Journey of an intruder through the fluidization and jamming transitions of a dense granular media

Force renormalization for probes immersed in an active bath

Langevin equations or generalized Langevin equations (GLEs) are popular models for describing the motion of a particle in a fluid medium in an effective manner. Here we examine particles immersed in an inherently nonequilibrium fluid, i.e., an active bath, which are subject to an external force. Specifically, we consider two types of forces that are highly relevant for microrheological studies: A harmonic, trapping force and a constant, "drag" force. We study such systems by molecular simulations and use the simulation data to extract an effective GLE description. We find that within this description, in an active bath, the external force in the GLE is not equal to the physical external force, but rather a renormalized external force, which can be significantly smaller. The effect cannot be attributed to the mere temperature renormalization, which is also observed.

Pedestrians in static crowds are not grains, but game players

The local navigation of pedestrians is assumed to involve no anticipation beyond the most imminent collisions, in most models. These typically fail to reproduce some key features experimentally evidenced in dense crowds crossed by an intruder, namely, transverse displacements toward regions of higher density due to the anticipation of the intruder's crossing. We introduce a minimal model based on mean-field games, emulating agents planning out a global strategy that minimizes their overall discomfort. By solving the problem in the permanent regime thanks to an elegant analogy with the nonlinear Schrödinger's equation, we are able to identify the two main variables governing the model's behavior and to exhaustively investigate its phase diagram. We find that, compared to some prominent microscopic approaches, the model is remarkably successful in replicating the experimental observations associated with the intruder experiment. In addition, the model can capture other daily-life situations such as partial metro boarding.

Local Yield and Compliance in Active Cell Monolayers

The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multiphase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solidlike state and a fluidlike state tuned by cell motility and deformability-the ratio of the energetic costs of steric cell-cell repulsion and cell-edge tension. When perturbed, solid tissues exhibit local yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different and point to ways in which it can be controlled.

Disentangling intrinsic motion from neighborhood effects in heterogeneous collective motion

Most real-world collectives, including animal groups, pedestrian crowds, active particles, and living cells, are heterogeneous. The differences among individuals in their intrinsic properties have emergent effects at the group level. It is often of interest to infer how the intrinsic properties differ among the individuals based on their observed movement patterns. However, the true individual properties may be masked by the nonlinear interactions in the collective. We investigate the inference problem in the context of a bidisperse collective with two types of agents, where the goal is to observe the motion of the collective and classify the agents according to their types. Since collective effects, such as jamming and clustering, affect individual motion, the information in an agent's own movement is insufficient for accurate classification. A simple observer algorithm, based only on individual velocities, cannot accurately estimate the level of heterogeneity of the system and often misclassifies agents. We propose a novel approach to the classification problem, where collective effects on an agent's motion are explicitly accounted for. We use insights about the phenomenology of collective motion to quantify the effect of the neighborhood on an agent's motion using a neighborhood parameter. Such an approach can distinguish between agents of two types, even when their observed motion is identical. This approach estimates the level of heterogeneity much more accurately and achieves significant improvements in classification. Our results demonstrate that explicitly accounting for neighborhood effects is often necessary to correctly infer intrinsic properties of individuals.

Universal features of the stick-slip dynamics of an intruder moving through a confined granular medium

Experiments and simulations of an intruder dragged by a spring through a two-dimensional annulus of granular material exhibit robust force fluctuations. At low packing fractions (ϕ<ϕ_{0}), the intruder clears an open channel. Above ϕ_{0}, stick-slip dynamics develop, with an average energy release that is independent of the particle-particle and particle-base friction coefficients but does depend on the width W of the annulus and the diameter D of the intruder. A simple model predicts the dependence of ϕ_{0} on W and D, allowing for a data collapse for the average energy release as a function of ϕ/ϕ_{0}. These results pose challenges for theories of mechanical failure in amorphous materials.

