Steering chiral active Brownian motion via stochastic position-orientation resetting

TL;DR

This work shows that stochastic resetting can steer two-dimensional chiral active Brownian particles by interrupting circular trajectories set by chirality, introducing a competing resetting timescale that yields a nonequilibrium steady state with tunable transport. Using a renewal-equation approach on top of a Fokker-Planck framework, the authors derive exact expressions for orientation autocorrelation, mean-squared displacement, and higher moments, revealing a rich phase diagram with three steady-state regimes: Rotating Active, Resetting I, and Resetting II. The boundaries are governed by the total reorientation rate $r+D_r$ relative to the intrinsic chirality $\Omega_0$ and by excess kurtosis, which distinguishes heavy-tailed resetting-dominated states from Gaussian-like activity-driven ones. The findings offer a practical strategy for optimizing search and transport in circle swimmers and suggest experimental implementations across diverse active-matter platforms.

Abstract

Guiding active motion is important for targeted delivery, sensing, and search tasks. Many active systems exhibit circular swimming, ubiquitous in chemical, physical, and biological systems, that biases motion and reduces transport efficiency. We show that stochastic position-orientation resetting can overcome these limitations in two-dimensional chiral active Brownian particles by interrupting circular motion, resulting in tunable dynamics. When resets are infrequent compared to chiral rotation, the steady-state mean-squared displacement varies non-monotonically with rotational diffusion. Steady state excess kurtosis and orientation autocorrelation yields spatiotemporal state diagram comprising three states: an activity-dominated chiral state, and two resetting-dominated states with and without chiral rotation; in contrast, the achiral(or non-chiral) counterpart supports only the resetting-dominated state without chiral rotation. Chirality thus enriches the dynamical landscape, enabling tunable transitions between transport modes absent in achiral systems. A simple reset protocol can therefore transform chiral active dynamics and offer a practical strategy for optimizing search and transport in circle swimmers.

Figures (9)

• Figure 1: Schematic representation of the dynamics of a chiral active Brownian particle subject to stochastic resetting of both its position and orientation (a). Steady-state trajectories for reset rates $r=0.01$ (b), $0.5$ (c), and $10$ (d), obtained using parameters $v_{0}=20$, $\Omega_{0}=2.5$, $D=1$, and $D_{r}=0.05$. Increasing $r$ progressively suppresses spatial exploration from (b,c) chiral rotation($r+D_r<\Omega_0$) with (b) scattered loop and (c) concentrated loop to (d) non-rotating($r+D_r>\Omega_0$) excursions.
• Figure 2: Steady-state mean squared displacement $\langle {\bf r}^2\rangle^{\rm st}_{r}$ as a function of $D_r$ in (a) for $r=0.1,~1,~2$ and of $r$ in (b) for $D_r=0.1,~2.5,~10$. Resetting suppressed non-monotonic behavior of $\langle {\bf r}^2\rangle^{\rm st}_{r}$ with $D_r$. Solid lines are analytic prediction of Eq. \ref{['eq:r2avg_reset_st']} and symbols are from simulation. Initial position is at the origin with the initial orientation along the $x$-axis. Fixed parameters are $v_0=10$, $\Omega_0=2.5$, and $D=1$.
• Figure 3: Steady-state excess kurtosis $\mathcal{K}_{r}^{\rm st}$ as function of $r$ in (a) and of $\Omega_0$ in (b) for rotational diffusion coefficient $D_r=0.01,~0.1,~1,~10$. Negative values of $\mathcal{K}_{r}^{\rm st}$ indicate the weakly active state in both plots. Symbols correspond to simulation, and lines show the prediction from Eq. \ref{['eq:excess_kurtosis_st']}. Fixed parameters are $v_0=10$, $\Omega_0=2.5$, and $D=1$.
• Figure 4: (a) State diagram on $r-\Omega_0$ plane. The colormap depicts the steady-state excess kurtosis $\mathcal{K}_{r}^{\mathrm{st}}$ (Eq. \ref{['eq:excess_kurtosis_st']}). The black solid line correspond to $r+D_r=\Omega_0$ sets boundary between oscillatory (chiral rotation) and non-oscillatory (Non-rotating) regime. The red dashed line correspond to passive state by $\mathcal{K}^{\rm st}_{r}=0$ sets boundary between resetting ($\mathcal{K}^{\rm st}_{r}>0$) or activity ($\mathcal{K}^{\rm st}_{r}<0$) dominated regime. Three regions identified: Rotating Active, rotating Resetting, and Non-Rotating Resetting while Non-Rotating Active ($\mathcal{K}^{\rm st}_{r}<0$ with $\Omega_0 < r+D_r$) state is absent. (b) Orientation autocorrelation $\langle {\hat{\mathbf{u}}}(\tau)\cdot {\hat{\mathbf{u}}}(0)\rangle_r$ for $r=0.01,~0.5,$ and $10$ at $\Omega_0=2.5$(marked symbols in (a)); analytic predictions from Eq. \ref{['eq:ncorr_resetting']} are shown as solid lines and simulation as points. (c) Plot of steady-state radial position distribution $P_{\rm st}(| {\bf r}|)$ for the same parameter values as (b); points are from simulation and dashed lines are corresponding Gaussian($P^{G}_{\rm st}(| {\bf r}|)$) using MSD $\langle {\bf r}^2\rangle_{r}^{\rm st}$(Eq. \ref{['eq:r2avg_reset_st']}). (d,e,f) Plot of the steady-state position distribution $P_{\rm st}(x,y)$. Fixed parameters are $v_0=20$, $D_r=0.05$, and $D=1$.
• Figure 5: (a,b) Orientation autocorrelation $\langle {\hat{\mathbf{u}}}(\tau)\cdot {\hat{\mathbf{u}}}(0)\rangle_{r}$ and (c,d) mean parallel displacement $\langle {\bf r}_{\parallel}\rangle_{r}$ along initial orientation direction in two dimension under stochastic resetting. The points are from simulation. The solid lines are the plot of Eq. \ref{['eq:ncorr_resetting']} in (a,b) and Eq. \ref{['eq:rpara_resetting']} in (c,d). The initial position is at the origin with the initial orientation along the $x$-axis. Fixed parameter are $v_0=0.01$, $\Omega_0=1$, $D=1$ with $D_r=0.01$ in (a,c) and $r=0.25$ in (b,d).