Glass transition for driven granular fluids

Rheological Regimes in Agitated Granular Media under Shear

Agitated granular media have a rich rheology: they exhibit Newtonian behavior at low shear rate and density, develop a yield stress at high density, and cross over to Bagnoldian shear thickening when sheared rapidly-making it challenging to encompass them in one theoretical framework. We measure the rheology of air-fluidized glass particles, spanning 5 orders of magnitude in shear rate. By comparing fluidization-induced to Brownian agitation, we show that all rheological regimes can be delineated by two dimensionless numbers-the Péclet number, Pe, and the ratio of shear-to-fluidization power, Π-and propose a constitutive relation that captures all flow behaviors, qualitatively and quantitatively, in one unified framework.

Irreversible Boltzmann samplers in dense liquids: Weak-coupling approximation and mode-coupling theory

Exerting a nonequilibrium drive on an otherwise equilibrium Langevin process brings the dynamics out of equilibrium but can also speed up the approach to the Boltzmann steady state. Transverse forces are a minimal framework to achieve dynamical acceleration of the Boltzmann sampling. We consider a simple liquid in three space dimensions subjected to additional transverse pairwise forces, and quantify the extent to which transverse forces accelerate the dynamics. We first explore the dynamics of a tracer in a weak coupling regime describing high temperatures. The resulting acceleration is correlated with a monotonous increase of the magnitude of odd transport coefficients (mobility and diffusivity) with the amplitude of the transverse drive. We then develop a nonequilibrium version of the mode-coupling theory able to capture the effect of transverse forces, and more generally of forces created by additional degrees of freedom. Based on an analysis of transport coefficients, both odd and longitudinal, both for the collective modes and for a tracer particle, we find a systematic acceleration of the dynamics. Quantitatively, the gain, which is guaranteed throughout the ergodic phase, turns out to be a decreasing function of temperature beyond a temperature crossover, in particular as the glass transition is approached. Our theoretical results are in good agreement with available numerical results.

Dynamical yield criterion for granular matter from first principles

We investigate, using a recently developed model of liquid state theory describing the rheology of dense granular flows, how a yield stress appears in granular matter at the yielding transition. Our model allows us to predict an analytical equation of the corresponding dynamical yield surface, which is compared to the usual models of solid fracture. In particular, this yield surface interpolates between the typical failure behaviors of soft and hard materials. This work also underlines the central role played by the effective friction coefficient at the yielding transition.

Enskog kinetic theory of binary granular suspensions: Heat flux and stability analysis of the homogeneous steady state

The Enskog kinetic theory of multicomponent granular suspensions employed previously [Gómez González, Khalil, and Garzó, Phys. Rev. E 101, 012904 (2020)2470-004510.1103/PhysRevE.101.012904] is considered further to determine the four transport coefficients associated with the heat flux. These transport coefficients are obtained by solving the Enskog equation by means of the application of the Chapman-Enskog method around the local version of the homogeneous state. Explicit forms of the heat flux transport coefficients are provided in steady-state conditions by considering the so-called second Sonine approximation to the distribution function of each species. Their quantitative variation on the control parameters of the mixture (masses and diameters, coefficients of restitution, concentration, volume fraction, and the background temperature) is demonstrated and the results show that in general the dependence of the heat flux transport coefficients on inelasticity is clearly different from that found in the absence of the gas phase (dry granular mixtures). As an application of the general results, the stability of the homogeneous steady state is analyzed by solving the linearized Navier-Stokes hydrodynamic equations. The linear stability analysis (which holds for wavelengths long compared with the mean free path) shows that the transversal and longitudinal modes are always stable with respect to long-enough wavelength excitations. This conclusion agrees with previous results derived for monocomponent and (dilute) bidisperse granular suspensions but contrasts with the instabilities found in previous works in dry (no gas phase) granular mixtures.

Diffusion and Velocity Correlations of the Phase Transitions in a System of Macroscopic Rolling Spheres

We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts.

Homogeneous Crystallization in Cyclically Sheared Frictionless Grains

Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear via Newtonian dynamics with linear viscous drag at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction ϕ=0.646±0.001. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media. Understanding how crystal formation is initiated within a homogeneous disordered state gives key insights into the old open problem of glass formation in fluids.

Integration through transients approach to the μ(I) rheology

This work generalizes the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)10.1103/PhysRevLett.121.148002] to the determination of the pressure. We focus on the Bagnold regime and provide theoretical support to the empirical μ(I) rheology laws that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the μ(I) laws apply.

Active glasses

Active glassy matter has recently emerged as a novel class of non-equilibrium soft matter, combining energy-driven, active particle movement with dense and disordered glass-like behavior. Here we review the state-of-the-art in this field from an experimental, numerical, and theoretical perspective. We consider both non-living and living active glassy systems, and discuss how several hallmarks of glassy dynamics (dynamical slowdown, fragility, dynamical heterogeneity, violation of the Stokes-Einstein relation, and aging) are manifested in such materials. We start by reviewing the recent experimental evidence in this area of research, followed by an overview of the main numerical simulation studies and physical theories of active glassy matter. We conclude by outlining several open questions and possible directions for future work.

Slow Dynamics in a Quasi-Two-Dimensional Binary Complex Plasma

Slow dynamics in an amorphous quasi-two-dimensional complex plasma, comprised of microparticles of two different sizes, was studied experimentally. The motion of individual particles was observed using video microscopy, and the self-part of the intermediate scattering function as well as the mean-squared particle displacement was calculated. The long-time structural relaxation reveals the characteristic behavior near the glass transition. Our results suggest that binary complex plasmas can be an excellent model system to study slow dynamics in classical supercooled fluids.

Rheology of Inelastic Hard Spheres at Finite Density and Shear Rate

Considering a granular fluid of inelastic smooth hard spheres, we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress σ to the shear rate γ[over ˙] and predictions of the yield stress complete our discussion of granular rheology derived from first principles.

A random first-order transition theory for an active glass

How does nonequilibrium activity modify the approach to a glass? This is an important question, since many experiments reveal the near-glassy nature of the cell interior, remodeled by activity. However, different simulations of dense assemblies of active particles, parametrized by a self-propulsion force, [Formula: see text], and persistence time, [Formula: see text], appear to make contradictory predictions about the influence of activity on characteristic features of glass, such as fragility. This calls for a broad conceptual framework to understand active glasses; here, we extend the random first-order transition (RFOT) theory to a dense assembly of self-propelled particles. We compute the active contribution to the configurational entropy through an effective model of a single particle in a caging potential. This simple active extension of RFOT provides excellent quantitative fits to existing simulation results. We find that whereas [Formula: see text] always inhibits glassiness, the effect of [Formula: see text] is more subtle and depends on the microscopic details of activity. In doing so, the theory automatically resolves the apparent contradiction between the simulation models. The theory also makes several testable predictions, which we verify by both existing and new simulation data, and should be viewed as a step toward a more rigorous analytical treatment of active glass.

Dense fluidized granular media in microgravity

Handling and transport of granular media are inevitably governed by the settling of particles. Settling into a dense state is one of the defining characteristics of granular media, among dissipation and absence of thermal agitation. Hence, settling complicates the adaptation of microscopic theories from atomic, molecular, or colloidal media to granular media. It is desirable to provide experiments in which selectively one of the granular characteristics is tuned to test suitable adaptation of a theory. Here we show that gas fluidization of granular media in microgravity is a suitable approach to achieve steady states closer to thermally agitated systems free of settling. We use diffusing-wave spectroscopy to compare the spatial homogeneity and the microscopic dynamics of gas-fluidized granular media on the ground and in drop tower flights with increasing packing densities up to full arrest. The gas fluidization on the ground leads to inhomogeneous states as known from fluidized beds, and partial arrest occurs at packing fractions lower than the full arrested packing. The granular medium in microgravity in contrast attains a homogeneous state with complete mobilization even close to full arrest. Fluidized granular media thus can be studied in microgravity with dynamics and packing fractions not achievable on the ground.

Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles

The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We develop a nonequilibrium mode-coupling theory (MCT) for such systems, where activity is included as a colored noise with the particles having a self-propulsion force f₀ and a persistence time τ_p. Using the extended MCT and a generalized fluctuation-dissipation theorem, we calculate the effective temperature T_eff of the active fluid. The nonequilibrium nature of the systems is manifested through a time-dependent T_eff that approaches a constant in the long-time limit, which depends on the activity parameters f₀ and τ_p. We find, phenomenologically, that this long-time limit is captured by the potential energy of a single, trapped active particle (STAP). Through a scaling analysis close to the MCT glass transition point, we show that τ_α, the α-relaxation time, behaves as τ_α ∼ f₀^-2γ, where γ = 1.74 is the MCT exponent for the passive system. τ_α may increase or decrease as a function of τ_p depending on the type of active force correlations, but the behavior is always governed by the same value of the exponent γ. Comparison with the numerical solution of the nonequilibrium MCT and simulation results give excellent agreement with scaling analysis.

Glassy dynamics of Brownian particles with velocity-dependent friction

We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles is described by a Langevin equation with Rayleigh-Helmholtz velocity-dependent friction. In the case of noninteracting particles, the time evolution equations lead to a non-Gaussian velocity distribution. The velocity-dependent friction allows negative values of the friction or energy intakes by slow particles, which we consider active motion, and also causes breaking of the fluctuation dissipation relation. Defining the effective temperature proportional to the second moment of velocity, it is shown that for a constant effective temperature the higher the noise strength, the lower the number of active particles in the system. Using the Mori-Zwanzig formalism and the mode-coupling approximation, the equations of motion for the density autocorrelation function are derived. The equations are solved using the equilibrium structure factors. The integration-through-transients approach is used to derive a relation between the structure factor in the stationary state considering the interacting forces, and the conventional equilibrium static structure factor.

Active fluidization in dense glassy systems

Dense soft glasses show strong collective caging behavior at sufficiently low temperatures. Using molecular dynamics simulations of a model glass former, we show that the incorporation of activity or self-propulsion, f0, can induce cage breaking and fluidization, resulting in the disappearance of the glassy phase beyond a critical f0. The diffusion coefficient crosses over from being strongly to weakly temperature dependent as f0 is increased. In addition, we demonstrate that activity induces a crossover from a fragile to a strong glass and a tendency of active particles to cluster. Our results are of direct relevance to the collective dynamics of dense active colloidal glasses and to recent experiments on tagged particle diffusion in living cells.

Slow and long-ranged dynamical heterogeneities in dissipative fluids

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, Nc, and their radius of gyration, RG. We show that , providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, df, that is observed to increase with packing fraction ϕ. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., ϕ→ϕc. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor S4(q,t) and the dynamical susceptibility χ4(t). S4(q,t) is shown to obey scaling in the full range of packing fractions, 0.6 ≤ϕ≤ 0.805, and to become increasingly long-ranged as ϕ→ϕc. Finite size scaling of χ4(t) provides a consistency check for the previously analyzed divergences of χ4(t) ∝ (ϕ-ϕc)(-γχ) and the correlation length ξ∝ (ϕ-ϕc)(-γξ). We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for ϕ→ϕc suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.

Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach

A theory for jammed granular materials is developed with the aid of a nonequilibrium steady-state distribution function. The approximate nonequilibrium steady-state distribution function is explicitly given in the weak dissipation regime by means of the relaxation time. The theory quantitatively agrees with the results of the molecular dynamics simulation on the critical behavior of the viscosity below the jamming point without introducing any fitting parameter.

Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory

We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. Our simulations reveal that when the persistence time of the self-propulsion is increased, the local structure becomes more pronounced, whereas the long-time dynamics first accelerates and then slows down. We explain these surprising findings by constructing a nonequilibrium microscopic theory that yields nontrivial predictions for the glassy dynamics. These predictions are in qualitative agreement with the simulations and reveal the importance of steady-state correlations of the local velocities to the nonequilibrium dynamics of dense self-propelled particles.

Reentrance in an active glass mixture

Active matter, whose motion is driven, and glasses, whose dynamics are arrested, seem to lie at opposite ends of the spectrum in nonequilibrium systems. In spite of this, both classes of systems exhibit a multitude of stable states that are dynamically isolated from one another. While this defining characteristic is held in common, its origin is different in each case: for active systems, the irreversible driving forces can produce dynamically frozen states, while glassy systems vitrify when they get kinetically trapped on a rugged free energy landscape. In a mixture of active and glassy particles, the interplay between these two tendencies leads to novel phenomenology. We demonstrate this with a spin glass model that we generalize to include an active component. In the absence of a ferromagnetic bias, we find that the spin glass transition temperature depresses with the active fraction, consistent with what has been observed for fully active glassy systems. When a bias does exist, however, a new type of transition becomes possible: the system can be cooled out of the glassy phase. This unusual phenomenon, known as reentrance, has been observed before in a limited number of colloidal and micellar systems, but it has not yet been observed in active glass mixtures. Using low order perturbation theory, we study the origin of this reentrance and, based on the physical picture that results, suggest how our predictions might be measured experimentally.

(Ir)reversibility in dense granular systems driven by oscillating forces

We use computer simulations to study highly dense systems of granular particles that are driven by oscillating forces. We implement different dissipation mechanisms that are used to extract the injected energy. In particular, the action of a simple local Stokes' drag is compared with non-linear and history-dependent frictional forces that act either between particle pairs or between particles and an external container wall. The Stokes' drag leads to particle motion that is periodic with the driving force, even at high densities around close packing where particles undergo frequent collisions. With the introduction of inter-particle frictional forces this "interacting absorbing state" is destroyed and particles start to diffuse around. By reducing the density of the material we go through another transition to a "non-interacting" absorbing state, where particles independently follow the force-induced oscillations without collisions. In the system with particle-wall frictional interactions this transition has signs of a discontinuous phase transition. It is accompanied by a diverging relaxation time, but not by a vanishing order parameter, which rather jumps to zero at the transition.

Strong dynamical heterogeneity and universal scaling in driven granular fluids

Large-scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor S(4)(q,t). Both cases, elastic (ϵ=1) and inelastic (ϵ<1) collisions, are studied. As the fluid approaches structural arrest, i.e., for packing fractions in the range 0.6≤ϕ≤0.805, scaling is shown to hold: S(4)(q,t)/χ(4)(t)=s(qξ(t)). Both the dynamic susceptibility χ(4)(τ(α)) and the dynamic correlation length ξ(τ(α)) evaluated at the α relaxation time τ(α) can be fitted to a power law divergence at a critical packing fraction. The measured ξ(τ(α)) widely exceeds the largest one previously observed for three-dimensional (3d) hard sphere fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, χ(4)(τ(α))≈ξ(d-p)(τ(α)), with an exponent d-p≈1.6. This scaling is remarkably independent of ϵ, even though the strength of the dynamical heterogeneity at constant volume fraction depends strongly on ϵ.

Functional significance of complex fluctuations in brain activity: from resting state to cognitive neuroscience

Behavioral studies have shown that human cognition is characterized by properties such as temporal scale invariance, heavy-tailed non-Gaussian distributions, and long-range correlations at long time scales, suggesting models of how (non observable) components of cognition interact. On the other hand, results from functional neuroimaging studies show that complex scaling and intermittency may be generic spatio-temporal properties of the brain at rest. Somehow surprisingly, though, hardly ever have the neural correlates of cognition been studied at time scales comparable to those at which cognition shows scaling properties. Here, we analyze the meanings of scaling properties and the significance of their task-related modulations for cognitive neuroscience. It is proposed that cognitive processes can be framed in terms of complex generic properties of brain activity at rest and, ultimately, of functional equations, limiting distributions, symmetries, and possibly universality classes characterizing them.

Nonequilibrium glassy dynamics of self-propelled hard disks

We analyze the collective dynamics of self-propelled particles in the large-density regime where passive particles undergo a kinetic arrest to an amorphous glassy state. We capture the competition between self-propulsion and crowding effects using a two-dimensional model of self-propelled hard disks, which we study using Monte Carlo simulations. Although the activity drives the system far from equilibrium, self-propelled particles undergo a kinetic arrest, which we characterize in detail and compare with its equilibrium counterpart. In particular, the critical density for dynamic arrest continuously shifts to larger densities with increasing activity, and the relaxation time is surprisingly well described by an algebraic divergence resulting from the emergence of highly collective dynamics. These results show that dense assemblies of active particles undergo a nonequilibrium glass transition that is profoundly affected by self-propulsion mechanisms.

Hydrodynamic granular segregation induced by boundary heating and shear

Segregation induced by a thermal gradient of an impurity in a driven low-density granular gas is studied. The system is enclosed between two parallel walls from which we input thermal energy to the gas. We study here steady states occurring when the inelastic cooling is exactly balanced by some external energy input (stochastic force or viscous heating), resulting in a uniform heat flux. A segregation criterion based on Navier-Stokes granular hydrodynamics is written in terms of the tracer diffusion transport coefficients, whose dependence on the parameters of the system (masses, sizes, and coefficients of restitution) is explicitly determined from a solution of the inelastic Boltzmann equation. The theoretical predictions are validated by means of Monte Carlo and molecular dynamics simulations, showing that Navier-Stokes hydrodynamics produces accurate segregation criteria even under strong shearing and/or inelasticity.

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.

Melting a granular glass by cooling

Driven granular systems readily form glassy phases at high particle volume fractions and low driving amplitudes. We use computer simulations of a driven granular glass to evidence a reentrance melting transition into a fluid state, which, contrary to intuition, occurs by reducing the amplitude of the driving. This transition is accompanied by anomalous particle dynamics and superdiffusive behavior on intermediate time scales. We highlight the special role played by frictional interactions, which help particles to escape their glassy cages. Such an effect is in striking contrast to what friction is expected to do: reduce particle mobility by making them stick.

Glass transition in driven granular fluids: a mode-coupling approach

We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear equation of motion for the coherent scattering function in two and three space dimensions. A glass transition is observed for all coefficients of restitution, ε, at a critical packing fraction φ(c)(ε) below random close packing. The divergence of timescales at the glass transition implies a dependence on compression rate upon further increase of the density-similar to the cooling-rate dependence of a thermal glass. The critical dynamics for coherent motion as well as tagged particle dynamics is analyzed and shown to be nonuniversal with exponents depending on space dimension and degree of dissipation.

Nonequilibrium mode-coupling theory for uniformly sheared underdamped systems

Nonequilibrium mode-coupling theory (MCT) for uniformly sheared underdamped systems is developed, starting from the microscopic thermostated Sllod equation and the corresponding Liouville equation. Special attention is paid to the translational invariance in the sheared frame, which requires an appropriate definition of the transient time correlators. The derived MCT equation satisfies the alignment of the wave vectors and is manifestly translationally invariant. Isothermal condition is implemented by the introduction of current fluctuation in the dissipative coupling to the thermostat. This current fluctuation grows in the α relaxation regime, which generates a pronounced relaxation of the yield stress compared to the overdamped case. This result fills the gap between the molecular dynamics simulation and the overdamped MCT reported previously. The response to a perturbation of the shear rate demonstrates an inertia effect which is not observed in the overdamped case. Our theory turns out to be a nontrivial extension of the theory by Fuchs and Cates [J. Rheol. 53, 957 (2009)] to underdamped systems. Since our starting point is identical to that of Chong and Kim [Phys. Rev. E 79, 021203 (2009)], the contradictions between Fuchs-Cates and Chong-Kim are resolved.

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

Structure factors in granular experiments with homogeneous fluidization

Velocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2D fluidized granular experiment, with packing fractions φ ∈ [10%, 40%]. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the "bath" temperature T(b), depending on shaking parameters, and the "granular" temperature T(g) < T(b), which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with φ, after proper rescaling with the mean free path.

Segregation of an intruder in a heated granular dense gas

A recent segregation criterion [Phys. Rev. E 78, 020301(R) (2008)] based on the thermal diffusion factor Λ of an intruder in a heated granular gas described by the inelastic Enskog equation is revisited. The sign of Λ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE). The present theory incorporates two extra ingredients not accounted for by the previous theoretical attempt. First, the theory is based upon the second Sonine approximation to the transport coefficients of the mass flux of the intruder. Second, the dependence of the temperature ratio (intruder temperature over that of the host granular gas) on the solid volume fraction is taken into account in the first and second Sonine approximations. In order to check the accuracy of the Sonine approximation considered, the Enskog equation is also numerically solved by means of the direct simulation Monte Carlo method to get the kinetic diffusion coefficient D(0). The comparison between theory and simulation shows that the second Sonine approximation to D(0) yields an improvement over the first Sonine approximation when the intruder is lighter than the gas particles in the range of large inelasticity. With respect to the form of the phase diagrams for the BNE-RBNE transition, the kinetic theory results for the factor Λ indicate that while the form of these diagrams depends sensitively on the order of the Sonine approximation considered when gravity is absent, no significant differences between both Sonine solutions appear in the opposite limit (gravity dominates the thermal gradient). In the former case (no gravity), the first Sonine approximation overestimates both the RBNE region and the influence of dissipation on thermal diffusion segregation.

Slow dynamics and precursors of the glass transition in granular fluids

We use event driven simulations to analyze glassy dynamics as a function of density and energy dissipation in a two-dimensional bidisperse granular fluid under stationary conditions. Clear signatures of a glass transition are identified, such as an increase of relaxation times over several orders of magnitude. As the inelasticity is increased, the glass transition is shifted to higher densities, and the precursors of the transition become less and less pronounced, in agreement with a recent mode-coupling theory. We analyze the long-time tails of the velocity autocorrelation and discuss its consequences for the nonexistence of the diffusion constant in two dimensions.

Effects of hydrodynamic interactions in binary colloidal mixtures driven oppositely by oscillatory external fields

The collective dynamics in a binary mixture of colloidal particles which are driven in opposite directions by an external oscillatory field is examined by computer simulations in two spatial dimensions. Both Brownian dynamics (BD) computer simulations, which ignore solvent-mediated hydrodynamic interactions between the colloidal particles, and multi-particle collision dynamics (MPCD) simulations, which include hydrodynamic interactions, are employed. We first review recent results obtained by BD. Depending on the driving frequency and amplitude, lane formation parallel to the drive and band formation perpendicular to the drive occur. Band formation is stable only in a finite window of oscillation frequencies and driving strengths and is taken over by lane formation if the driving force is increased or the oscillation frequency is decreased. MPCD simulations, on the other hand, reveal that band formation is blurred by hydrodynamic interactions. During the front collisions of oppositely driven particles there is a strong vortical movement of the solvent which tends to mix particles and broaden the interface of the bands. This can either lead to a novel intermittent dynamical behaviour or to band rupture into local clusters. These effects, which are absent for BD, are characterized by the strengths of the enstrophy and its spectrum. We finally discuss possible experimental realizations of the models employed.

Microscopic mean-field theory of the jamming transition

Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions by using equilibrium statistical mechanics and develop a fully microscopic, mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain new predictions for microscopic correlation functions of jammed states that are amenable to experimental verifications and whose accuracy we confirm by using computer simulations.

Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function F(incoh)(q,t) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function C(l)(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

Diffusivity and weak clustering in a quasi-two-dimensional granular gas

We present results from a detailed simulation of a quasi-two-dimensional dissipative granular gas, kept in a noncondensed steady state via vertical shaking over a rough substrate. This gas shows a weak power-law decay in the tails of its pair distribution functions, indicating clustering. This clustering depends monotonically on the dissipation coefficient and disappears when the sphere-sphere collisions are conservative. Clustering is also sensitive to the packing fraction. This gas also displays the standard nonequilibrium characteristics of similar systems, including non-Maxwellian velocity distributions. The diffusion coefficients are calculated over all the conditions of the simulations, and it is found that diluted gases are more diffusive for smaller restitution coefficients.