Moving efficiently through a crowd: A nature-inspired traffic rule

In this article, we propose a traffic rule inspired from nature that instructs how a crowd made up of inert agents should respond to an elite agent to facilitate its motion through the crowd. When an object swims in a fluid medium or an intruder is forced through granular matter, characteristic flow fields are created around them. We show that if inert agents made small movements based on a traffic rule derived from these characteristic flow fields, then they efficiently reorganize and transport enough space for the elite to pass through. The traffic rule used in the article is a dipole field which satisfactorily captures the features of the flow fields around a moving intruder. We study the effectiveness of this dipole traffic rule using numerical simulations in a two-dimensional periodic domain, where one self-propelled elite agent tries to move through a crowd of inert agents that prefer to stay in a state of rest. Simulations are carried out for a wide range of strengths of the traffic rule and packing densities of the crowd. We characterize and analyze four regions in the parameter space-free-flow, motion due to cooperation and frozen and collective drift regions-and discuss the consequence of the traffic rule in light of the collective behavior observed. We believe that the proposed method can be of use in a swarm of robots working in constrained environments.

Stress propagation in locally loaded packings of disks and pentagons

The mechanical strength and flow of granular materials can depend strongly on the shapes of individual grains. We report quantitative results obtained from photoelasticimetry experiments on locally loaded, quasi-two-dimensional granular packings of either disks or pentagons exhibiting stick-slip dynamics. Packings of pentagons resist the intruder at significantly lower packing fractions than packings of disks, transmitting stresses from the intruder to the boundaries over a smaller spatial extent. Moreover, packings of pentagons feature significantly fewer back-bending force chains than packings of disks. Data obtained on the forward spatial extent of stresses and back-bending force chains collapse when the packing fraction is rescaled according to the packing fraction of steady state open channel formation, though data on intruder forces and dynamics do not collapse. We comment on the influence of system size on these findings and highlight connections with the dynamics of the disks and pentagons during slip events.

Attraction and condensation of driven tracers in a narrow channel

Emergent bath-mediated attraction and condensation arise when multiple particles are simultaneously driven through an equilibrated bath under geometric constraints. While such scenarios are observed in a variety of nonequilibrium phenomena with an abundance of experimental and numerical evidence, little quantitative understanding of how these interactions arise is currently available. Here we approach the problem by studying the behavior of two driven "tracer" particles, propagating through a bath in a 1D lattice with excluded-volume interactions. We apply the mean-field approximation to analytically explore the mechanism responsible for the tracers' emergent interactions and compute the resulting effective attractive potential. This mechanism is then numerically shown to extend to a realistic model of hard driven Brownian disks confined to a narrow 2D channel.

Particle dynamics in two-dimensional point-loaded granular media composed of circular or pentagonal grains

Granular packings exhibit significant changes in rheological and structural properties when the rotational symmetry of spherical or circular particles is broken. Here, we report on experiments exploring the differences in dynamics of a grain-scale intruder driven through a packing of either disks or pentagons, where the presence of edges and vertices on grains introduces the possibility of rotational constraints at edge-edge contacts. We observe that the intruder’s stick-slip dynamics are comparable between the disk packing near the frictional jamming fraction and the pentagonal packing at significantly lower packing fractions. We connect this stark contrast in packing fraction with the average speed and rotation fields of grains during slip events, finding that rotation of pentagons is limited and the flow of pentagonal grains is largely confined in front of the intruder, whereas disks rotate more on average and circulate around the intruder to fill the open channel behind it. Our results indicate that grain-scale rotation constraints significantly modify collective motion of grains on mesoscopic scales and correspondingly enhance resistance to penetration of a local intruder.

Directional clogging and phase separation for disk flow through periodic and diluted obstacle arrays

We model collective disk flow though a square array of obstacles as the flow direction is changed relative to the symmetry directions of the array. At lower disk densities there is no clogging for any driving direction, but as the disk density increases, the average disk velocity decreases and develops a drive angle dependence. For certain driving angles, the flow is reduced or drops to zero when the system forms a heterogeneous clogged state consisting of high density clogged regions coexisting with empty regions. The clogged states are fragile and can be unclogged by changing the driving angle. For large obstacle sizes, we find a uniform clogged state that is distinct from the collective clogging regime. Within the clogged phases, depinning transitions can occur as a function of increasing driving force, with intermittent motion appearing just above the depinning threshold. The clogging is robust against the random removal or dilution of the obstacle sites, and the disks are able to form system-spanning clogged clusters even under increasing dilution. If the dilution becomes too large, however, the clogging behavior is lost.

