Chemotaxis of artificial microswimmers in active density waves.

Living microorganisms are capable of a tactic response to external stimuli by swimming toward or away from the stimulus source; they do so by adapting their tactic signal transduction pathways to the environment. Their self-motility thus allows them to swim against a traveling tactic wave, whereas a simple fore-rear asymmetry argument would suggest the opposite. Their biomimetic counterpart, the artificial microswimmers, also propel themselves by harvesting kinetic energy from an active medium, but, in contrast, lack the adaptive capacity. Here we investigate the transport of artificial swimmers subject to traveling active waves and show, by means of analytical and numerical methods, that self-propelled particles can actually diffuse in either direction with respect to the wave, depending on its speed and waveform. Moreover, chiral swimmers, which move along spiraling trajectories, may diffuse preferably in a direction perpendicular to the active wave. Such a variety of tactic responses is explained by the modulation of the swimmer's diffusion inside traveling active pulses.

Extreme events due to localization of energy.

We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localization of energy, this system exhibits extreme events in the sense that individual elements of the chain show very large excitations. A detailed statistical analysis of extremes in this system reveals some unexpected properties, e.g., a pronounced pattern in the interevent interval statistics. We relate these statistical properties to underlying system dynamics and notice that often when extreme events occur the system dynamics adopts (at least locally) an oscillatory behavior, resulting in, for example, a quick succession of such events. The model therefore might serve as a paradigmatic model for the study of the interplay of nonlinearity, energy transport, and extreme events.