Glassy systems under time-dependent driving forces: application to slow granular rheology

Continuous symmetry breaking of low-dimensional systems driven by inhomogeneous oscillatory driving forces

The driving forces of chiral active particles and deformations of cells are often modeled by spatially inhomogeneous but temporally periodic driving forces. Such inhomogeneous oscillatory driving forces have only recently been proposed in the context of active matter, and their effects on the systems are not yet fully understood. In this work, we theoretically study the impact of spatially inhomogeneous oscillatory driving forces on continuous symmetry breaking. We first analyze the linear model for the soft modes in the ordered phase to derive the lower critical dimension of the model, and then analyze the spherical model to investigate more detailed phase behaviors. Interestingly, our analysis reveals that symmetry breaking occurs even in one and two dimensions, where the Hohenberg-Mermin-Wagner theorem prohibits continuous symmetry breaking in equilibrium. Furthermore, fluctuations of conserved quantities, such as density, are anomalously suppressed in the long-wavelength, i.e., show hyperuniformity.

How to study a persistent active glassy system

We explore glassy dynamics of dense assemblies of soft particles that are self-propelled by active forces. These forces have a fixed amplitude and a propulsion direction that varies on a timescaleτ_p, the persistence timescale. Numerical simulations of such active glasses are computationally challenging when the dynamics is governed by large persistence times. We describe in detail a recently proposed scheme that allows one to study directly the dynamics in the large persistence time limit, on timescales around and well above the persistence time. We discuss the idea behind the proposed scheme, which we call 'activity-driven dynamics', as well as its numerical implementation. We establish that our prescription faithfully reproduces all dynamical quantities in the appropriate limitτ_p→ ∞. We deploy the approach to explore in detail the statistics of Eshelby-like plastic events in the steady state dynamics of a dense and intermittent active glass.

Multiple Types of Aging in Active Glasses

Recent experiments and simulations have revealed glassy features in, e.g., cytoplasm, living tissues and dense assemblies of self-propelled colloids. This leads to a fundamental question: how do these nonequilibrium (active) amorphous materials differ from conventional passive glasses, created by lowering temperature or increasing density? To address this we investigate the aging after a quench to an almost arrested state of a model active glass former, a Kob-Andersen glass in two dimensions. Each constituent particle is driven by a constant propulsion force whose direction diffuses over time. Using extensive molecular dynamics simulations we reveal rich aging behavior of this dense active matter system: short persistence times of the active forcing give effective thermal aging; in the opposite limit we find a two-step aging process with active athermal aging at short times and activity-driven aging at late times. We develop a dedicated simulation method that gives access to this longtime scaling regime for highly persistent active forces.

Rheological properties vs. local dynamics in model disordered materials at low temperature

We study the rheological response at low temperature of a sheared model disordered material as a function of the bond rigidity. We find that the flow curves follow a Herschel-Bulkley law, whatever is the bond rigidity, with an exponent close to 0.5. Interestingly, the apparent viscosity can be related to a single relevant time scale t rel, suggesting a strong connection between the local dynamics and the global mechanical behaviour. We propose a model based on the competition between the nucleation and the avalanche-like propagation of spatial strain heterogeneities. This model can explain the Herschel-Bulkley exponent on the basis of the size dependence of the heterogeneities on the shear rate.

Yielding and shear banding in soft glassy materials

Yield stress fluids have proven difficult to characterize, and a reproducible determination of the yield stress is difficult. We study two types of yield stress fluids (YSF) in a single system: simple and thixotropic ones. This allows us to show that simple YSF are simply a special case of thixotropic ones, and to pinpoint the difference between static and dynamic yield stresses, one of the major problems in the field. The thixotropic systems show a strong time dependence of the viscosity due to the existence of an internal percolated structure that confers the yield stress to the material. Using loaded emulsions to control the thixotropy, we show that the transition to flow at the yield stress is discontinuous for thixotropic materials, and continuous for ideal ones. The discontinuity leads to a critical shear rate below which no steady flows can be observed, accounting for the ubiquitous shear banding observed in these materials.