Intruder in a two-dimensional granular system: Effects of dynamic and static basal friction on stick-slip and clogging dynamics

We present simulation results for an intruder pulled through a two-dimensional granular system by a spring using a model designed to mimic the experiments described by Kozlowski et al. [Phys. Rev. E 100, 032905 (2019)2470-004510.1103/PhysRevE.100.032905]. In that previous study the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick-slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions of particles with each other and with boundaries. We then use simulations to explore a broader range of parameter space, focusing on the friction between the particles and the base. We consider both static and dynamic basal friction coefficients, which are difficult to vary smoothly in experiments. The simulations show that dynamic friction strongly affects the stick-slip behavior when the coefficient is decreased below 0.1, while static friction plays only a marginal role.

Dynamics of a grain-scale intruder in a two-dimensional granular medium with and without basal friction

We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a two-dimensional granular material composed of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: A frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: Intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid events. When basal friction is present, we observe a smooth crossover between the two regimes as a function of packing fraction, and we find that reducing the interparticle friction coefficient causes the stick-slip regime to shift to higher packing fractions. When basal friction is eliminated, we observe intermittent flow at all accessible packing fractions. For all cases, we present results for the statistics of stick events, the intruder velocity, and the force exerted on the intruder by the grains. Our results indicate the qualitative importance of basal friction at high packing fractions and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows.

Active microrheology, Hall effect, and jamming in chiral fluids

We examine the motion of a probe particle driven through a chiral fluid composed of circularly swimming disks. We find that the probe particle travels in both the longitudinal direction, parallel to the driving force, and in the transverse direction, perpendicular to the driving force, giving rise to a Hall angle. Under constant driving force, we show that the probe particle velocity in both the longitudinal and transverse directions exhibits nonmonotonic behavior as a function of the activity of the circle swimmers. The Hall angle is maximized when a resonance occurs between the frequency of the chiral disks and the motion of the probe particle. As the density of the chiral fluid increases, the Hall angle gradually decreases before reaching zero when the system enters a jammed state. We show that the onset of jamming depends on the chiral particle swimming frequency, with a fluid state appearing at low frequencies and a jammed solid occurring at high frequencies.

Hysteresis of the drag force of an intruder moving into a granular medium

We numerically investigate the force-displacement relation of a moving intruder initially at rest into a granular medium. Our model granular medium is composed of one layer of coplanar polydisperse spheres subjected to a gravity field. The interactions between the grains are modelled by Hertzian contacts to which a viscous damping is applied. Moving it horizontally and with alternating positive and negative velocity, we recover a hysteresis of the force-displacement curve. Considering that the flow is plastic as the yield strength has been reached, we describe the transient part of the flow around the intruder. We show that the drag stress increases as its distance to an ultimate drag stress [Formula: see text] with a typical deformation [Formula: see text]: the drag stress-strains curve appears to exponentially decay as it saturates to this ultimate drag stress. This protocol of deformation highlights that the deformation of the grains is negligible compared to the deformation of the packing, i.e. related to the irreversible displacements of grains allowing the intruder to pass through. Simultaneously, the lift force is constant on average during the displacement of the intruder. We then give the different scaling laws of the yield strength, this ultimate drag stress, the characteristic deformation of the packing and the lift stress. Finally, we recover the complete hysteresis cycle of the drag force around the intruder.

