The transient behavior of a Brownian motor is investigated for more detailed particle transport occurring therein. The asymmetric nature of the time-dependent mean particle velocity is examined during the transition between two different levels of thermal noise. The possibility of current inversion is also investigated. It is found that the detailed shape of the asymmetric potential is crucial for such an inversion to occur.

We develop in this work flux reconstruction (FR) schemes for one-dimensional Fokker-Planck equations with drift-admitting jumps, which have applications in describing the propagators of piecewise-smooth stochastic differential equations. Since the propagators are nonsmooth at the jumps of the drift, difficulties arise in finding the corresponding solutions not only theoretically but also numerically. To be more specific, the main difficulties lie in the fact that two matching conditions have to be imposed simultaneously at each jump, i.e., where the the propagator and the probability current are continuous. In this work, we show that the FR method is an ideal choice for designing numerical schemes for solving this problem. The corresponding FR schemes are given in details. Some benchmark examples are also employed to validate the proposed schemes numerically.