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.

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by Wyart and others.

We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.

We construct a statistical framework for static assemblies of deformable grains which parallels that of equilibrium statistical mechanics but with a conservation principle based on the mechanical stress tensor. We define a state function that has all the attributes of entropy. In particular, maximizing this function leads to a well-defined granular temperature and the equivalent of the Boltzman distribution for ensembles of grain packings. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks.

Minimal models of active Brownian colloids consisting of self-propelled spherical particles with purely repulsive interactions have recently been identified as excellent quantitative testing grounds for theories of active matter and have been the subject of extensive numerical and analytical investigation. These systems do not exhibit aligned or flocking states, but do have a rich phase diagram, forming active gases, liquids and solids with novel mechanical properties. This article reviews recent advances in the understanding of such models, including the description of the active gas and its swim pressure, the motility-induced phase separation and the high-density crystalline and glassy behavior.

We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational spectrum and the nature of the modes are very similar to those predicted for zero-temperature idealized sphere models and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.PACS numbers: 63. 63.50 Lm, 82.70 Dd Crystalline solids are all alike in their vibrational properties at low frequencies; every disordered solid is disordered in its own way. Disordered solids nonetheless exhibit common low-frequency vibrational properties that are completely unlike those of crystals, which are dominated by sound modes. Disordered atomic or molecular solids generically exhibit a "boson peak," where many more modes appear than expected for sound. The excess modes of the boson peak are believed to be responsible for the unusual behavior of the heat capacity and thermal conductivity at low-to-intermediate temperatures in disordered solids [2].It has been proposed that a zero-temperature jamming transition may provide a framework for understanding this unexpected commonality [3]. For frictionless, idealized spheres this jamming transition lies at the threshold of mechanical stability, known as the isostatic point [3,4]. As a result of this coincidence, the vibrational behavior of the marginally jammed solid at densities just above the jamming transition is fundamentally different from that of ordinary elastic solids [5][6][7][8]. A new class of lowfrequency vibrational modes arises because the system is at the threshold of mechanical stability [10]; these modes give rise to a divergent boson peak at zero frequency [5]. As the system is compressed beyond the jamming transition, the boson peak shrinks in height and shifts upwards in frequency [5]. Generalizations of the idealized sphere model suggest that the boson peaks of a wide class of disordered solids may arise from proximity to the jamming transition [9][10][11][12]. Moreover, the jamming scenario predicts that systems with larger constituents such as colloids should also have boson peaks.Colloidal glasses offer signal advantages over atomic or molecular disordered solids because colloids can be tracked by video microscopy. Vibrational behavior has been explored in hard-sphere colloids [13] and vibrated granular packings [14], but difficulties with statistics [13] or micro-cracks [14] were encountered. In contrast, we use deformable, thermosensitive hydrogel particles to tune the packing fraction in situ. Our experiments show unambiguously that the commonality in vibrational properties observed in atomic and molecular glas...

Epithelial cell monolayers show remarkable long-range displacement and velocity correlations reminiscent of supercooled liquids and active nematics. Here we show that many of the observed features can be understood within the framework of active matter at high densities. In particular, we argue that uncoordinated but persistent cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce characteristic swirl-like correlations. This includes a divergent correlation length in the limit of infinite persistence time. We derive this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based models of soft elastic particles and in-vitro experiments of confluent corneal epithelial cell sheets. Our analytical model is able to fit measured velocity correlation functions without any free parameters. SIGNIFICANCEUnderstanding how cells in confluent epithelial sheets coordinate to create coherent motion patterns is a central question in cell and developmental biology. We show that a simple active matter model that couples crawling of an individual cell to the elastic environment provided by the surrounding cells, faithfully captures large-scale coherent motion patterns observed in the epithelial cell monolayers. The linear elastic model can be analyzed analytically and is able to match numerical simulations of two complementary models without any fitting parameters. It is a good match for experiments on corneal epithelial cells.