Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thickening Medium

Abstract

We study the dynamics of an athermal inertial run-and-tumble particle moving in a shear-thickening medium in $d=1$. The viscosity of the medium is represented by a nonlinear function $f(v)\sim \tan (v)$, while a symmetric dichotomous noise of strength $\Sigma$ and flipping rate $\lambda$ models the activity of the particle. Starting from the Fokker-Planck~(FP) equation for the time-dependent probability distribution $W_{\pm \Sigma }(v,t)$ of the particle's velocity $v$ at time $t$ and the active force is $\pm \Sigma$, we analytically derive the steady-state velocity distribution function $W_s(v)$ and a quadrature expression for the effective diffusion coefficient $D_{\mathrm{eff}}$. For a fixed $\Sigma$, $W_s(v)$ undergoes multiple transitions with varying $\lambda$, and we have identified the corresponding transition points. We then numerically compute $W_s(v)$, the mean-squared velocity $⟨v^2⟩(t)$, and the diffusion coefficient $D_{\mathrm{eff}}$, all of which show excellent agreement with the analytical results in the steady-state. Finally, we test the robustness of the transitions in $W_s(v)$ by considering an alternative $f(v)$ function that also capture the shear-thickening behavior of the medium.

arXiv comment17 Pages, 6 Figures, Accepted in Phys. Rev. E

References in corpus (29)

• Active Particles in Complex and Crowded Environments
• The Mechanics and Statistics of Active Matter
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• How far from equilibrium is active matter?
• Pressure is not a state function for generic active fluids
• Superfluid transport of information in turning flocks of starlings
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Shear thickening of cornstarch suspensions as a re-entrant jamming transition
• Inertial effects of self-propelled particles: from active Brownian to active Langevin motion
• Dynamics of a self-propelled particle in a harmonic trap
• Generalized energy equipartition in harmonic oscillators driven by active baths
• Sorting of Chiral Microswimmers
• Active Brownian Motion in Two Dimensions
• Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation
• Run-and-tumble particles in two-dimensions : Marginal position distributions
• Active Ornstein-Uhlenbeck model for self-propelled particles with inertia
• Active Brownian particles and run-and-tumble particles separate inside a maze
• Active Janus particles in a complex plasma
• Phototactic Robot Tunable by Sensorial Delays
• Role of rotational inertia for collective phenomena in active matter
• Inertial active matter with Coulomb friction
• Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed
• Stochastic motion under nonlinear friction representing shear thinning
• Harmonically trapped inertial run-and-tumble particle in one dimension
• Inertial Dynamics of Run-and-Tumble Particle
• Velocity Distribution and Diffusion of an Athermal Inertial Run-and-Tumble Particle in a Shear-Thinning Medium
• Domain Growth Kinetics in Active Binary Mixtures