Flow Studies

In this paper, one of the symmetric Brownian motors is investigated sys-tematically. In chapter one, the development and the study significance of the Brownian motor are briefly introduced. In addition, the study significance of probability current and its status are roughly expounded. In chapter two, the conventional methods on the current are illustrated. The contents of chapter three are my research work:in delayed symmetric Brownian motor, how delay time affects the Brownian motor is analytically studied; for the Brownian motor driven by Gaussian colored noise, the current is mainly discussed in numerical simulation.For the delayed symmetric Brownian motor, the expression of stable cur-rent is analytically derived by exploiting adiabatic approximation in the small time delay. Based upon this, how delay time, noise intensity ratio and correla-tion coefficient affect current is discussed. By means of numerical calculation, the results are shown that the current increases first with the delay time increas-ing. Then the current decreases with the delay time increasing. Furthermore, there is a critical point in this system. When delay time is larger than the critical point, the current will be minus and the current is reversed. In order to confirm these, the results got by means of the numerical simulation is given and they are true to the results by means of the numerical calculation. Meanwhile, the relationship between the current and noise intensity ratio can confirm what is got by means of the numerical calculation, so can the relationship of the cur-rent and correlation coefficient. At last, the results are explained by discussing corrected potential.The Brownian motor driven by colored noise is studied. The result is indicated that correlation time of Gaussian colored noise can change the size of the current on the proper parameters.