Models for active particles: common features and differences

TL;DR

It is found that changes in the model of the active agents can lead to similar statistics in the dilute regime and different collective behavior in the dense regime, and is concluded that active particle models do not easily generalize for different real active agents, but instead require a clear understanding of the agents'microscopic properties.

Abstract

Systems of active particles can show a large variety of collective behavior. In theory, two aspects determine the collective behavior: the model at the particle level and the parameter regime. While many studies consider a single model and study its parameter regime, here, we focus on the former aspect. Motivated by experiments that study dilute suspensions of Chlamydomonas reinhardtii in a self-generated oxygen gradient, we compare various models with external field-dependent motility to understand how the collective behavior changes between models. We vary the particle-particle interaction from no interactions to steric interactions, the particle shape from round disks to dumbbells, the self-propulsion mechanism from constant speed to rocking motion, and the particle's center of mass from the geometric center to off-center. We find that changes in the model of the active agents can lead to similar statistics in the dilute regime and different collective behavior in the dense regime. We conclude that active particle models do not easily generalize for different real active agents, but instead require a clear understanding of the agents' microscopic properties.

Figures (23)

• Figure 1: Five models for active particles inside an external field (blue color code). The particles can fully move through the square box with periodic boundary conditions and deplete the external field inside the dashed circular area. Solid lines indicate excluded volume interactions and the red dots mark the particles' centers of mass.
• Figure 2: Snapshot of one quadrant and radial profiles of the system of sterically repulsive active disks (model II, $\phi_0=0.1$). The particles consume the external field which leads to a gradient that decreases towards the center ($r=0$). There, the particles slow down and aggregate. The particles' root-mean square velocity $v_\mathrm{rms}$ is smaller than the self-propulsion speed $v(c)$ but still larger than the effective velocity $v_\mathrm{eff}$.
• Figure 3: The product of velocity and packing fraction shows the deviation from inverse scaling behavior for the self-propulsion speed $v(c(r))$ and root mean square velocity $v_\mathrm{rms}(r)$. In comparison, the effective velocity $v_\mathrm{eff}(r)$ is close to the inverse scaling behavior. The three curves for model IV ($d_\mathrm{gc}=0.4$) correspond to a shifted center of mass to the front (a: $\varphi_\mathrm{gc}=0$), diagonal back (b: $\varphi_\mathrm{gc}=3\pi/4$), and back (c: $\varphi_\mathrm{gc}=\pi$). We used the packing fraction $\phi_0=0.1$ for all models except model IV a for which we used $\phi_0=0.08$ to avoid clustering.
• Figure 4: Radial and azimuthal components of the conditional force average $f_r(r=\text{const},\chi)$ and $f_\varphi(r=\text{const},\chi)$ are cosine and sine functions of the angular difference $\chi=\theta-\varphi$. They vary in amplitude depending on the radial distance from the center of the box. The amplitudes $A(r)$ and $B(r)$ are equal and agree with the deviation of the effective velocity from the self-propulsion speed $v_\mathrm{eff}-v(c)$. The data shown is from simulations of active disks (model II, $\phi_0=0.1$) as in Fig. \ref{['fig:snapshot-and-radial-profiles']}.
• Figure 5: Radial amplitude $A(r)$ of the conditional force average as well as the conditional torque average $\tau(r,\chi)$ for different models and same parameters as in Fig. \ref{['fig:scaling']}.