Memory of the unjamming transition during cyclic tiltings of a granular pile

Discrete numerical simulations are performed to study the evolution of the microstructure and the response of a granular packing during successive loading-unloading cycles, consisting of quasistatic rotations in the gravity field between opposite inclination angles. We show that internal variables--e.g., stress and fabric of the pile--exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behavior of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modifications of the pile state occurring close to the unjamming transition. More specifically, we show that for cycles with maximal inclination larger than the repose angle, the weak-contact network carries the memory of the unjamming transition. These results demonstrate the relevance of a two-phase description--strong- and weak-contact networks--for a granular system, as soon as it has approached the unjamming transition.

Reentrant behavior of the spinodal curve in a nonequilibrium ferromagnet

The metastable behavior of a kinetic Ising-type ferromagnetic model system in which a generic type of microscopic disorder induces nonequilibrium steady states is studied by computer simulation and a mean-field approach. We pay attention, in particular, to the spinodal curve or intrinsic coercive field that separates the metastable region from the unstable one. We find that, under strong nonequilibrium conditions, this exhibits reentrant behavior as a function of temperature. That is, metastability does not happen in this regime for both low and high temperatures, but instead emerges for intermediate temperature, as a consequence of the nonlinear interplay between thermal and nonequilibrium fluctuations. We argue that this behavior, which is in contrast with equilibrium phenomenology and could occur in actual impure specimens, might be related to the presence of an effective multiplicative noise in the system.

Scaling of the linear response in simple aging systems without disorder

The time-dependent scaling of the thermoremanent and zero-field-cooled susceptibilities in ferromagnetic spin systems undergoing aging after a quench to a temperature at or below criticality is studied. A recent debate on their interpretation is resolved by showing that for systems with a short-ranged equilibrium spin-spin correlator and above their roughening temperature, the field-cooled susceptibility chi(FC)(t)-chi(0) approximately t(-A), where chi(0) is related to the equilibrium magnetization and the exponent A is related to the time-dependent scaling of the interface width between ordered domains. The same effect also dominates the scaling of the zero-field-cooled susceptibility chi(ZFC)(t,s), but does not enter into the thermoremanent susceptibility rho(TRM)(t,s). However, there may be large finite-time corrections to the scaling of rho(TRM)(t,s) which are explicitly derived and may be needed in order to extract reliable aging exponents. Consistency with the predictions of local scale invariance is confirmed in the Glauber-Ising and spherical models.

Mean-field theory, mode-coupling theory, and the onset temperature in supercooled liquids

We consider the relationship between the temperature at which averaged energy landscape properties change sharply (T(o)) and the breakdown of mean-field treatments of the dynamics of supercooled liquids. First, we show that the solution of the wave vector dependent mode-coupling equations undergoes an ergodic-nonergodic transition consistently close to T(o). Generalizing the landscape concept to include hard-sphere systems, we show that the property of inherent structures that changes near T(o) is governed more fundamentally by packing and free volume than potential energy. Lastly, we study the finite-size random orthogonal model (ROM), and show that the onset of noticeable corrections to mean-field behavior occurs at T(o). These results highlight connections between the energy landscape and mode-coupling approach to supercooled liquids, and identify which features of the relaxation of supercooled liquids are properly captured by mode-coupling theory.

Dynamic heterogeneities in the out-of-equilibrium dynamics of simple spherical spin models

The response of spherical two-spin interaction models, the spherical ferromagnet (s-FM) and the spherical Sherrington-Kirkpatrick (s-SK) model, is calculated for the protocol of the so-called nonresonant hole burning (NHB) experiment for temperatures below the respective critical temperatures. It is shown that it is possible to select dynamic features in the out-of-equilibrium dynamics of both models, one of the hallmarks of dynamic heterogeneities. The behavior of the s-SK model and the s-FM model in three dimensions is very similar, showing dynamic heterogeneities in the long-time behavior, i.e., in the aging regime. The appearance of dynamic heterogeneities in the s-SK model explicitly demonstrates that these are not necessarily related to spatial heterogeneities. For the s-FM model, it is shown that the nature of the dynamic heterogeneities changes as a function of dimensionality. With the increasing dimension, the frequency selectivity of the NHB diminishes and the dynamics in the mean-field limit of the s-FM model becomes homogeneous.

