Anisotropic active Brownian particle in two dimensions under stochastic resetting

TL;DR

This work investigates how two-dimensional anisotropic active Brownian particles respond to stochastic resetting under three distinct schemes: complete resetting, position-only resetting, and orientation-only resetting. Using renewal theory and exact moment calculations, it demonstrates that complete and position resetting drive the system to non-equilibrium steady states with finite, rate-dependent MSDs, while orientation resetting preserves anisotropy and prevents a steady state. The analysis reveals rich transient dynamics including short-time super-diffusion and long-time anisotropic diffusion, with explicit connections to Run-and-Tumble dynamics for multi-angle orientation resetting. The findings illuminate how resetting protocols can tune diffusion, anisotropy, and steady-state properties in active matter, with potential implications for controlled transport and search strategies in anisotropic systems.

Abstract

We analytically investigate the dynamic behavior of an an-isotropic active Brownian particle under various stochastic resetting protocols in two dimensions. The motion of shape-asymmetric active Brownian particles in two dimensions leads to an-isotropic diffusion at short times, whereas rotational diffusion causes the transport to become isotropic at longer times. We have considered three different resetting protocols: (a) complete resetting, when both position and orientation are reset to their initial states, (b) only position is reset to its initial state, (c) only orientation is reset to its initial state. We reveal that orientation resetting sustains asymmetry even at late times. When both the spatial position and orientation are subject to resetting, a complex position probability distribution forms in the steady state. All the analytical findings are thoroughly validated by corresponding simulation results.

Figures (10)

• Figure 1: (a) The basic model of an anisotropic ABP incorporates parallel, perpendicular, and rotational diffusion coefficients, with the propulsion velocity $v_0$ directed along the particle's major axis. (b) In the position-orientation complete resetting protocol, both the particle's position and orientation are reset simultaneously. (c) The position-only resetting protocol involves resetting the particle's position to the origin while leaving its orientation unchanged. (d) The orientation-only resetting protocol resets the particle's orientation to its initial orientation as $\theta=0$ without altering its position.
• Figure 2: Position-orientation resetting: Mean squared displacements along $x$ and $y$ directions as a function of time $t$ for $D_\theta=1$, $D_\parallel=1$, $D_\perp=0.1$, $v_0=1$, $\theta_0=0$ and varying resetting rates $r$. The simulation data are represented by symbols, while the solid curves correspond to the analytical predictions from Eqs.(\ref{['msdx']}) and (\ref{['msdy']}). The stationary values decrease as the resetting rate $r$ increases.
• Figure 3: Steady state position distribution along $x$ and $y$ directions of anisotropic ABP under position-orientation resetting when $D_\theta=0.1$, $D_\parallel=1$, $D_\perp=0.1$, $v_0=1$ and $\theta_0=0$ for different values of reset rate $r$ as shown in the legends taken at $t=100$.
• Figure 4: Position resetting: Mean square displacements along $x$ and $y$ as a function of time $t$ for $D_\theta=1$, $D_\parallel=1$, $D_\perp=0.1$, $v_0=1$, $\theta_0=0$ and different values of resetting rate $r$. Symbols represent the data from simulations. Solid lines are representing expressions from Eq.(\ref{['msdx_pos']}) and (\ref{['msdy_pos']}).
• Figure 5: Position distribution along $x$ and $y$ of anisotropic ABP under position resetting at $t=100$ (stationary state) when $D_\theta=0.1$, $D_\parallel=1$, $D_\perp=0.1$, $v_0=1$ and $\theta_0=0$ for different values of reset rate $r$ as shown in the legends.