The physics of jamming for granular materials: a review

Granular materials consist of macroscopic grains, interacting via contact forces, and unaffected by thermal fluctuations. They are one of a class systems that undergo jamming, i.e. a transition between fluid-like and disordered solid-like states. Roughly twenty years ago, proposals by Cates et al for the shear response of colloidal systems and by Liu and Nagel, for a universal jamming diagram in a parameter space of packing fraction, ϕ, shear stress, τ, and temperature, T raised key questions. Contemporaneously, experiments by Howell et al and numerical simulations by Radjai et al and by Luding et al helped provide a starting point to explore key insights into jamming for dry, cohesionless, granular materials. A recent experimental observation by Bi et al is that frictional granular materials have a a re-entrant region in their jamming diagram. In a range of ϕ, applying shear strain, γ, from an initially force/stress free state leads to fragile (in the sense of Cates et al), then anisotropic shear jammed states. Shear jamming at fixed ϕ is presumably conjugate to Reynolds dilatancy, involving dilation under shear against deformable boundaries. Numerical studies by Radjai and Roux showed that Reynolds dilatancy does not occur for frictionless systems. Recent numerical studies by several groups show that shear jamming occurs for finite, but not infinite, systems of frictionless grains. Shear jamming does not lead to known ordering in position space, but Sarkar et al showed that ordering occurs in a space of force tiles. Experimental studies seeking to understand random loose and random close packings (rlp and rcp) and dating back to Bernal have probed granular packings and their response to shear and intruder motion. These studies suggest that rlp's are anisotropic and shear-jammed-like, whereas rcp's are likely isotropically jammed states. Jammed states are inherently static, but the jamming diagram may provide a context for understanding rheology, i.e. dynamic shear in a variety of systems that include granular materials and suspensions.

Tracer diffusion in crowded narrow channels

We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.

Sinking in a bed of grains activated by shearing

We show how a weak force f enables intruder motion through dense granular materials subject to external mechanical excitations, in the present case, stepwise shearing. A force acts on a Teflon disk in a two-dimensional system of photoelastic disks. This force is much smaller than the smallest force needed to move the disk without any external excitation. In a cycle, the material plus intruder are sheared quasistatically from γ=0 to γ_{max}, and then backwards to γ=0. During various cycle phases, fragile and jammed states form. Net intruder motion δ occurs during fragile periods generated by shear reversals. δ per cycle, e.g., the quasistatic rate c, is constant, linearly dependent on γ_{max} and f. It vanishes as c∝(ϕ_{c}-ϕ)^{a}, with a≃3 and ϕ_{c}≃ϕ_{J}, reflecting the stiffening of granular systems under shear [J. Ren, J. A. Dijksman, and R. P. Behringer, Phys. Rev. Lett. 110, 018302 (2013)]PRLTAO0031-900710.1103/PhysRevLett.110.018302 as ϕ→ϕ_{J}. The intruder motion induces large-scale grain circulation. In the intruder frame, this motion is a granular analog to fluid flow past a cylinder, where f is the drag force exerted by the flow.

Clogging and depinning of ballistic active matter systems in disordered media

We numerically examine ballistic active disks driven through a random obstacle array. Formation of a pinned or clogged state occurs at much lower obstacle densities for the active disks than for passive disks. As a function of obstacle density, we identify several distinct phases including a depinned fluctuating cluster state, a pinned single-cluster or jammed state, a pinned multicluster state, a pinned gel state, and a pinned disordered state. At lower active disk densities, a drifting uniform liquid forms in the absence of obstacles, but when even a small number of obstacles are introduced, the disks organize into a pinned phase-separated cluster state in which clusters nucleate around the obstacles, similar to a wetting phenomenon. We examine how the depinning threshold changes as a function of disk or obstacle density and find a crossover from a collectively pinned cluster state to a disordered plastic depinning transition as a function of increasing obstacle density. We compare this to the behavior of nonballistic active particles and show that as we vary the activity from completely passive to completely ballistic, a clogged phase-separated state appears in both the active and passive limits, while for intermediate activity, a readily flowing liquid state appears and there is an optimal activity level that maximizes the flux through the sample.

Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium

We study the quasistatic penetration of a flexible beam into a two-dimensional dense granular medium lying on a horizontal plate. Rather than a buckling-like behavior we observe a transition between a regime of crack-like penetration in which the fiber only shows small fluctuations around a stable straight geometry and a bending regime in which the fiber fully bends and advances through series of loading and unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single nondimensional parameter L/L_{c}, which is the ratio of the length of the flexible beam L to L_{c}, a bending elastogranular length scale that depends on the rigidity of the fiber and on the departure from the jamming packing fraction of the granular medium. We show, moreover, that the dynamics of the bending transition in the course of the penetration experiment is gradual and is accompanied by a symmetry breaking of the granular packing fraction in the vicinity of the fiber. Together with the progressive bending of the fiber, a cavity grows downstream of the fiber and the accumulation of grains upstream of the fiber leads to the development of a jammed cluster of grains. We discuss our experimental results in the framework of a simple model of bending-induced compaction and we show that the rate of the bending transition only depends on the control parameter L/L_{c}.

Velocity force curves, laning, and jamming for oppositely driven disk systems

Using simulations we examine a two-dimensional disk system in which two disk species are driven in opposite directions. We measure the average velocity of one of the species versus the applied driving force and identify four phases as function of drive and disk density: a jammed state, a completely phase separated state, a continuously mixing phase, and a laning phase. The transitions between these phases are correlated with jumps in the velocity-force curves that are similar to the behavior observed at dynamical phase transitions in driven particle systems with quenched disorder such as vortices in type-II superconductors. In some cases the transitions between phases are associated with negative differential mobility in which the average absolute velocity of either species decreases with increasing drive. We also consider the situation where the drive is applied to only one species as well as systems in which both species are driven in the same direction with different drive amplitudes. We show that the phases are robust against the addition of thermal fluctuations. Finally, we discuss how the transitions we observe could be related to absorbing phase transitions where a system in a phase separated or laning regime organizes to a state in which contacts between the disks no longer occur and dynamical fluctuations are lost.

Cooperative behavior of biased probes in crowded interacting systems

We study, via extensive numerical simulations, dynamics of a crowded mixture of mutually interacting (with a short-range repulsive potential) colloidal particles immersed in a suspending solvent, acting as a heat bath. The mixture consists of a majority component - neutrally buoyant colloids subject to internal stimuli only, and a minority component - biased probes (BPs) also subject to a constant force. In such a system each of the BPs alters the distribution of the colloidal particles in its vicinity, driving their spatial distribution out of equilibrium. This induces effective long-range interactions and multi-tag correlations between the BPs, mediated by an out-of-equilibrium majority component, and prompts the BPs to move collectively assembling in clusters. We analyse the size-distribution of the self-assembling clusters in the steady-state, their specific force-velocity relations and also properties of the effective interactions emerging between the BPs.

Universal Long Ranged Correlations in Driven Binary Mixtures

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.

Casimir effect between pinned particles in two-dimensional jammed systems

The Casimir effect arises when long-ranged fluctuations are geometrically confined between two surfaces, leading to a macroscopic force. Traditionally, these forces have been observed in quantum systems and near critical points in classical systems. Here we show the existence of Casimir-like forces between two pinned particles immersed in two-dimensional systems near the jamming transition. We observe two components to the total force: a short-ranged, depletion force and a long-ranged, repulsive Casimir-like force. The Casimir-like force dominates as the jamming transition is approached, and when the pinned particles are much larger than the ambient jammed particles. We show that this repulsive force arises due to a clustering of particles with strong contact forces around the perimeter of the pinned particles. As the separation between the pinned particles decreases, a region of high-pressure develops between them, leading to a net repulsive force.

Driven tracers in narrow channels

Steady-state properties of a driven tracer moving in a narrow two-dimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a one-dimensional (1D) SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of mean-field theory and exact solution in the limit where no exchange is allowed gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.

