Transport Properties of Active Particles Moving on Adjustable Networks

TL;DR

We address how active particles diffuse when moving on networks that adapt in response to motion. The authors introduce a minimal run-and-tumble model on a triangular lattice where each traversed bond closes temporarily for a healing time $\tau_h$, and particles experience excluded-volume constraints. In fixed networks, diffusion is nonmonotonic in the persistence time $\tau_p$, with an optimal $\tau_p^*$; when the network can remodel ($\tau_h>1$), $\tau_p^*$ increases with $\tau_h$ and decreases with density $\phi$ due to two distinct blocking mechanisms. The findings reveal a fundamental difference between trail-induced and steric blocking, offering insights for guiding transport in adaptive active-matter systems and informing designs of responsive materials and biological analogues.

Abstract

Active adaptive matter has attracted considerable interest due to its rich, largely unexplained dynamics and its relevance to a wide range of synthetic and biological materials. An important subclass of such systems consists of active particles that can remodel the network in which they move. Here, we introduce a minimal yet versatile model of active particles moving on an adjustable network. In this model, particles undergo discrete run-and-tumble motion along the links of a triangular lattice and leave behind a trail of temporarily blocked links. These closed links cannot be traversed by other particles and reopen only after a characteristic healing time. The resulting trail-mediated blocking mechanism is fundamentally distinct from more familiar interactions such as excluded-volume effects. In the high-persistence limit, we find a qualitative contrast between the two mechanisms: while steric blocking leads to reduced diffusivity with increasing persistence, trail-induced blocking causes diffusivity to increase monotonically. We characterize this fundamental difference and the associated, unexpected transport properties, and discuss potential applications of our findings.

Figures (8)

• Figure 1: Illustration of our network model. Run-and-tumble active particles are added to the nodes of a regular triangular lattice with nearest-neighbor connections. Blocked and moving particles are represented by red and blue disks, respectively. The arrows indicate the direction of self-propulsion. Light blue and yellow lines represent open and closed bonds, respectively. A particle $d$ in (b) changes its configuration to $d^\prime$ in (c) by tumbling, i.e. changing its self-propulsion direction, with a rate $\alpha_{p} = 1 / \tau_p$. An open bond $b$ in (a) traversed by a particle has its configuration changed to a closed bond $b^\prime$ in (b). The closed bond $b^\prime$ in (b) can then spontaneously "heal" to an open bond state $b^{\prime \prime}$ in (c) with healing rate, $\alpha_{h} = 1 / \tau_h$. A particle will be blocked either if it tries to move to an occupied site [$a$ in (a)] or if it tries to move through a closed bond [$c$ in (b)].
• Figure 2: (a) Effective diffusion coefficient as a function of persistence time for different packing fractions. (b) Fraction of particles in the deep interior of a cluster (particles surrounded by $z$ other particles). The dashed vertical line indicates $\tau_{p}^{\star}\approx 32$, corresponding to the maximum diffusion for the system with packing fraction $\phi = 0.064$ (magenta curve), as well as the onset of a finite population of particles in the interior of a cluster.
• Figure 3: (a,b) Snapshots corresponding to a single realization of the steady state for $\phi = 0.064$ at persistence times $\tau_{p}^{(1)}=10$ (a) and $\tau_{p}^{(2)}=100$ (b), respectively.
• Figure 4: (a) Scaling collapse plot showing re-scaled effective diffusion coefficient as a function of re-scaled persistence time. The exponent $\lambda \approx 1$ was chosen to yield the best scaling of the data. (b) Density plot of the fraction of particles in the deep interior of a cluster as a function of density and persistence time. White squares represent a numerical calculation of the optimal persistence time at each density, and the solid red line is a best fit using Eq. \ref{['eq:tauStar']}.
• Figure 5: Effective diffusion coefficient as a function of persistence time for packing fractions $\phi = 0.064$ (a) and $\phi = 0.256$ (b), and several values of the healing time $\tau_h$.