Wave front propagation in the active coagulation model

Spreading processes on top of active dynamics provide a novel theoretical framework for capturing emerging collective behavior in living systems. I consider run-and-tumble dynamics coupled with coagulation/decoagulation reactions that lead to an absorbing state phase transition. While the active dynamics does not change the location of the transition point, the relaxation toward the stationary state depends on motility parameters. Because of the competition between spreading dynamics and active motion, the system can support long-living currents whose typical time scale is a nontrivial function of motility and reaction rates. Because of this interplay between time-scales, the wave front propagation qualitatively changes from traveling to diffusive waves. Moving beyond the mean-field regime, instability at finite length scales regulates a crossover from periodic to diffusive modes. Finally, it is possible to individuate different mechanisms of pattern formation on a large time scale, ranging from the Fisher-Kolmogorov to the Kardar-Parisi-Zhang equation.