Experimental Evidence of the Gardner Phase in a Granular Glass

Analyzing the dynamics of a vibrated bidimensional packing of bidisperse granular disks below jamming, we provide evidence of a Gardner phase deep into the glass phase. To do so, we perform several compression cycles within a given realization of the same glass and show that the particles select different average vibrational positions at each cycle, while the neighborhood structure remains unchanged. The separation between the cages obtained for different compression cycles plateaus with an increasing packing fraction, while the mean square displacement steadily decreases. This phenomenology is strikingly similar to that reported in recent numerical observations when entering the Gardner phase, for a mean-field model of glass as well as for hard spheres in finite dimension. We also characterize the distribution of the cage order parameters. Here we note several differences from the numerical results, which could be attributed to activated processes and cage heterogeneities.

Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments

We study analytically the dynamics and the microstructural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active microrheology experiments, we consider here a minimal model comprising a geometrically confined lattice system (a two-dimensional striplike or a three-dimensional capillary-like system) populated by two types of hard-core particles with stochastic dynamics (a tracer particle driven by a constant external force and bath particles moving completely at random). Resorting to a decoupling scheme, which permits us to go beyond the linear-response approximation (Stokes regime) for arbitrary densities of the lattice gas particles, we determine the force-velocity relation for the tracer particle and the stationary density profiles of the host medium particles around it. These results are validated a posteriori by extensive numerical simulations for a wide range of parameters. Our theoretical analysis reveals two striking features: (a) We show that, under certain conditions, the terminal velocity of the driven tracer particle is a nonmonotonic function of the force, so in some parameter range the differential mobility becomes negative, and (b) the biased particle drives the whole system into a nonequilibrium steady state with a stationary particle density profile past the tracer, which decays exponentially, in sharp contrast with the behavior observed for unbounded lattices, where an algebraic decay is known to take place.

Local-heterogeneous responses and transient dynamics of cage breaking and formation in colloidal fluids

Quantifying the interactions in dense colloidal fluids requires a properly designed order parameter. We present a modified bond-orientational order parameter, ψ̄6, to avoid problems of the original definition of bond-orientational order parameter. The original bond-orientational order parameter can change discontinuously in time but our modified order parameter is free from the discontinuity and, thus, it is a suitable measure to quantify the dynamics of the bond-orientational ordering of the local surroundings. Here we analyze ψ̄6 in a dense driven monodisperse quasi-two-dimensional colloidal fluids where a single particle is optically trapped at the center. The perturbation by the trapped and driven particle alters the structure and dynamics of the neighboring particles. This perturbation disturbs the flow and causes spatial and temporal distortion of the bond-orientational configuration surrounding each particle. We investigate spatio-temporal behavior of ψ̄6 by a Wavelet transform that provides a time-frequency representation of the time series of ψ̄6. It is found that particles that have high power in frequencies corresponding to the inverse of the timescale of perturbation undergo distortions of their packing configurations that result in cage breaking and formation dynamics. To gain insight into the dynamic structure of cage breaking and formation of bond-orientational ordering, we compare the cage breaking and formation dynamics with the underlying dynamical structure identified by Lagrangian Coherent Structures (LCSs) estimated from the finite-time Lyapunov exponent (FTLE) field. The LCSs are moving separatrices that effectively divide the flow into distinct regions with different dynamical behavior. It is shown that the spatial distribution of the FTLE field and the power of particles in the wavelet transform have positive correlation, implying that LCSs provide a dynamic structure that dominates the dynamics of cage breaking and formation of the colloidal fluids.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Aspects of jamming in two-dimensional athermal frictionless systems

In this work we provide an overview of jamming transitions in two dimensional systems focusing on the limit of frictionless particle interactions in the absence of thermal fluctuations. We first discuss jamming in systems with short range repulsive interactions, where the onset of jamming occurs at a critical packing density and where certain quantities show a divergence indicative of critical behavior. We describe how aspects of the dynamics change as the jamming density is approached and how these dynamics can be explored using externally driven probes. Different particle shapes can produce jamming densities much lower than those observed for disk-shaped particles, and we show how jamming exhibits fragility for some shapes while for other shapes this is absent. Next we describe the effects of long range interactions and jamming behavior in systems such as charged colloids, vortices in type-II superconductors, and dislocations. We consider the effect of adding obstacles to frictionless jamming systems and discuss connections between this type of jamming and systems that exhibit depinning transitions. Finally, we discuss open questions such as whether the jamming transition in all these different systems can be described by the same or a small subset of universal behaviors, as well as future directions for studies of jamming transitions in two dimensional systems, such as jamming in self-driven or active matter systems.

