Direct transport of fractional overdamped deterministic motors in spatial symmetric potentials driven by biharmonic forces

Abstract

Physical significance of fractional damping for order 0 p 2 is demonstrated from the perspective that it can be explained as the memory of acceleration. Based on Caputo's fractional derivatives, the transport phenomenon of fractional overdamped deterministic motors in spatial symmetric potentials driven by biharmonic forces is investigated numerically. Relationships between transport velocity and model parameters are analyzed. The effect of fractional order is discussed in detail. Research shows that the contribution of historical acceleration increases or decreases monotonously with the historical moment varying with different fractional orders. With certain parameters the transport velocity can show generalized resonance when the spatial potential depth or the external force frequency varies. Furthermore, for some large orders, the velocity varies in step with the variation of potential depth and is in a direct proportional to the frequency if there is transport. Effect of fractional damping is intimately linked with the shape of the force. The memory of damping force can promote or inhibit the particle transport under different conditions, thus triggering abundant transport behaviors.