Collective Dynamics of Macroscopic Photoactive Matter Under Alternating Excitation Patterns

Abstract

We present experiments on the collective dynamics of macroscopic photoactive self-propelled particles subjected to spatiotemporally varying excitation. The particles move within an arena divided into two regions with different illumination intensities, creating alternating bright (more active) and dark (less active) zones. Under such conditions, the system exhibits a robust migration from the more active region toward the less active region, demonstrating a strong response to external modulation. This response depends sensitively on the frequency of the illumination pattern: at low frequencies, particles follow the changing landscape, whereas at higher frequencies, the response diminishes. We show that this behavior arises from the interplay between the imposed excitation and the intrinsic dynamics of the particle clusters that form spontaneously. To explain these features, we extend a kinetic model previously introduced in [Phys. Rev. Lett. \textbf{135}, 098301 (2025)], hence revealing the most important parameters governing the transition between the responsive and unresponsive regimes.

Figures (10)

• Figure 1: (a): Schematic representation of the experimental setup with the photoactive agent, a hexbug equipped with a photovoltaic cell, moving on a glass sheet, while the external control is attained by an LED panel. (b): Initial, random configuration of the agents. (c): Snapshot of the system: the right-hand side is illuminated with high intensity ($P_{\text{high}}=72$ mW, represented by red), while the left-hand side is illuminated with low intensity (represented by gray). Note that we have applied an additional gray shading on the left-hand side of the images to emphasize the different illumination of the two sides. Equally colored hexbugs belong to the same cluster, defined as groups of at least four agents that remain in contact during at least one second. (d-g): Time evolution of agent populations for both sides of the arena in experiments with stationary halved illumination. The right-hand side illumination is $P_{\text{high}}=72$ mW while the left side illumination is always lower and different in each panel: (d) $P_{\text{low}}=23$ mW, (e) $P_{\text{low}}=33$ mW, (f) $P_{\text{low}}=43$ mW, and (g) $P_{\text{low}}=52$ mW. Supplemental Material (SM) videos 1-4 SM represent these four example cases, respectively.
• Figure 2: (a): Probability distribution functions (PDFs) of the relative population size obtained for the left (low-activity) side of the system ($n_L=N_L/N_T$) for levels of $P_{\text{low}}=23, 33, 43, 52$ mW for the stationary halved illumination. (The deeper the color, the lower the illumination.) The right (high-activity) side was always illuminated with $P_{\text{high}}=72$ mW. (b): PDFs of the relative population measured on the left-hand side when the arena is homogeneously illuminated in the experiments of Ref. levay2025cluster. To facilitate the comparison, we display the cases where the homogeneous illumination level is the same as $P_{\text{low}}$ of the halved case of panel (a). (c): Separation times measured in the stationary halved experiments corresponding to the four distinct $P_{\text{low}}$ levels. Each experiment was repeated ten times. Gray dots show separation times of individual experiments, while blue diamonds represent the median.
• Figure 3: (a): Relative population ($n_L$) measured at the left-hand side of the system with a switching period of $T{=}60$ s, in a $10$-minute-long experiment. The dashed lines mark the different periods of illumination. The gray background represents a period with $P_{\text{low}}$ on the left-hand side. Time intervals I and II correspond to the first two periods whose snapshots are presented in (c). (b): Similar to (a) but for an experiment with $T{=}70$ s switching period. In the first five periods, we have a strong response, particles are accumulating at the low illumination sides (see snapshot III), and in the fifth period, the cluster on the left-hand side stabilizes. After this point, the response stops completely, and the population stays larger on the left-hand side, even when the illumination is high, as shown in snapshot IV. See SM videos 5-6 SM for the experiments presented in panels (b) and (c), respectively. (c): Snapshots of the experiments with alternating low and high intensities at the two halves of the system. Note that we apply an additional gray shading on the low-illuminated side of the images to emphasize the difference between sides.
• Figure 4: Analysis of permanent clusters. Dark red represents the probability that a permanent cluster forms during the $t_{\text{exp}}=10$ minute long experiments as a function of period $T$. Experiments with $T<60$ s were repeated $5$ times, while experiments with $T \geq 60$ s were repeated $6$ times. Orange represents the proportion of the total experimental time that the system spends in a state of permanent clustering (like snapshot IV in Fig. \ref{['Fig:alternating']}).
• Figure 5: Analysis of the influence of cluster dynamics on system response. $\Delta n$, the increment of the number of agents in the dark side of the arena during a period, is plotted against the relative size of the largest detected cluster, $c_{\text{largest}}$, for experiments with $T > 5$ s. Data points are color-coded: blue indicates that the largest cluster resides in the low-activity region, while orange signifies its presence in the high-activity region of the arena. Two distinct behavioral regimes are identified, highlighted by ellipses and background colors. The right-hand regime is associated with large, stable clusters that exhibit a significantly low dynamic response, whereas the left-hand regime corresponds to smaller and medium-sized clusters that display an enhanced dynamic response.