Physics in ordered and disordered colloidal matter composed of poly(N-isopropylacrylamide) microgel particles

This review collects and describes experiments that employ colloidal suspensions to probe physics in ordered and disordered solids and related complex fluids. The unifying feature of this body of work is its clever usage of poly(N-isopropylacrylamide) (PNIPAM) microgel particles. These temperature-sensitive colloidal particles provide experimenters with a 'knob' for in situ control of particle size, particle interaction and particle packing fraction that, in turn, influence the structural and dynamical behavior of the complex fluids and solids. A brief summary of PNIPAM particle synthesis and properties is given, followed by a synopsis of current activity in the field. The latter discussion describes a variety of soft matter investigations including those that explore formation and melting of crystals and clusters, and those that probe structure, rearrangement and rheology of disordered (jammed/glassy) and partially ordered matter. The review, therefore, provides a snapshot of a broad range of physics phenomenology which benefits from the unique properties of responsive microgel particles.

Active microrheology of driven granular particles

When pulling a particle in a driven granular fluid with constant force Fex, the probe particle approaches a steady-state average velocity v. This velocity and the corresponding friction coefficient of the probe ζ=Fex/v are obtained within a schematic model of mode-coupling theory and compared to results from event-driven simulations. For small and moderate drag forces, the model describes the simulation results successfully for both the linear as well as the nonlinear region: The linear response regime (constant friction) for small drag forces is followed by shear thinning (decreasing friction) for moderate forces. For large forces, the model demonstrates a subsequent increasing friction in qualitative agreement with the data. The square-root increase of the friction with force found in [Fiege et al., Granul. Matter 14, 247 (2012)] is explained by a simple kinetic theory.

Colloidal lattice shearing and rupturing with a driven line of particles

We examine the dynamics of two-dimensional colloidal systems using numerical simulations of a system with a drive applied to a thin region in the middle of the sample to produce a local shear. For a monodisperse colloidal assembly, we find a well-defined decoupling transition separating a regime of elastic motion from a plastic phase where the driven particles break away or decouple from the bulk particles and produce a shear band. For a bidisperse assembly, the onset of a bulk disordering transition coincides with the broadening of the shear band. We identify several distinct dynamical regimes that are correlated with features in the velocity-force curves. As a function of bidispersity, the decoupling force shows a nonmonotonic behavior associated with features in the noise fluctuations, power spectra, and bulk velocity profiles. When pinning is added in the bulk, we find that the shear band regions can become more localized, causing a decoupling of the driven particles from the bulk particles. For a system with thermal noise and no pinning, the shear band region becomes more extended and the average velocity of the driven particles drops at the thermal disordering transition of the bulk system.

Anomalous field-induced growth of fluctuations in dynamics of a biased intruder moving in a quiescent medium

We present exact results on the dynamics of a biased, by an external force F, intruder (BI) in a two-dimensional lattice gas of unbiased, randomly moving hard-core particles. Going beyond the usual analysis of the force-velocity relation, we study the probability distribution P(R(n)) of the BI displacement R(n) at time n. We show that despite the fact that the BI drives the gas to a nonequilibrium steady state, P(R(n)) converges to a Gaussian distribution as n→∞. We find that the variance σ(x)(2) of P(R(n)) along F exhibits a weakly superdiffusive growth σ(x)(2)~ν(1)nln(n), and a usual diffusive growth, σ(y)(2)~ν(2)n, in the perpendicular direction. We determine ν(1) and ν(2) exactly for arbitrary bias, in the lowest order in the density of vacancies, and show that ν(1)~|F|(2) for small bias, which signifies that superdiffusive behavior emerges beyond the linear-response approximation. We also present analytical arguments predicting a striking field-induced superdiffusive behavior σ(x)(2)~n(3/2) for two-dimensional stripes and three-dimensional capillaries, which is confirmed by Monte Carlo simulations.

