Reaction processes among self-propelled particles

Abstract

We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state maintains physical contact with another particle for a finite period of time. We refer to this process as a reaction process and to the different internal states as particle species making an analogy to chemical reactions. The studied system may fall into an absorbing phase, where due to the disappearance of one of the particle species no further reaction can occur or remain in an active phase where particles constantly react. Combining individual-based simulations and mean-field arguments, we study the dependence of the equilibrium densities of particle species with motility parameters, specifically the active speed $v_0$ and tumbling frequency $λ$. We find that the equilibrium densities of particle species exhibit two very distinct, non-trivial scaling regimes with $v_0$ and $λ$ depending on whether the system is in the so-called ballistic or diffusive regime. Our mean-field estimates lead to an effective renormalization of reaction rates that allow building the phase-diagram $v_0$--$λ$ that separates the absorbing and active phase. We find an excellent agreement between numerical simulations and estimates. This study is a necessary step to an understanding of phase transitions into an absorbing state in active systems and sheds light on the spreading of information/signaling among moving elements.