Directed transport and collective dynamics of pulsing particles in topological lattices

We investigated the directed transport and collective patterns of pulsing particles with periodic size variation in topological lattices. Self-pulsing provides energy input at the individual level and serves as nonequilibrium driving. The distribution of the topological lattice determines the direction of particle motion, with pulsing particles preferentially moving toward high-density lattice regions, in contrast to the behavior of conventional active particles. The competition dynamics of repulsion contraction and synchronization give rise to deformation waves in dense particle environments, including both planar and circular waves, corresponding to a disordered state. These deformation waves exhibit local order but global disorder. Notably, directed transport is most pronounced in the disordered state, whereas particles exhibit no directed transport in the arrested ordered state. Additionally, optimal values of the self-pulsing parameters (the driving frequency, the self-pulsation amplitude, and the strengths of synchronization) lead to a peak in the average velocity. The particle number density also significantly influences directed transport, as an increase in number density promotes directed transport.