We study numerically and analytically a model of self-propelled polar disks on a substrate in two dimensions. The particles interact via isotropic repulsive forces and are subject to rotational noise, but there is no aligning interaction. As a result, the system does not exhibit an ordered state. The isotropic fluid phase separates well below close packing and exhibits the large number fluctuations and clustering found ubiquitously in active systems. Our work shows that this behavior is a generic property of systems that are driven out of equilibrium locally, as for instance by self-propulsion.
Pressure is the mechanical force per unit area that a confined system exerts on its container. In thermal equilibrium, it depends only on bulk properties-such as density and temperature-through an equation of state. Here we show that in a wide class of active systems the pressure depends on the precise interactions between the active particles and the confining walls. In general, therefore, active fluids have no equation of state. Their mechanical pressure exhibits anomalous properties that defy the familiar thermodynamic reasoning that holds in equilibrium. The pressure remains a function of state, however, in some specific and well-studied active models that tacitly restrict the character of the particle-wall and/or particle-particle interactions.
We study numerically the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. The model is motivated by recent in vitro experiments on confluent monolayers of migratory epithelial and endothelial cells. The phase diagram exhibits a liquid phase with giant number fluctuations at low packing fraction φ and high self-propulsion speed v0 and a jammed phase at high φ and low v0. The dynamics of the jammed phase is controlled by the low frequency modes of the jammed packing.PACS numbers: 87.18.Hf, 05.65.+b, 63.50.+x How do collections of active particles behave in very dense situations? What are the mechanical properties of the ensuing materials? The answers to these questions are fundamentally important for a wide range of physical and biological systems, from tissue formation [1][2][3][4][5] and vibrated granular materials [6,7] to the behavior of packed crowds [8].The name "active matter" refers to soft materials composed of many interacting units that individually consume energy and collectively generate motion or mechanical stress. Examples range from bacterial suspensions to epithelial cell layers and flocks of birds. The phases of active matter have been studied extensively since the seminal work of Vicsek et al [9]. Self-propelled particles have a polarity provided by the direction of selfpropulsion. In the presence of noisy polar aligning interactions, they order into a moving state at high density or low noise [10,11]. The ordered state has giant number fluctuations [6,7,12] and a rich spatio-temporal dynamics. Continuum theories have been formulated for these systems and provide a powerful tool for understanding the generic aspects of their behavior [13]. While the low density phase of various models of self-propelled particles is comparatively well understood, much less is known about the high density phase.In a separate development, much effort has been devoted to the study of passive thermal and athermal granular matter. These systems undergo a transition between a flowing, liquid-like state at low density or high temperature and a glassy state [14,15]. Near the glass transition, the relaxation is controlled by dynamical heterogeneities, consisting of spatially and temporally correlated collective rearrangements of particles [16]. In the zero-temperature limit, soft repulsive disks undergo a jamming transition to mechanically stable state at φ = 0.842 in two dimensions [17]. The elastic properties of the jammed state are determined by an excess number of low frequency modes [18] which are also closely linked to the large-scale rearrangements that microscopic packings undergo when strained [19] or thermalized [20].Recent in vitro experiments on confluent monolayers of migratory epithelial and endothelial cells have revealed displacement fields and stress distributions that strongly resemble both dynamical heterogeneities of glasses and the soft modes of jammed packings [1][2][3][4][5], and an analogy between the dynamics of these liv...
We study numerically a model of non-aligning self-propelled particles interacting through steric repulsion, which was recently shown to exhibit active phase separation in two dimensions in the absence of any attractive interaction or breaking of the orientational symmetry. We construct a phase diagram in terms of activity and packing fraction and identify three distinct regimes: a homogeneous liquid with anomalous cluster size distribution, a phase-separated state both at high and at low density, and a frozen phase. We provide a physical interpretation of the various regimes and develop scaling arguments for the boundaries separating them.
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