Jamming in systems with quenched disorder

We numerically study the effect of adding quenched disorder in the form of randomly placed pinning sites on jamming transitions in a disk packing that jams at a well-defined point J in the clean limit. Quenched disorder decreases the jamming density and introduces a depinning threshold. The onset of a finite threshold coincides with point J at the lowest pinning densities, but for higher pinning densities there is always a finite depinning threshold even well below jamming. We find that proximity to point J strongly affects the transport curves and noise fluctuations, and we observe a change from plastic behavior below jamming, where the system is highly heterogeneous, to elastic depinning above jamming. Many of the general features we find are related to other systems containing quenched disorder, including the peak effect observed in vortex systems.

Probability Densities of a Forced Probe Particle in Glass: Results from Mode Coupling Theory and Simulations of Active Microrheology

We investigate the displacements of a probe particle inside a glass, when a strong external force is applied to the probe (active nonlinear microrheology). Calculations within mode coupling theory are presented for glasses of hard spheres and compared to Langevin and Brownian dynamics simulations. Under not too strong forces where the probe remains trapped, the probe density distribution becomes anisotropic. It is shifted towards the direction of the force, develops an enhanced tail in that direction (signalled by a positive skewness), and exhibits different variances along and perpendicular to the force direction. A simple model of an harmonically trapped probe rationalizes the low force limit, with strong strain softening setting in at forces of the order of a few thermal energies per particle radius.

Dynamical flow arrest in confined gravity driven flows of soft jammed particles

Using numerical simulations, we study the gravity driven flow of jammed soft disks in confined channels. We demonstrate that confinement results in increasing the yield threshold for the Poiseuille flow, in contrast to the planar Couette flow. By solving a nonlocal flow model for such systems, we show that this effect is due to the correlated dynamics responsible for flow, coupled with the stress heterogeneity imposed for the Poiseuille flow. We also observe that with increasing confinement, the cooperative nature of the flow results in increasing intermittent behavior. Our studies indicate that such features are generic properties of a wide variety of jammed materials.

Numerical simulation of the sedimentation of a sphere in a sheared granular fluid: a granular Stokes experiment

We study, computationally, the sedimentation of a sphere of higher mass in a steady, gravity-driven granular flow of otherwise identical spheres, on a rough inclined plane. Taking a hydrodynamic approach at the scale of the particle, we find the drag force to be given by a modified Stokes law and the buoyancy force by the Archimedes principle, with excluded volume effects taken into account. We also find significant differences between the hydrodynamic case and the granular case, which are highlighted.

Fluctuations, jamming, and yielding for a driven probe particle in disordered disk assemblies

Using numerical simulations we examine the velocity fluctuations and velocity-force curve characteristics of a probe particle driven with constant force through a two-dimensional disordered assembly of disks which has a well-defined jamming point J at a density of ϕJ=0.843. As ϕ increases toward ϕJ, the average velocity of the probe particle decreases and the velocity fluctuations show an increasingly intermittent or avalanchelike behavior. When ϕ is within a few percent of the jamming density, the velocity distributions are exponential, while when ϕ is less than 1% away from jamming, the velocity distributions have a power-law character with exponents in agreement with recent experiments. The velocity power spectra exhibit a crossover from a Lorentzian form to a 1/f shape near jamming. We extract a correlation length exponent ν which is in good agreement with recent shear simulations. For ϕ>ϕJ, there is a critical threshold force F(c) that must be applied for the probe particle to move through the sample which increases with increasing ϕ. The velocity-force curves are linear below jamming, while at jamming they have a power-law form. The onset of the probe motion above ϕJ occurs via a local yielding of the particles around the probe particle which we term a local shear banding effect.