Effect of reorientation statistics on torque response of self-propelled particles

We consider the dynamics of self-propelled particles subject to external torques. Two models for the reorientation of self-propulsion are considered: run-and-tumble particles and active Brownian particles. Using the standard tools of nonequilibrium statistical mechanics we show that the run and tumble particles have a more robust response to torques. This macroscopic signature of the underlying reorientation statistics can be used to differentiate between the two types of self-propelled particles.

Figure 1

Orientation probability distribution functions for RTPs [red (solid)] and ABPs [blue (dashed)] in the case of both a nematic aligning (left) field and a polar aligning field (right). RTP distributions are sharply peaked about the optimal direction while the ABP distribution is the smooth equilibrium result.

Figure 2

(a) RTPs exhibit higher nematic order than ABPs as shown by the nematic order parameter being higher for RTPs (red) than for ABPs [blue (dashed)]. (b) The percentage of particles oriented within some range $[\pi /18,\pi /18]$ of the two minima as a function of the parameter $\kappa$.

Figure 3

(a) The polarization as a function of the parameter $\kappa$. The polarization for RTPs [red (solid)] is less than for ABPs [blue (dashed)] (b) The percentage of particles oriented within some range $[\pi /18,\pi /18]$ as a function of the parameter $\kappa$. It is clear that the percentage of RTPs [red (square)] oriented in that range is higher than ABPs [blue (circle)].

Figure 4

For RTPs a large number of terms in the series must be included. Above shows the percent difference in the value of $\psi \left(\theta \right)$ whether truncating at the $n\text{th}$ term or $n_{\mathrm{th}}+1$ term. Here we examine the value at $\theta =0$. The first point on the horizontal axis represents the percent difference in $\psi \left(\theta \right)$ by truncating the series at $n=2$ and $n=3$, the next point represents the percent difference when truncating the series at $n=3$ and $n=4$, and this is continued up to the last point which represents the percent difference by truncating the series at $n=14$ and $n=15$.

Figure 5

The ratio of correlation to response for RTPs in the presence of a polar aligning torque [red (dashed)] and a nematic aligning torque [blue (dot-dashed)] as a function of $\kappa$. The constant line at 1 represents the value of this ratio for ABPs.