Time-dependent properties of interacting active matter: dynamical behavior of one-dimensional systems of self-propelled particles

Abstract

We study an interacting high-density one-dimensional system of self-propelled particles described by the Active Ornstein-Uhlenbeck particle (AOUP) model where, even in the absence of alignment interactions, velocity and energy domains spontaneously form in analogy with those already observed in two dimensions. Such domains are regions where the individual velocities are spatially correlated as a result of the interplay between self-propulsion and interactions. Their typical size is controlled by a characteristic correlation length. In the present work, we focus on a novel and lesser-known aspect of the model, namely its dynamical behavior. To this purpose, we investigate theoretically and numerically the time-dependent velocity autocorrelation and spatio-temporal velocity correlation functions. The study of these correlations provides a measure of the average life-time and, thus, the stability in time of the velocity domains.

Active Matter at high density: velocity distribution and kinetic temperature

“…As already reported in [16,35,57], the study of the velocity dynamics reveals the existence of hidden collective behavior of self-propelled particles at high density in the regime of large persistence times. Nevertheless, many single-particle properties, such as the velocity distribution and its moments, have not been yet explored.…”

“…In what follows, we develop an exact, analytical prediction valid in active the solid-state for the kinetic temperature which will explain the scaling with τ numerically observed shedding light also on the role of the other parameters. Indeed, the periodicity of the almost-solid structure and, in particular, its hexagonal order suggests switching in the Fourier space to perform calculations [35,57]. As reported in Appendix A, the velocity correlation in the Fourier space reads:…”

Inertial self-propelled particles

“…Starting from the AOUP, several predictions or approximations for the probability distribution [42,46,47], pressures [48,49] and surface currents near boundaries [39,48] have been derived. More recently, AOUP has been employed to derive the analytical expression for the spatial correlation of the velocity spontaneously appearing in active hexatic and solid phases [50,51].…”

Active mixtures in a narrow channel: motility diversity changes cluster sizes

“…One-dimensional (1D) models are currently a subject of increasing interest. [10][11][12] In many cases, such systems produce, at least approximately, a purely exponential CSD, as shown across models of run-and-tumble bacteria, active Brownian particles, and active Ornstein-Uhlenbeck particles, both on-lattice and offlattice. 2,13 For a simple on-lattice model, it has been demonstrated that no high-density transition exists, 14 but other lattice models do phase separate more conventionally, e.g.…”