Hard core run and tumble particles on a one dimensional lattice

Abstract

We study the large scale behavior of a collection of hard core run and tumble particles on a one dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady state single site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the non-gradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.

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

“…6 Average cluster size L c versus the polydispersity parameter λ at fixed average tumbling rate α = 0.01 for φ = 0.2 and φ = 0.5. The points show the simulation results and the lines are the theoretical predictions for the CSD length scale l c , eqn (10). For the simulations with λ > 2.5, the numerical results no longer agree with the theory, as discussed in Section 4.…”

“…Considering that the typical bacterium body size and speed are ≈ 2 µm and ≈ 14 µm/s, 44 our units are such that one time step is roughly 1/7 s, and thus α 0 = 0.216 s −1 corresponds to α 0 ≈ 0.03. For φ = 0.2, the theoretical estimate via eqn (10) for the fully polydisperse case with λ = 1.62 is L c ≈ 5.57. For the monodisperse case (λ = 0) with the same α and φ as in the fully polydisperse case, we find L c ≈ 2.11.…”

“…the tumbling rate distribution is unknown, one might be tempted to estimate L c via eqn (3) by considering that the system is monodisperse and has α = α . The error in doing so can be expressed by comparison with the length scale in eqn (10) as…”

“…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.…”

Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension

“…Some of these interesting features, for instance clustering at boundaries [33], motility-induced phase separation [34], jamming [35], emerge from the interactions of many RTPs. However, relevant properties, such as non-Boltzmann stationary state in a confining potential [36][37][38][39][40], can be observed even at the single-particle level. Moreover, many interesting quantities have been computed exactly in the onedimensional case [38,[41][42][43][44][45][46][47].…”