arXiv subjects

Silke Henkes

Publications and source records attributed to Silke Henkes.

35 records · Page 2Linked to original sources

arXiv2017

Dynamical patterns in active nematics on a sphere

Using agent-based simulations of self-propelled particles subject to short-range repulsion and nematic alignment we explore the dynamical phases of a dense active material confined to the surface of a sphere. We map the dynamical phase diagram as a function of curvature, alignment strength and activity and reproduce phases seen in recent experiments on active microtubules moving on the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a band of polar matter wrapping around an equator, with large bald spots corresponding to two +1 defects at the poles. Finally, bands fold onto themselves, followed by the system moving into a turbulent state marked by active proliferation of pairs of topological defects. We highlight the role of nematic persistence length and time for pattern formation in these confined systems with finite curvature.

cond-mat.soft↗

arXiv2016

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.

physics.bio-ph↗

arXiv2016

Self-Organized Hydrodynamics with nonconstant velocity

Motivated by recent experimental and computational results that show a motility-induced clustering transition in self-propelled particle systems, we study an individual model and its corresponding Self-Organized Hydrodynamic model for collective behaviour that incorporates a density-dependent velocity, as well as inter-particle alignment. The modal analysis of the hydrodynamic model elucidates the relationship between the stability of the equilibria and the changing velocity, and the formation of clusters. We find, in agreement with earlier results for non-aligning particles, that the key criterion for stability is $(ρv(ρ))'> 0$, i.e. a non-rapid decrease of velocity with density. Numerical simulation for both the individual and hydrodynamic models with a velocity function inspired by experiment demonstrates the validity of the theoretical results.

nlin.AO↗

arXiv2016

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.

cond-mat.soft↗

arXiv2015

Rigid cluster decomposition reveals criticality in frictional jamming

We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game including frictional contacts. We discover a second-order transition controlled by the emergence of a system-spanning rigid cluster accompanied by a critical cluster size distribution. Rigid clusters also correlate with common measures of rigidity. We contrast this result with frictionless jamming, where the rigid cluster size distribution is noncritical.

cond-mat.soft↗

arXiv2014

Active swarms on a sphere

Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-propelled particles with polar alignment on a sphere. Hallmarks of these motion patterns are a polar vortex and a circulating band arising due to the incompatibility between spherical topology and uniform motion - a consequence of the hairy ball theorem. We present analytical results showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.

cond-mat.soft↗

arXiv2014

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 only on a few macroscopic parameters such as temperature, pressure, volume, and energy. In this review article, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune from the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates of equilibrium 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.

cond-mat.stat-mech↗

arXiv2013

Freezing and phase separation of self-propelled disks

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.

cond-mat.soft↗

arXiv2011

Dynamical fluctuations close to Jamming versus Vibrational Modes : a pedagogical discussion illustrated on hard spheres simulations, colloidal and granular experiments

Studying 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 system. Only recently however, these modes have been accessed experimentally in colloidal and granular media, computing the eigenmodes of the covariance matrix of the particle positions. At the same time new conceptual and methodological questions have appeared, regarding the interpretation of these results. In the present paper, we first give an overview of the theoretical framework which is appropriate to discuss the interpretation of 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 which are necessary to extract reliable results from experimental data. Concentrating on the case of hard sphere simulations, colloidal and granular experiments, we discuss how to test the existence of a metastable state, the statistical independence of the sampling, the effect of the experimental resolution, and the harmonic hypothesis underlying the approach, highlighting both its promises and limitations.

cond-mat.soft↗

arXiv2011

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 and high self-propulsion speed and a jammed phase at high packing fraction and low self-propulsion speed. The dynamics of the jammed phase is controlled by the low frequency modes of the jammed packing.

cond-mat.soft↗

arXiv2010

Low-frequency vibrations of soft colloidal glasses

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.

cond-mat.soft↗

arXiv2010

Local Coulomb versus Global Failure Criterion for Granular Packings

Contacts at the Coulomb threshold are unstable to tangential perturbations and thus contribute to failure at the microscopic level. How is such a local property related to global failure, beyond the effective picture given by a Mohr-Coulomb type failure criterion? Here, we use a simulated bed of frictional disks slowly tilted under the action of gravity to investigate the link between the avalanche process and a global generalized isostaticity criterion. The avalanche starts when the packing as a whole is still stable according to this criterion, underlining the role of large heterogeneities in the destabilizing process: the clusters of particles with fully mobilized contacts concentrate local failure. We demonstrate that these clusters, at odds with the pile as a whole, are also globally marginal with respect to generalized isostaticity. More precisely, we observe how the condition of their stability from a local mechanical proprety progressively builds up to the generalized isostaticity criterion as they grow in size and eventually span the whole system when approaching the avalanche.

cond-mat.soft↗

arXiv2009

Local contact numbers in two dimensional packings of frictional disks

We analyze the local structure of two dimensional packings of frictional disks numerically. We focus on the fractions x_i of particles that are in contact with i neighbors, and systematically vary the confining pressure p and friction coefficient μ. We find that for all μ, the fractions x_i exhibit powerlaw scaling with p, which allows us to obtain an accurate estimate for x_i at zero pressure. We uncover how these zero pressure fractions x_i vary with μ, and introduce a simple model that captures most of this variation. We also probe the correlations between the contact numbers of neighboring particles.

cond-mat.soft↗

arXiv2009

Entropic origin of stress correlations in granular materials

We study the response of granular materials to external stress using experiment, simulation, and theory. We derive an entropic, Ginzburg-Landau functional that enforces mechanical stability and positivity of contact forces. In this framework, the elastic moduli depend only on the applied stress. A combination of this feature and the positivity constraint leads to stress correlations whose shape and magnitude are extremely sensitive to the applied stress. The predictions from the theory describe the stress correlations for both simulations and experiments semiquantitatively.

cond-mat.stat-mech↗

arXiv2008

Why Do Granular Materials Stiffen with Shear Rate? A 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, \dotγ. 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 that of (\ln (\dotγ))^{1/2}.

cond-mat.soft↗

arXiv2007

Entropy and Temperature of a Static Granular Assembly

Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength. A comprehensive theory of the properties of granular matter, therefore, requires a statistical framework. In molecular matter, equilibrium statistical mechanics, which is founded on the principle of conservation of energy, provides this framework. Grains, however, are small but macroscopic objects whose interactions are dissipative since energy can be lost through excitations of the internal degrees of freedom. In this work, we construct a statistical framework for static, mechanically stable packings of grains, which parallels that of equilibrium statistical mechanics but with conservation of energy replaced by the conservation of a function related to the mechanical stress tensor. Our analysis demonstrates the existence of a state function that has all the attributes of entropy. In particular, maximizing this state function leads to a well-defined granular temperature for these systems. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks. Our demonstration that a statistical ensemble can be constructed through the identification of conserved quantities other than energy is a new approach that is expected to open up avenues for statistical descriptions of other non-equilibrium systems.

cond-mat.stat-mech↗

arXiv2005

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 non-zero 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 F shows the characteristic plateau observed in static granular piles. The theory makes falsifiable predictions about the spatial fluctuations of the contact forces. Implications for finite temperature dynamics and generalizations to frictional packings and higher dimensions are discussed

cond-mat.stat-mech↗