William D. Pineros and Etienne FodorDepartment of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg We discover unexpected connections between packing configurations and rare fluctuations in dense systems of active particles subject to pulsation of size. Using large deviation theory, we examine biased ensembles which select atypical realizations of the dynamics exhibiting high synchronization in particle size. We show that the order emerging at high bias can manifest as distinct dynamical states with either a finite or a vanishing size current. Remarkably, transitions between these states arise from changing the system geometry at fixed bias and constant density. We rationalize such transitions as stemming from a change in the packing configurations favored by the geometry.Specifically, we reveal that a master curve in the unbiased dynamics, correlating polydispersity and current, helps predict the dynamical state emerging in the biased dynamics. Finally, we demonstrate that deformation waves can propagate under suitable geometries when biasing with local order.
Overall, our results for (N, ) = (32, 1.6) show that packing configurations, imposed by the box geometry, impact both unbiased and biased dynamics. Importantly, we reveal that the unbiased statistics actually allows one to anticipate how the system orders as a function of L/ in our BE. We find a similar effect is generically observed for other values of (N, ); for instance, see the phase diagram for (N, ) = (26, 1.6) in Fig. S4 of . Ensembles biased by local order: Deformation waves. In synchronizing PAM [11, 17], deformation waves emerge as a competition between arrest and cycling. Given that in non-synchronizing PAM the BE promoting global order [Eq. (7)] yields arrest and cycles [Fig. 3], it is intriguing to understand what class of BE may also induce deformation waves. To this end, we introduce the local order parameter lc = 1 N N (cid:88) i=1 ni(cid:88) j=1
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To improve sampling, we now consider locally synchronizing interactions: i = iV + ni(cid:88) sin(j i) + (cid:112) 2Di. j=1
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In practice, Eq. (11) enhances convergence for the BE in Eq. (10) at moderate |s|, while Eq. (8) actually works better for the same BE at large |s|. At each s, we systematically compare results obtained by employing either type of interaction (i.e., with local or global synchronization), and select the ones with optimal convergence . Interestingly, for values of L/ coincident with the minimum of [Fig. 2(b)], we observe again the emergence of an arrested state with local and global order [Figs. 4(a) and 4(b)] comparable to the results from the previous BE [Eq. (3)]. In contrast, for L/ sufficiently far away from the minimum of , phase ordering now occurs through two distinct states. As |s| increases, local order increases with negligible change in global order, i.e. lclc > lc and gblc gb. In this state, particle sizes cycle periodically in a locally coordinated way, yielding the spontaneous emergence of deformation waves [Figs. 4(d) and 4(e)] not present in the unbiased dyna
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4(c)]. For higher |s|, the range of particle coordination increases, which increases global order (gblc > gb) and ultimately results in a cycling state [Figs. 4(f)] similar to that of the previous BE [Fig. 1(e)]. In this manner, the BE promoting local order [Eq. (10)] reproduces all the states of synchronizing PAM [11, 17]: disorder, arrest, cycles, and waves. Furthermore, waves only arise for box sizes L accommodating at least one wavelength. As the wavelength increases with |s|, waves are only stable over a finite range of s. As such, waves can be seen as precursory to cycles. In contrast, arrest does not display such a gradual ordering from local to global, but rather directly emerges from disorder at comparatively low bias. Moreover, the critical s for this transition is almost unchanged when biasing with either global [Fig. 3(a)] or local [Fig. 4(b)] order.
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