Active jamming: Self-propelled soft particles at high density

Abstract

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...

Freezing and phase separation of self-propelled disks

“…One can then speculate that activity, in spite of injecting energy locally rather than globally, be equivalent to a homogeneous shear in the limitν r → 0. Finally, we stress that a shift of the kinetic arrest to values of packing fractions above the glass transition was also reported for self-propelled disks with aligning interactions 23 .…”

Giant fluctuations and structural effects in a flocking epithelium

“…We interpret these results through the well-known Toner and Tu hydrodynamic theory of flocking [26,27], and by making use of a minimal model of self-propelled soft disks, first introduced in [44,45]. Our numerical results show that a simple self-propelled mechanical model with no adhesion forces is able to reproduce qualitatively and even quantitatively the static structure factor and the number fluctuations of both the highly confluent reawakened samples and the near-jammed controls.…”

“…For finite τ (and not too large noise values) the CVM is known to display a transition from a disordered gas-like state to a flocking state [44] (i,e, an ordered polar liquid) characterised by GNF [45] as expected by hydrodynamic theory. A completely jammed state, finally, is still present at high packing fraction and low self propulsion speed [45]. In this work, we will not explore this part of the phase diagram, limiting ourselves to regions where the system is in a gas-like or liquid-like state, both in the presence and in the absence of polar order.…”

“…In the τ → ∞ limit, the CVM is a model for non-ordering active brownian particles and is characterised by a phase diagram showing a liquid phase with non-equilibrium clustering, phase separation and a completely jammed state [51]. For finite τ (and not too large noise values) the CVM is known to display a transition from a disordered gas-like state to a flocking state [44] (i,e, an ordered polar liquid) characterised by GNF [45] as expected by hydrodynamic theory. A completely jammed state, finally, is still present at high packing fraction and low self propulsion speed [45].…”

“…To simulate the epithelial monolayer we use a collisional Vicsek-like model (CVM), first introduced in [44,45]. In this agent-based model, N 0 soft disks with position r i and interaction radius σ i (i = 1, .…”