Symmetry breaking: Abnormal transport induced by mass modulation.

Here, we investigate transport of an inertial particle in a symmetric periodic potential and subjected to an external signal, such that mass of the particle is modulated sinusoidally. Our numerical results indicate that the mass modulation can induce abnormal transport in the system, whereas no current appears in the case of constant mass. In the absence of external bias, direction of mean velocity of the particle changes several times as amplitude and frequency of the mass modulation are varied, i.e., a multiple current reversals (CR) phenomenon. The multiple CRs result from temporal symmetry breaking of the system. In the presence of external bias, multiple absolute negative mobilities (ANM) take place in the system. Intrinsic physical mechanisms responsible for the occurrence of the multiple ANMs are analyzed in detail.

Heat conduction of symmetric lattices.

Heat conduction of symmetric Frenkel-Kontorova (FK) lattices with a coupling displacement was investigated. Through simplifying the model, we derived analytical expression of thermal current of the system in the overdamped case. 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 temperature 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 coupling 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.

Multiple current reversals and diffusion enhancement in a symmetrical periodic potential.

Transport and diffusion of Brownian particles in a symmetrical periodic potential were investigated for both overdamped and underdamped cases, where the ratchet potential is driven by an external unbiased time periodic force and correlation between thermal and potential fluctuations. It is shown that the correlation between two noises breaks the symmetry of the potential to generate motion of the Brownian particles in particular direction, and the current can reverse its direction by changing the sign of the noise correlation. For the overdamped case, the systemic parameters only induce the directed current, and the noise correlation suppresses the diffusion of the overdamped Brownian particles. However for the underdamped case, the current reverses its direction multiple times with increasing the systemic parameters, i.e., the multiple current reversal is observed, and the noise negative correlation suppresses the diffusion of the underdamped Brownian particles, while the noise positive correlation enhances it.

Effects of time delay on symmetric two-species competition subject to noise.

Noise and time delay act simultaneously on real ecological systems. The Lotka-Volterra model of symmetric two-species competition with noise and time delay was investigated in this paper. By means of stochastic simulation, we find that (i) the time delay induces the densities of the two species to periodically oscillate synchronously; (ii) the stationary probability distribution function of the two-species densities exhibits a transition from multiple to single stability as the delay time increases; (iii) the characteristic correlation time for the sum of the two-species densities squared exhibits a nonmonotonic behavior as a function of delay time. Our results have the implication that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems.