Approach to jamming in an air-fluidized granular bed

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.

Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation

The Enskog kinetic theory is applied to compute the mean square displacement of impurities or intruders (modeled as smooth inelastic hard spheres) immersed in a granular gas of smooth inelastic hard spheres (grains). Both species (intruders and grains) are surrounded by an interstitial molecular gas (background) that plays the role of a thermal bath. The influence of the latter on the motion of intruders and grains is modeled via a standard viscous drag force supplemented by a stochastic Langevin-like force proportional to the background temperature. We solve the corresponding Enskog-Lorentz kinetic equation by means of the Chapman-Enskog expansion truncated to first order in the gradient of the intruder number density. The integral equation for the diffusion coefficient is solved by considering the first two Sonine approximations. To test these results, we also compute the diffusion coefficient from the numerical solution of the inelastic Enskog equation by means of the direct simulation Monte Carlo method. We find that the first Sonine approximation generally agrees well with the simulation results, although significant discrepancies arise when the intruders become lighter than the grains. Such discrepancies are largely mitigated by the use of the second Sonine approximation, in excellent agreement with computer simulations even for moderately strong inelasticities and/or dissimilar mass and diameter ratios. We invoke a random walk picture of the intruders' motion to shed light on the physics underlying the intricate dependence of the diffusion coefficient on the main system parameters. This approach, recently employed to study the case of an intruder immersed in a granular gas, also proves useful in the present case of a granular suspension. Finally, we discuss the applicability of our model to real systems in the self-diffusion case. We conclude that collisional effects may strongly impact the diffusion coefficient of the grains.

Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag

We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog-Fokker-Planck equation for the one-particle velocity distribution function. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects such as Mpemba and Kovacs-like ones.

Anomalous diffusion in a monolayer of lightweight spheres fluidized in air flow

This paper presents statistical analyses of random motions in a single layer of fluidized lightweight spherical particles. Foam polystyrene spheres were driven by an upward airflow through the sieve mesh, and their two-dimensional motion was acquired using image analysis. In the bulk region, the particle velocity distributions changed from Gaussian to heavy-tailed distribution as the bulk packing fraction ϕ_{b} was increased. The mean square displacement of the particles exhibited transition to subdiffusion at much lower ϕ_{b} than observed in previous studies using similar setup but with heavier particles. A slight superdiffusion and significant growth of the correlation length in the two-body velocity correlation was observed at further large ϕ_{b}. The effect of the wall on the dynamics of the particles was also investigated, and the anisotropy of the granular temperature was found to be a useful index to discriminate between the wall region and the bulk. The turbulence statistics in the wake of a particle indicated a strong wall-normal asymmetry of aerodynamic forcing as the "thermal" agitation in the wall region.

Pseudo-two-dimensional dynamics in a system of macroscopic rolling spheres

We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted so that the particles do not levitate over the grid, resulting in quasi-two-dimensional dynamics. We show that the behavior of diffusion and correlations in this system is particularly rich. Noticeably as well (and related to the complex dynamical behavior), a variety of phases appear, with important peculiarities with respect to analogous setups. We observe gas, liquid, glass, and hexagonal crystal phases. Most notably, we show that the melting of the hexagonal crystal occurs in coexistence with a liquid phase. This strikingly differs from the corresponding transition in a purely two-dimensional systems of air-fluidized disks, for which no phase coexistence has been reported in the literature.

Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the system after a transient regime. In contrast to previous studies (which considered dilute or quasielastic systems), our analysis is based on the results obtained from the inelastic Enskog kinetic equation, which takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on dissipation and applies to moderate densities. As in earlier studies, the analysis shows that the HSS is linearly stable with respect to long enough wavelength excitations.

Vibration controlled foam yielding

In rheological terms, foams are time independent yield stress fluids, displaying properties of both solid and liquid materials. Here we measure the propagation of a 2D dry foam in a radially symmetric Hele-Shaw cell forcing local yielding. The yield rate is manipulated by mechanical vibration with frequencies from 0 to 150 Hz. The flow speed is then extracted from the video stream and analyzed using digital image correlation software. The data are modeled analytically by a Guzman-Arrhenius type of energy landscape where the local yielding of foam correlates with the number of oscillations, i.e. attempts to cross the energy barrier. The model is confirmed in an auxiliary experiment where the vibrated foam stays in its flowing state at the same small driving pressures, where the flow of the unvibrated foam ceases. We conclude that the yield stress behaviour of foams under an external perturbation can be summarized using a simple energy landscape model. The vibration affects the films causing the stress to occasionally and locally exceed the yield threshold. This, thus, prevents the foam from jamming as in a static configuration even when the global driving is below the yield point of the foam.

Diffusion in agitated frictional granular matter near the jamming transition

We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction ϕ and mean-square velocity fluctuations 〈v^{2}〉 the mean-square displacement of the disks 〈d^{2}〉 spans four to five orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behavior at long times. The statistics of 〈d^{n}〉 at all times are multiscaling, since the probability distribution function (PDF) of displacements has very broad wings. Even where a diffusion constant can be identified it is a complex function of ϕ and 〈v^{2}〉. By identifying the relevant length and time scales and their interdependence one can rescale the data for the mean-square displacement and the PDF of displacements into collapsed scaling functions for all ϕ and 〈v^{2}〉. These scaling functions provide a predictive tool, allowing one to infer from one set of measurements (at a given ϕ and 〈v^{2}〉) what are the expected results at any value of ϕ and 〈v^{2}〉 within the scaling range.

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.

Heat flux of driven granular mixtures at low density: Stability analysis of the homogeneous steady state

The Navier-Stokes order hydrodynamic equations for a low-density driven granular mixture obtained previously [Khalil and Garzó, Phys. Rev. E 88, 052201 (2013)PLEEE81539-375510.1103/PhysRevE.88.052201] from the Chapman-Enskog solution to the Boltzmann equation are considered further. The four transport coefficients associated with the heat flux are obtained in terms of the mass ratio, the size ratio, composition, coefficients of restitution, and the driven parameters of the model. Their quantitative variation on the control parameters of the system is demonstrated by considering the leading terms in a Sonine polynomial expansion to solve the exact integral equations. As an application of these results, the stability of the homogeneous steady state is studied. In contrast to the results obtained in undriven granular mixtures, the stability analysis of the linearized Navier-Stokes hydrodynamic equations shows that the transversal and longitudinal modes are (linearly) stable with respect to long enough wavelength excitations. This conclusion agrees with a previous analysis made for single granular gases.

Fundamental structural characteristics of planar granular assemblies: Self-organization and scaling away friction and initial state

The microstructural organization of a granular system is the most important determinant of its macroscopic behavior. Here we identify the fundamental factors that determine the statistics of such microstructures, using numerical experiments to gain a general understanding. The experiments consist of preparing and compacting isotropically two-dimensional granular assemblies of polydisperse frictional disks and analyzing the emergent statistical properties of quadrons-the basic structural elements of granular solids. The focus on quadrons is because the statistics of their volumes have been found to display intriguing universal-like features [T. Matsushima and R. Blumenfeld, Phys. Rev. Lett. 112, 098003 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.098003]. The dependence of the structures and of the packing fraction on the intergranular friction and the initial state is analyzed, and a number of significant results are found. (i) An analytical formula is derived for the mean quadron volume in terms of three macroscopic quantities: the mean coordination number, the packing fraction, and the rattlers fraction. (ii) We derive a unique, initial-state-independent relation between the mean coordination number and the rattler-free packing fraction. The relation is supported numerically for a range of different systems. (iii) We collapse the quadron volume distributions from all systems onto one curve, and we verify that they all have an exponential tail. (iv) The nature of the quadron volume distribution is investigated by decomposition into conditional distributions of volumes given the cell order, and we find that each of these also collapses onto a single curve. (v) We find that the mean quadron volume decreases with increasing intergranular friction coefficients, an effect that is prominent in high-order cells. We argue that this phenomenon is due to an increased probability of stable irregularly shaped cells, and we test this using a herewith developed free cell analytical model. We conclude that, in principle, the microstructural characteristics are governed mainly by the packing procedure, while the effects of intergranular friction and initial states are details that can be scaled away. However, mechanical stability constraints suppress slightly the occurrence of small quadron volumes in cells of order ≥6, and the magnitude of this effect does depend on friction. We quantify in detail this dependence and the deviation it causes from an exact collapse for these cells. (vi) We argue that our results support strongly the view that ensemble granular statistical mechanics does not satisfy the uniform measure assumption of conventional statistical mechanics. Results (i)-(iv) have been reported in the aforementioned reference, and they are reviewed and elaborated on here.

Glassy dynamics of nanoparticles in semiflexible ring polymer nanocomposite melts

By employing molecular dynamics simulations, we explore the dynamics of NPs in semiflexible ring polymer nanocomposite melts. A novel glass transition is observed for NPs in semiflexible ring polymer melts as the bending energy (Kb) of ring polymers increases. For NPs in flexible ring polymer melts (Kb = 0), NPs move in the classic diffusive behavior. However, for NPs in semiflexible ring polymer melts with large bending energy, NPs diffuse very slowly and exhibit the glassy state in which the NPs are all irreversibly caged be the neighbouring semiflexible ring polymers. This glass transition occurs well above the classical glass transition temperature at which microscopic mobility is lost, and the topological interactions of semiflexible ring polymers play an important role in this non-classical glass transition. This investigation can help us understand the nature of the glass transition in polymer systems.

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.

Direct observation of melting in a two-dimensional driven granular system

Melting is considered to be one of the most fundamental problems in physical science. Generally, dimensionality plays an important role in melting. In three-dimension, it’s well known that a crystal melts directly into a liquid via a first-order transition. In two-dimension (2D), however, the melting process has been widely debated whether it is a first-order transition or a two-step transition with an intermediate hexatic phase. Experimentally 2D melting has been intensively studied in equilibrium systems such as molecular and colloidal crystals, but rarely been explored in non-equilibrium system such as granular materials. In this paper, we experimentally studied the 2D melting in a driven granular model system at single particle level using video recording and particle tracking techniques. Measurements of orientational/translational correlation functions show evidences that the melting is a two-step transition. A novel concept of orientational/translational susceptibilities enable us to clearly resolve the intermediate hexatic phase. Our results are in excellent agreement with the two-step melting scenario predicted by KTHNY theory, and demonstrate that the KTHNY melting scenario can be extended to non-equilibrium systems.

Modifying self-assembly and species separation in three-dimensional systems of shape-anisotropic particles

The behaviors of large, dynamic assemblies of macroscopic particles are of direct relevance to geophysical and industrial processes and may also be used as easily studied analogs to micro- or nano-scale systems, or model systems for microbiological, zoological, and even anthropological phenomena. We study vibrated mixtures of elongated particles, demonstrating that the inclusion of differing particle "species" may profoundly alter a system's dynamics and physical structure in various diverse manners. The phase behavior observed suggests that our system, despite its athermal nature, obeys a minimum free energy principle analogous to that observed for thermodynamic systems. We demonstrate that systems of exclusively spherical objects, which form the basis of numerous theoretical frameworks in many scientific disciplines, represent only a narrow region of a wide, multidimensional phase space. Thus, our results raise significant questions as to whether such models can accurately describe the behaviors of systems outside this highly specialized case.

Length scales in glass-forming liquids and related systems: a review

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.

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.

Collective motion of macroscopic spheres floating on capillary ripples: dynamic heterogeneity and dynamic criticality

When a densely packed monolayer of macroscopic spheres floats on chaotic capillary Faraday waves, a coexistence of large scale convective motion and caging dynamics typical for glassy systems is observed. We subtract the convective mean flow using a coarse graining (homogenization) method and reveal subdiffusion for the caging time scales followed by a diffusive regime at later times. We apply the methods developed to study dynamic heterogeneity and show that the typical time and length scales of the fluctuations due to rearrangements of observed particle groups significantly increase when the system approaches its largest experimentally accessible packing concentration. To connect the system to the dynamic criticality literature, we fit power laws to our results. The resultant critical exponents are consistent with those found in densely packed suspensions of colloids.

How the ideal jamming point illuminates the world of granular media

The zero temperature properties of frictionless soft spheres near the jamming point have been extensively studied both numerically and theoretically; these studies provide a reliable base for the interpretation of experiments. However, recent work by Ikeda et al. showed that, in a parameter space of the temperature and packing fraction, experiments to date on colloids have been rather far from the theoretical scaling regime. An important question is then whether theoretical results concerning point-J are applicable to any physical/experimental system, including granular media, which we consider here. On the surface, such a-thermal, frictional systems might appear even further from the idealized case of thermal soft spheres. In this work we address this question via experiments on shaken granular materials near jamming. We have systematically investigated such systems over a number of years using hard metallic grains. The important feature of the present work is the use of much softer grains, cut from photoelastic materials, making it possible to determine forces at the grain scale, the details of the contact networks and the motion of individual grains. Using this new type of particle, we first show that the contact network exhibits remarkable dynamics. We find strong heterogeneities, which are maximum at the packing fraction ϕ*, distinct from and smaller than the packing fraction ϕ(†), where the average number of contacts per particle, z, starts to increase. In the limit of zero mechanical excitation, these two packing fractions converge at point J. We also determine dynamics on time scales ranging from a small fraction of the shaking cycle to thousands of cycles. We can then map the observed system behavior onto results from simulations of ideal thermal soft spheres. Our results indicate that the ideal jamming point indeed illuminates the world of granular media.

Transport coefficients for driven granular mixtures at low density

The transport coefficients of a granular binary mixture driven by a stochastic bath with friction are determined from the inelastic Boltzmann kinetic equation. A normal solution is obtained via the Chapman-Enskog method for states near homogeneous steady states. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. They are given in terms of the solutions of a set of coupled linear integral equations. As in the monocomponent case, since the collisional cooling cannot be compensated for locally by the heat produced by the external driving, the reference distributions (zeroth-order approximations) f(i)((0)) (i=1,2) for each species depend on time through their dependence on the pressure and the temperature. Explicit forms for the diffusion transport coefficients and the shear viscosity coefficient are obtained by assuming the steady-state conditions and by considering the leading terms in a Sonine polynomial expansion. A comparison with previous results obtained for granular Brownian motion and by using a (local) stochastic thermostat is also carried out. The present work extends previous theoretical results derived for monocomponent dense gases [Garzó, Chamorro, and Vega Reyes, Phys. Rev. E 87, 032201 (2013)] to granular mixtures at low density.

Probing a liquid to glass transition in equilibrium

We use computer simulations to investigate the static properties of a simple glass-forming fluid in which the positions of a finite fraction of the particles have been frozen. By probing the equilibrium statistics of the overlap between independent configurations of the liquid, we find strong evidence that this random pinning induces a glass transition. At low temperatures, our numerical findings are consistent with the existence of a random first-order phase transition rounded by finite size effects.

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.

Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: configuration changes and vibration modes

We investigate the dynamic heterogeneities of glassy particle systems in the theoretical schemes of bond breakage and four-point correlation functions. In the bond-breakage scheme, we introduce the structure factor S(b)(q,t) and the susceptibility χ(b)(t) to detect the spatial correlations of configuration changes. Here χ(b)(t) attains a maximum at t=t(b)(max) as a function of time t, where the fraction of the particles with broken bonds φ(b)(t) is about 1/2. In the four-point scheme, treating the structure factor S(4)(q,t) and the susceptibility χ(4)(t), we detect superpositions of the heterogeneity of bond breakage and that of thermal low-frequency vibration modes. While the former grows slowly, the latter emerges quickly to exhibit complex space-time behavior. In two dimensions, the vibration modes extending over the system yield significant contributions to the four-point correlations, which depend on the system size logarithmically. A maximum of χ(4)(t) is attained at t=t(4)(max), where these two contributions become of the same order. As a result, t(4)(max) is considerably shorter than t(b)(max).

Temperature-pressure scaling for air-fluidized grains near jamming

We present experiments on a monolayer of air-fluidized beads in which a jamming transition is approached by increasing pressure, increasing packing fraction, and decreasing kinetic energy. This is accomplished, along with a noninvasive measurement of pressure, by tilting the system and examining behavior versus depth. We construct an equation of state and analyze relaxation time versus effective temperature. By making time and effective temperature dimensionless using factors of pressure, bead size, and bead mass, we obtain a good collapse of the data but to a functional form that differs from that of thermal hard-sphere systems. The relaxation time appears to diverge only as the effective temperature to pressure ratio goes to zero.

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.

Propagating waves in a monolayer of gas-fluidized rods

We report on an observation of propagating compression waves in a quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow of air. The collective wave speed is an order of magnitude faster than the speed of the particles. This gives rise to anomalously large number fluctuations, ΔN~N(0.72±0.04), which are greater than ordinary number fluctuations of N(1/2). We characterize the waves by calculating the spatiotemporal power spectrum of the density. The position of observed peaks, as a function of frequency ω and wave vector k, yields a linear dispersion relationship in the long-time, long-wavelength limit and a wave speed c=ω/k. Repeating this analysis for systems at different densities and air speeds, we observe a linear increase in the wave speed with increasing packing fraction with almost no dependence on the air flow. We also observe that the parallel and perpendicular root-mean-square speeds of the rods are identical when waves are present, but become different at low packing fractions where there are no waves. Based on this apparent exclusivity, we map out the phase behavior for the existence of waves vs speed anisotropy as a function of density and fluidizing air flow.

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.

Application of Edwards' statistical mechanics to high-dimensional jammed sphere packings

The isostatic jamming limit of frictionless spherical particles from Edwards' statistical mechanics [Song et al., Nature (London) 453, 629 (2008)] is generalized to arbitrary dimension d using a liquid-state description. The asymptotic high-dimensional behavior of the self-consistent relation is obtained by saddle-point evaluation and checked numerically. The resulting random close packing density scaling ϕ∼d2(-d) is consistent with that of other approaches, such as replica theory and density-functional theory. The validity of various structural approximations is assessed by comparing with three- to six-dimensional isostatic packings obtained from simulations. These numerical results support a growing accuracy of the theoretical approach with dimension. The approach could thus serve as a starting point to obtain a geometrical understanding of the higher-order correlations present in jammed packings.

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.

Spatiotemporal hierarchy of relaxation events, dynamical heterogeneities, and structural reorganization in a supercooled liquid

We identify the pattern of microscopic dynamical relaxation for a two-dimensional glass-forming liquid. On short time scales, bursts of irreversible particle motion, called cage jumps, aggregate into clusters. On larger time scales, clusters aggregate both spatially and temporally into avalanches. This propagation of mobility takes place along the soft regions of the systems, which have been identified by computing isoconfigurational Debye-Waller maps. Our results characterize the way in which dynamical heterogeneity evolves in moderately supercooled liquids and reveal that it is astonishingly similar to the one found for dense glassy granular media.

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node bifurcation point in the weak-noise limit, while the final value of the deterministic solution changes discontinuously at the point. A systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method. In this formulation, the critical nature turns out to originate from the neutrality of exiting time from a saddle point. The theoretical calculation explains results of numerical simulations.

Glass transition for driven granular fluids

We investigate the dynamics of a driven system of dissipative hard spheres within mode-coupling theory. The dissipation is modeled by normal restitution, and driving is applied to individual particles in the bulk. In such a system, a glass transition is predicted for a finite transition density. With increasing dissipation, the transition shifts to higher densities. Despite the strong driving at high dissipation, the transition persists up to the limit of totally inelastic normal restitution.

Jammed frictionless disks: Connecting local and global response

By calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and nonaffine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale l* up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as 1/Deltaz , where Deltaz is the difference between contact number and its isostatic value, and appears to scale identically to the length scale which had been introduced earlier in the interpretation of the spectrum of vibrational modes. It governs the crossover from isostatic behavior at the small scale to continuum behavior at the large scale; indeed we identify this length scale with the coarse graining length needed to obtain a smooth stress field. We characterize the nonaffine displacements of the particles using the displacement angle distribution, a local measure for the amount of relative sliding, and analyze the connection between local relative displacements and the elastic moduli.

Creep motion of an intruder within a granular glass close to jamming

We experimentally study the dynamics of an intruder dragged at a constant force in a horizontally vibrated monolayer of grains. At moderate packing fractions, the intruder moves rapidly as soon as the force is applied. Above some threshold value it has an intermittent creep motion with strong fluctuations reminiscent of "crackling noise". These fluctuations are critical at the jamming transition varphi_{J} unveiled in a previous study. The transition separates a regime with local free volume rearrangements from a regime where the displacement field is strongly heterogeneous and resembles force chain patterns.

The experimental realization of a two-dimensional colloidal model system

We present the technical details of an experimental method to realize a model system for two-dimensional (2D) phase transitions and the glass transition. The system consists of several hundred thousand colloidal superparamagnetic particles confined by gravity at a flat water-air interface of a pending water droplet where they are subjected to Brownian motion. The dipolar pair potential and, therefore, the system temperature are not only known precisely but also directly and instantaneously controllable via an external magnetic field H. In the case of a one-component system of monodisperse particles the system can crystallize upon application of H whereas in a two component system it undergoes a glass transition. Up to 10,000 particles are observed by video microscopy and image processing provides their trajectories on all relative length and time scales. The position of the interface is actively regulated thereby reducing surface fluctuations to less than 1 microm and the setup inclination is controlled to an accuracy of +/-1 murad. The sample quality being necessary to enable the experimental investigation of the 2D melting scenario, 2D crystallization, and the 2D glass transition, is discussed.

Ultra-small-angle neutron scattering: a tool to study packing of relatively monodisperse polymer spheres and their binary mixtures

We measured ultra-small-angle neutron scattering (USANS) from polymethylmethacrylate spheres tamped down in air. Two slightly polydisperse pure sphere sizes (1.5 and 7.5 microm diameters) and five mixtures of these were used. All were loose packed (packing fractions of 0.3-0.6) with nongravitational forces (e.g., friction) important, preventing close packing. The USANS data are rich in information on powder packing. A modified Percus-Yevick fluid model was used to parametrize the data-adequately but not well. The modifications required the introduction of small voids, less than the sphere size, and a parameter reflecting substantial deviation from the Percus-Yevick prediction of the sphere-sphere correlation function. The mixed samples fitted less well, and two further modifying factors were necessary. These were local inhomogeneities, where the concentration of same-size spheres, both large and small, deviated from the mean packing, and a factor accounting for the presence within these "clusters" of self-avoidance of the large spheres (that is, large spheres coated with more small spheres than Percus-Yevick would predict). The overall deviations from the hard-sphere Percus-Yevick model that we find here suggest that fluid models of loose packed powders are unlikely to be successful but lay the ground work for future theoretical and computational works.

Critical behaviors of sheared frictionless granular materials near the jamming transition

Critical behaviors of sheared dense and frictionless granular materials in the vicinity of the jamming transition are numerically investigated. From the extensive molecular dynamics simulation, we verify the validity of the scaling theory near the jamming transition proposed by Otsuki and Hayakawa [Prog. Theor. Phys. 121, 647 (2009)]]. We also clarify the critical behaviors of the shear viscosity and the pair correlation function based on both a mean field theory and the simulation.

Growing length and time scales in a suspension of athermal particles

We simulate a relaxation process of non-Brownian particles in a sheared viscous medium; the system is subject to the small shear strain and then undergoes relaxation. We estimate the exponents with which the relaxation time and the correlation length diverge as the density approaches the jamming density from below. In particular, the dynamic critical exponent is estimated as 4.6(2). It is also found that shear stress undergoes power-law decay at the jamming density, which is reminiscent of critical slowing down.

Long-time tails and cage effect in driven granular fluids

We study the velocity autocorrelation function of a driven granular fluid in the stationary state in three dimensions. As the critical volume fraction of the glass transition in the corresponding elastic system is approached, we observe pronounced cage effects in the velocity autocorrelation function as well as a strong decrease of the diffusion constant, depending on the inelasticity. At moderate densities the velocity autocorrelation function is shown to decay algebraically in time, like t(-3/2), if momentum is conserved locally, and like t(-1), if momentum is not conserved by the driving. A simple scaling argument supports the observed long-time tails.

Building blocks of dynamical heterogeneities in dense granular media

We investigate experimentally the connection between short time dynamics and long time dynamical heterogeneities within a dense granular media under cyclic shear. We show that dynamical heterogeneities result from a two time scales process. Short time but already collective events consisting in clustered cage jumps concentrate most of the nonaffine displacements. On larger time scales, such clusters appear aggregated both temporally and spatially in avalanches which eventually build the large scales dynamical heterogeneities. Our results indicate that facilitation plays an important role in the relaxation process although it does not appear to be conserved as proposed in many models studied in the literature.

Normal modes in model jammed systems in three dimensions

Vibrational spectra and normal modes of mechanically stable particle packings in three dimensions are analyzed over a range of compressions, from near the jamming transition, where the packings lose their rigidity, to far above it. At high frequency, the normal modes are localized at all compressions. At low frequency, the nature of the modes depends somewhat on compression. At large compressions, far from the transition, the lowest-frequency normal modes have some plane-wave character, though less than one would expect for a crystalline or isotropic solid. At low compressions near the jamming transition, the lowest-frequency modes are neither plane-wave-like nor localized. We characterize these differences, highlighting the unusual dispersion behavior that emerges for marginally jammed solids.

Correlation between particle motion and Voronoi-cell-shape fluctuations during the compaction of granular matter

We track particle motions in a granular material subjected to compaction using a laser scattering-based imaging method where compaction is achieved through thermal cycling. Particle displacements in this jammed fluid correlate strongly with rearrangements of the Voronoi cells defining the local environment about the particles, similar to previous observations of Rahman on cooled liquids. Our observations provide further evidence of commonalities between particle dynamics in granular matter close to jamming and supercooled liquids.

Effective temperatures and activated dynamics for a two-dimensional air-driven granular system on two approaches to jamming

We present experiments on several distinct effective temperatures in a granular system at a sequence of increasing packing densities and at a sequence of decreasing driving rates. This includes single-grain measurements based on the mechanical energies of both the grains and an embedded oscillator, as well as a collective measurement based on the Einstein relation between diffusivity and mobility, which all probe different time scales. Remarkably, all effective temperatures agree. Furthermore, mobility data along the two trajectories collapse when plotted vs effective temperature and exhibit an Arrhenius form with the same energy barrier as the microscopic relaxation time.