Biased motility-induced phase separation: from chemotaxis to traffic jams

We propose a one-dimensional model of active particles interpolating between quorum sensing models used in the study of motility-induced phase separation (MIPS) and models of congestion of traffic flow on a single-lane highway. Particles have a target velocity with a density-dependent magnitude and a direction that flips with a finite rate that is biased toward moving right. Two key parameters are the bias and the speed relaxation time. MIPS is known to occur in such models at zero bias and zero relaxation time (overdamped dynamics), while a fully biased motion with no velocity reversal models traffic flow on a highway. Using both numerical simulations and continuum equations derived from the microscopic dynamics, we show that a single phase-separated state extends from the usual MIPS to congested traffic flow in the phase diagram defined by the bias and the speed relaxation time. However, in the fully biased case, inertia is essential to observe phase separation, making MIPS and congested traffic flow seemingly different phenomena if not simultaneously considering inertia and tumbling. We characterize the velocity of the dense phase, which is static for usual MIPS and moves backward in traffic congestion. We also find that in presence of bias, the phase diagram becomes richer, with an additional transition between phase separation and a microphase separation that is seen above a threshold bias or relaxation rate.