The transport of self-propelled particles with memory eects is investigated in a two-dimensional periodic channel. Funnel-shaped barriers are regularly arrayed in the channel. Due to the asymmetry of the barriers, the self-propelled particles can be rectified. It is found that the memory eects of the rotational diusion can strongly aect the rectified transport. The memory eects do not always break the rectified transport, and there exists an optimal finite value of correlation time at which the rectified eciency takes its maximal value. We also find that the optimal values of parameters (the self-propulsion speed, the translocation diusion coecient, the rotational noise intensity, and the self-rotational diusion coecient) can facilitate the rectified transport. When introducing a finite load, particles with dierent self-propulsion speeds move to dierent directions and can be separated.

Directed transport of anisotropic chiral particles is numerically investigated in the presence of the regular arrays of rigid half-circle obstacles. It is found that due to the rotational–translational coupling, the transport of anisotropic particles is considerably more complicated compared to the isotropic case. For isotropic chiral particles, the transport direction is completely determined by the chirality of particles. However, for anisotropic chiral particles, the competition between the chirality and the anisotropic degree determines the transport direction. For a given chirality, by suitably tailoring parameters (the anisotropic degree and the self-propulsion speed), particles with different anisotropic degrees (or self-propulsion speed) can move in different directions and can be separated.

Transport of Brownian particles in a periodic channel coexisting with an energetic barrier is investigated in the presence of a curl-free force and a divergence-free force. It is found that the phase difference between the energetic barrier and the entropic barrier can determine the direction of transport without pressure-driven flow. The pressure-driven flow induces the negative current. When the four driving factors (the ac driving force, the pressure-driven flow, the energetic barrier, and the entropic barrier) compete with each other, the system exhibits peculiar properties. Remarkably, we can obtain multiple current reversals by suitably tailoring the system parameters.

By coupling three nonlinear 1D lattice segments, we demonstrate a thermal insulator model, where the system acts like an insulator for large temperature bias and a conductor for very small temperature bias. We numerically investigate the parameter range of the thermal insulator and find that the nonlinear response (the role of on-site potential), the weakly coupling interaction between each segment, and the small system size collectively contribute to the appearance of bidirectional negative differential thermal resistance (BNDTR). The corresponding exhibition of BNDTR can be explained in terms of effective phonon-band shifts. Our results can provide a new perspective for understanding the microscopic mechanism of negative differential thermal resistance and also would be conducive to further developments in designing and fabricating thermal devices and functional materials.

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