Possible test of the thermodynamic approach to granular media

We study the steady state distribution of the energy of the Sherrington-Kirkpatrick model driven by a tapping mechanism which mimics the mechanically driven dynamics of granular media. The dynamics consists of two phases: a zero temperature relaxation phase which leads the system to a metastable state, then a tapping which excites the system thus reactivating the relaxational dynamics. Numerically, we investigate whether the distribution of the energies of the blocked states obtained agrees with a simple canonical form of the Edwards measure. It is found that this canonical measure is in good agreement with the dynamically measured energy distribution. A possible experimental test of the Edwards measure based on the study here is proposed.

Glassy dynamics and flow properties of soft colloidal pastes

The local dynamics and the nonlinear rheology of soft colloidal pastes are shown to exhibit a remarkable universal behavior in terms of a unique microscopic time scale. This variable is associated with structural relaxation under the combined action of local frictional forces and elastic driving forces. These results establish a link between the local dynamics of pastes and their nonlinear flow behavior and provide a unified description of paste rheology.

Thermodynamics and statistical mechanics of frozen systems in inherent states

We discuss a statistical mechanics approach in the manner of Edwards to the "inherent states" (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity the inherent states are distributed according a generalized Gibbs measure obtained assuming the validity of the principle of maximum entropy, under suitable constraints. In particular, we consider three lattice models (a diluted spin glass, a monodisperse hard-sphere system under gravity, and a hard-sphere binary mixture under gravity) undergoing a schematic "tap dynamics," showing via Monte Carlo calculations that the time averages of macroscopic quantities over the tap dynamics and over such a generalized distribution coincide. We also discuss about the general validity of this approach to nonthermal systems.

Glassy dynamics in granular compaction: sand on random graphs

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multispin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric frustration. We define an athermal dynamics designed to model repeated taps of a given strength. Amplitude cycling and the effect of permanently constraining a subset of the spins at a given amplitude is discussed. Finally we check the validity of Edwards's hypothesis for the athermal tapping dynamics.

Vibration-induced jamming transition in granular media

The quasistatic frequency response of a granular medium is measured by a forced torsion oscillator method, with forcing frequency f(p) in the range 10(-4) Hz to 5 Hz, while weak vibrations at high-frequency f(s), in the range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of vibration Gamma is below the fluidization limit. A loss factor peak is observed in the oscillator response as a function of Gamma or f(p). In a plot of ln f(p) against 1/Gamma, the position of the peak follows an Arrhenius-like behavior over four orders of magnitude in f(p). The data can be described as a stochastic hopping process involving a probability factor exp(-Gamma(j)/Gamma) with Gamma(j) a f(s)-dependent characteristic vibration intensity. An f(s)-independent description is given by exp(-tau(j)/tau), with tau(j) an intrinsic characteristic time, and tau=Gamma(n)/2pif(s), n=0.5-0.6, an empirical control parameter with unit of time. tau is seen as the effective average time during which the perturbed grains can undergo structural rearrangement. The loss factor peak appears as a crossover in the dynamic behavior of the vibrated granular system, which, at the time scale 1/f(p), is solid-like at low Gamma, and the oscillator is jammed into the granular material, and is fluid-like at high Gamma, where the oscillator can slide viscously.

Effective temperature of an aging powder

The aging dynamics and the fluctuation-dissipation relation between the spontaneous diffusion induced by a random noise and the drift motion induced by a small stirring force are numerically investigated in a 3D schematic model of compacting powder: a gravity-driven lattice-gas with purely kinetic constraints. The compaction dynamics is characterized by a super-aging behavior and, in analogy with glasses, exhibits a purely dynamical time-scale-dependent effective temperature. A simple experiment to measure this quantity is suggested.