Silke Henkes

Active jamming: Self-propelled soft particles at high density

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 v(0) and a jammed phase at high φ and low v(0). The dynamics of the jammed phase is controlled by the low-frequency modes of the jammed packing.

Statistical mechanics framework for static granular matter

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.

Soft-Sphere Packings at Finite Pressure but Unstable to Shear

When are athermal soft-sphere packings jammed? Any experimentally relevant definition must, at the very least, require a jammed packing to resist shear. We demonstrate that widely used (numerical) protocols, in which particles are compressed together, can and do produce packings that are unstable to shear-and that the probability of generating such packings reaches one near jamming. We introduce a new protocol which, by allowing the system to explore different box shapes as it equilibrates, generates truly jammed packings with strictly positive shear moduli G. For these packings, the scaling of the average of G is consistent with earlier results, while the probability distribution P(G) exhibits novel and rich scalings.

Minimal model of active colloids highlights the role of mechanical interactions in controlling the emergent behavior of active matter

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.

Jamming as a critical phenomenon: a field theory of zero-temperature grain packings.

A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a nonzero value of the packing fraction. The zero-temperature constraint of force balance plays a crucial role in determining the nature of the transition. Two order parameters, , the deviation of the average number of contacts from the isostatic value, and , the average magnitude of the force per contact, characterize the transition from the jammed (high packing fraction) to the unjammed (low packing fraction state). The critical point has a mixed character with the order parameters showing a jump discontinuity but with fluctuations of the contact force diverging. At the critical point, the distribution of phi shows the characteristic plateau observed in static granular piles. The theory makes falsifiable predictions about the spatial fluctuations of the contact forces.

Critical jamming of frictional grains in the generalized isostaticity picture

While frictionless spheres at jamming are isostatic, frictional spheres at jamming are not. As a result, frictional spheres near jamming do not necessarily exhibit an excess of soft modes. However, a generalized form of isostaticity can be introduced if fully mobilized contacts at the Coulomb friction threshold are considered as slipping contacts. We show here that, in this framework, the vibrational density of states (DOS) of frictional discs exhibits a plateau when the generalized isostaticity line is approached. The crossover frequency ω* scales linearly with the distance from this line. Moreover, we show that the frictionless limit, which appears singular when fully mobilized contacts are treated elastically, becomes smooth when fully mobilized contacts are allowed to slip. Finally, we elucidate the nature of the vibrational modes, both for slipping and for non-slipping fully mobilized contacts.

The Statistical Physics of Athermal Materials

At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends on only a few macroscopic parameters,suchastemperature,pressure,volume,andenergy.Inthis review, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune to the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates ofequilibrium statistical mechanics. However, granular materials exhibit distributions of microscopic quantities that are reproducible and often depend on only a few macroscopic parameters. We explore the history of statistical ensemble ideas in the context of granular materials, clarify the nature of such ensembles and their foundational principles, highlight advances in testing key ideas, and discuss applications of ensembles to analyze the collective behavior of granular materials.

Why do granular materials stiffen with shear rate? Test of novel stress-based statistics.

Recent experiments exhibit a rate dependence for granular shear such that the stress grows linearly in the logarithm of the shear rate, gamma. Assuming a generalized activated process mechanism, we show that these observations are consistent with a recent proposal for a stress-based statistical ensemble. By contrast, predictions for rate dependence using conventional energy-based statistical mechanics to describe activated processes, predicts a rate dependence of (ln(gamma))(1/2).

Active Vertex Model for cell-resolution description of epithelial tissue mechanics

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.

Extracting vibrational modes from fluctuations: a pedagogical discussion

The study of the jamming transition of granular and colloidal systems, has lead to a proliferation of theoretical and numerical results formulated in the language of the eigenspectrum of the dynamical matrix for these disordered systems. Only recently however, have these modes been accessed experimentally in colloidal and granular media, by computing the eigenmodes of the covariance matrix of the particle positions. At the same time, new conceptual and methodological questions regarding the interpretation of these results have appeared. In the present paper, we first give an overview of the theoretical framework which is appropriate to interpret the eigenmodes and eigenvalues of the correlation matrix in terms of the vibrational properties of these systems. We then illustrate several aspects of the statistical and data analysis techniques necessary to extract reliable results from experimental data. Concentrating on the cases of hard sphere simulations, colloidal and granular experiments, we discuss how to test, in turn, for the existence of a metastable state and the statistical independence of the sampling, the effect of experimental resolution, and the harmonic hypothesis underlying the approach; highlighting both the promises and limitations of this approach.