Macroscopic active matter under confinement: dynamical heterogeneity, bursts, and glassy behavior in a few-body system of self-propelling camphor surfers

TL;DR

We address how inertia and long-range interactions shape collective dynamics in a few-body macroscopic active-matter system confined in two dimensions. Using camphor surfers and minimal inertial active Brownian particle simulations, we analyze mean-squared displacements, overlap dynamics, and relaxation times to uncover dynamical slowing, bursting, and dynamical heterogeneity at intermediate densities. A simple hydrodynamic-oscillator theory explains density-dependent slowing of bursts, while simulations with a two-length-scale repulsion reproduce glass-like slowing and heterogeneity, highlighting an intermediate length scale that enables cage formation. The work provides a macroscopic active-glass analog driven by confinement and long-range interactions, with implications for designing nonequilibrium materials and understanding glass transitions in active systems.

Abstract

We study a few-body system composed of self-propelling camphor surfers confined within a circular boundary. These millimeter-sized particles move in a regime where inertia and long-ranged interactions play a significant role, leading to surprisingly complex and subtle collective dynamics. These dynamics include self-organized bursts and glassy behavior at intermediate densities--phenomena not apparent from ensemble-averaged steady-state measures. By analyzing quantities like the overlap order parameter, we observe that the system exhibits dynamical slowing down as particle density increases. This slowdown is also reflected in the bursting activity, where both the amplitude and frequency of bursts decrease with increasing particle density. A minimal inertial active-particle model reproduces these dynamical steady states, revealing the importance of a new intermediate length scale--larger than the particle size. This intermediate scale is critical for the formation of structures resembling caging and plays a key role in the glass-like transition. Our results describe a macroscopic analog of an active glass with the additional phenomena of bursting.

Figures (9)

• Figure 1: Slowing and Bursting Dynamics.Top Row: XY trajectories (in mm) of individual particles for increasing particle numbers ($\phi = 0.01, 0.06, 0.24$) show the effect of density on motion. The color code represents instantaneous speed (mm/s). At low density ($\phi = 0.01$), particles move freely, whereas at higher densities ($\phi = 0.06, 0.24$), trajectories exhibit increasing confinement and reduced speeds. Insets are representative images. Middle Row: Time series (in seconds) of ensemble-averaged particle speed (mm/s) demonstrate the transition in dynamics with density. At low density ($\phi = 0.01$), the speed is noisy and relatively constant. At intermediate density ($\phi = 0.06$), organized collective bursts dominate, while at high density ($\phi = 0.24$), bursts become less frequent and the overall speed decreases. Bottom Row: Speed histograms (in mm/s) illustrate the changes in speed distributions across densities. At low density, a broad distribution is observed. As density increases, distributions narrow, indicating a slowdown.
• Figure 2: Mean Squared Displacement: As packing fraction ($\phi$) increases, the particles systematically exhibit less motion. At low $\phi$, radial motion is ballistic with a plateau corresponding to container size, and angular motion is persistent. At intermediate $\phi$, particles become more diffusive in both radial and angular directions. At high $\phi$, particles exhibit short time scale caging, with diffusive-like behavior at longer times.
• Figure 3: Overlap parameter, average speed and relaxation time. Left: Overlap parameter, $Q(t)$, computed from experimental trajectories. Right: The structural relaxation time $\tau_\alpha$ computed through the overlap parameter increases as $\phi$ increases (blue circles). The last data point (diamond) provides a lower bound obtained from the experimental data, see the main text. This behavior mirrors the decay of the average velocity (red squares) that tends to zero as $\phi$ increases.
• Figure 4: Bursting Behavior and Slowing Down (a) Frequency and (b) amplitude of bursts as functions of the particle density, showing an overall decreasing trend with increasing density. Bursts are defined as peaks of the square speed exceeding a given threshold $p$ (see the main text); different realizations (gray lines) are averaged (red line). The shaded region in (a-c) indicates where bursts become rare, leading to limited statistics. (c) Burst breadth: typical length scale $L$ associated to a burst, obtained by combining the burst amplitude $V$ (dimensionally a velocity) of panel (b) and the burst frequency $\Omega$ of panel (a) as $L = V/\Omega$. This plot indicates that the typical displacements of a collection of particles during a burst event is locally maximized at intermediate density($\phi=0.06$). The burst breadth decreases at increasing density. (d) Speed (in mm/s) of an individual particle at varying packing fractions: from low (top) to high (bottom). At low packing fractions, higher peaks (corresponding to higher speeds) are observed, while peaks diminish and intervals between them increase at higher densities, reflecting particle slowdown.
• Figure 5: Analytic Model of Slowing Bursts. A minimal model of hydrodynamically coupled two-state oscillators. Each particle moves between positions ±sw under a harmonic potential $U(x)$ that switches sign at the turning points. Coupling is introduced via long-range hydrodynamic interactions that scale as $1/d$, where $d$ is the interparticle distance.