Long-Range Ordering of Vibrated Polar Disks

Abstract

Vibrated polar disks have been used experimentally to investigate collective motion of driven particles, where fully-ordered asymptotic regimes could not be reached. Here we present a model reproducing quantitatively the single, binary and collective properties of this granular system. Using system sizes not accessible in the laboratory, we show in silico that true long-range order is possible in the experimental system. Exploring the model's parameter space, we find a phase diagram qualitatively different from that of dilute or point-like particle systems.PACS numbers: 05.70. Ln, 64.60.Cn, 05.65.+b Collective motion in driven or self-propelled particle systems is a topic of recent interdisciplinary interest [3][4][5][6]. Within physics, following the works of Vicsek et al. [7,8] and Toner and Tu [9][10][11], most progress was achieved by studying microscopic models [7,8,[12][13][14][15][16][17][18][19][20][21][22][23][24] and their continuous descriptions [9][10][11][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. For the simplest situation in which the surrounding fluid can be neglected ("dry flocking") and the sole interaction is some local effective alignment, a picture of basic universality classes has emerged, which connects models similar to the Vicsek model [7] to continuous theories of the Toner-Tu type [9][10][11][25][26][27][28][29][30][31]. Among the landmark results are the possibility of true long-range orientational order in two dimensions, the generic presence of strong, long-range correlations [9][10][11]25] and/or spontaneously segregated dense and highly ordered nonlinear structures in moving, ordered, fluctuating phases [29,31].These numerical and theoretical results still largely lack experimental confirmation. This is mostly due to the fact that decisive experimental tests must be performed on large numbers of objects under controlled conditions. The advent of experiments using purified proteins (motors, filaments, etc.) offers a promising playground [39][40][41][42][43], but another line of attack, for dry flocking, is to build on the experience of the granular physics community, and to shake man-made objects [1,2,[44][45][46][47][48]. Recently, some of us have designed and studied the collective motion of vibrated polar disks, i.e. millimeter-size objects with a built-in oriented axis and a circular top metallic part rendering the particles isotropic with respect to collisions ( Fig. 1a,b; [1, 2]). Large-scale collective streams and anomalous, "giant" number fluctuations were reported in collections of approximately a thousand disks moving on a carefully vibrated plate. Unfortunately, in this experiment -as in others involving man-made objects [44][45][46][47][48] -the number of particles used was still too small to reach asymptotic results. Moreover, the most ordered regimes that could be explored were probably close to the onset of collective motion, making it impossible to disentangle the properties of the ordered moving phase from those of the order-disorder transition.In ...

Random bursts determine dynamics of active filaments

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“…active filaments | nonthermal statistics | molecular motors | gliding assay | kinetic model I n active systems, perpetual local energy input prevents relaxation into a thermal equilibrium state (1-3). Examples are living matter (4-10) or appropriately reconstituted or synthetic model systems (11)(12)(13)(14)(15)(16)(17). It is widely accepted that nonthermal fluctuations play a crucial role for the dynamics of active systems (8,9,(18)(19)(20)(21)(22)(23)(24) and may even cause an apparent violation of the fluctuation-dissipation theorem (11).…”

Theory of Active Suspensions

“…Numerous experiments have focused on the dynamics in suspensions of swimming bacteria. Some of the observations that have been made on this system include: the emergence of [1]; (b) dynamic clusters in swarms of bacteria, where arrows show the direction of motion of the particles [2]; (c) spontaneous motion in a suspension of microtubules and kinesin motors confined at a two-dimensional interface [3]; (d) large-scale swirling motion in a suspension of actin filaments transported by wall-tethered myosin molecular motors [4]; (e) swarming of self-propelling liquid droplets in a Hele-Shaw cell [5]; (f) long-range order of vibrated polar disks on a two-dimensional substrate [6]. (Reproduced with permission) complex chaotic flows on length scales much greater than the particle dimensions and characterized by unsteady whirls and jets [10-12, 26, 27], enhanced particle velocities [10], a transition to collective motion when the bacterial density exceeds a certain threshold [11], local polar ordering [11], complex patterns and density fluctuations [28], enhanced swimmer and passive tracer diffusion [29][30][31][32], efficient fluid mixing [28,33,34], and bizarre rheologies created by particle activity [35][36][37][38].…”

Coupling spin to velocity: collective motion of Hamiltonian polar particles

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