The relationship between the microscopic arrangement of molecules in a supercooled liquid and its slow dynamics at low temperature near glass transition is studied by Molecular Dynamics (MD) simulations. A Lennard-Jones liquid with polydispersity in size and mass of constituent particles is chosen as the model system. Our studies reveal that the local structure (that varies with polydispersity) plays a crucial role both in the slowing down of dynamics and in the growth of the dynamic heterogeneities, besides determining the glass forming ability (GFA) of the system. Increasing polydispersity at fixed volume fraction is found to suppress the rate of growth of dynamic correlations, as detected by the growth in the peak of the non-linear density response function. The growth in dynamical correlation is manifested in a stronger than usual breakdown of Stokes-Einstein relation at lower polydispersity at low temperatures and also leads to a decrease in the fragility of the system with polydispersity. We show that the suppression of the rate of growth of the dynamic heterogeneity can be attributed to the loss of structural correlations (as measured by the structure factor and the local bond orientational order) with polydispersity. While a critical polydispersity is required to avoid crystallization, we find that further increase in polydispersity lowers the glass forming ability (GFA).
We have carried out extensive molecular dynamics simulations of a supercooled polydisperse Lennard-Jones liquid with large variations in temperature at a fixed pressure. The particles in the system are considered to be polydisperse both in size and mass. The temperature dependence of the dynamical properties such as the viscosity ($η$) and the self-diffusion coefficients ($D_i$) of different size particles is studied. Both viscosity and diffusion coefficients show super-Arrhenius temperature dependence and fit well to the well-known Vogel-Fulcher-Tammann (VFT) equation. Within the temperature …
Polydispersity is found to have a significant effect on the potential energy landscape; the the average inherent structure energy with temperature decreases with polydispersity. Increasing polydispersity at fixed volume fraction decreases the glass transition temperature and the fragility of glass formation analogous to the antiplasticization seen in some polymeric melts. An interesting temperature dependent crossover of heterogeneity with polydispersity is observed at low temperature due to the faster build-up of dynamic heterogeneity at lower polydispersity.
A metastable state, characterized by a low degree of mass localization is identified using Density Functional Theory. This free energy minimum, located through the proper evaluation of the competing terms in the free energy functional, is independent of the specific form of the DFT used. Computer simulation results on particle motion indicate that this heterogeneous state corresponds to the supercooled state.
We report that the local Debye-Waller factor in a simulated 2D glass-forming mixture exhibits significant spatial heterogeneities and that these short time fluctuations provide an excellent predictor of the spatial distribution of the long time dynamic propensities [Phys.Rev.Lett. 93, 135701 (2004)]. In contrast, the potential energy per particle of the inherent structure does not correlate well with the spatially distributed dynamics.
The contributed paper by Naserifar and Goddard reports that their RexPoN water model under ambient conditions simulates liquid water as a dynamic polydisperse branched polymer, which they speculate explains the existence of the liquid-liquid critical point (LLCP) in the supercooled region. Our work addresses several serious factual errors and needless speculation in their paper about their interpretation of their model and its implication for the LLCP in supercooled water.
We study a highly supercooled two-dimensional fluid mixture via molecular dynamics simulation. We follow bond breakage events among particle pairs, which occur on the scale of the $α$ relaxation time $τ_α$. Large scale heterogeneities analogous to the critical fluctuations in Ising systems are found in the spatial distribution of bonds which are broken in a time interval with a width of order $0.05τ_α$. The structure factor of the broken bond density is well approximated by the Ornstein-Zernike form. The correlation length is of order $100 σ_1$ at the lowest temperature studied, $σ_1$ being th…
Using extensive non-equilibrium molecular dynamics simulations, we investigate a glassforming binary Lennard-Jones mixture under shear. Both supercooled liquids and glasses are considered. Our focus is on the characterization of inhomogeneous flow patterns such as shear bands that appear as a transient response to the external shear. For the supercooled liquids, we analyze the crossover from Newtonian to non-Newtonian behavior with increasing shear rate $\dotγ$. Above a critical shear rate $\dotγ_c$ where a non-Newtonian response sets in, the transient dynamics are associated with the occurren…
Water displays breakdown of the Stokes-Einstein relation at low temperatures. We hypothesize that the breakdown is a result of the structural changes and a sharp rise in dynamic heterogeneities that occurs low T upon crossing the Widom line.
An aqueous suspension of the synthetic clay Laponite undergoes a transition from a liquid-like ergodic state to a glass-like nonergodic arrested state. In an observation that closely resembles the dynamical slowdown observed in supercooled liquids, the phenomenon of kinetic arrest in Laponite suspensions is accompanied by a growth in the $α$-relaxation time with increasing sample aging time, $t_{w}$. The ubiquitous dynamic slowdown and fragile behavior observed in glass forming liquids approaching the glass transition is typically ascribed to the growth in the size of distinct dynamical hetero…
Using molecular dynamics simulations, we study the slow dynamics of supercooled liquids confined in a random matrix of immobile obstacles. We study the dynamical crossover from glass-like to Lorentz-gas-like behavior in terms of the density correlation function, the mean square displacement, the nonlinear dynamic susceptibility, the non-Gaussian parameter, and the fragility. Cooperative and spatially heterogeneous dynamics are suppressed as the obstacle density increases, which lead to the more Arrhenius-like behavior in the temperature dependence of the relaxation time. Our findings are quali…
Using simulations of hard rods in smectic-A states, we find non-gaussian diffusion and heterogeneous dynamics due to the equilibrium periodic smectic density profiles, which give rise to permanent barriers for layer-to-layer diffusion. This relaxation behavior is surprisingly similar to that of non-equilibrium supercooled liquids, although there the particles are trapped in transient (instead of permanent) cages. Interestingly, we also find stringlike clusters of up to 10 inter-layer rods exhibiting dynamic cooperativity in this equilibrium state.
Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The lengthscale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characterisitic timescale is several times larger…
Supercooled water exhibits a breakdown of the Stokes-Einstein relation between the diffusion constant $D$ and the alpha relaxation time $τ_α$. For water simulated with the TIP5P and ST2 potentials, we find that the temperature of the decoupling of diffusion and alpha relaxation correlates with the temperature of the maximum in specific heat that corresponds to crossing the Widom line $T_W(P)$. Specifically, we find that our results for $Dτ_α/T$ collapse onto a single master curve if temperature is replaced by $T-T_W(P)$, where $T_W(P)$ is the temperature where the constant-pressure specific he…
We propose a scenario for the glass transition based on the cooperative nature of nucleation processes and entropic effects. The main point is the relation between the off-equilibrium energy dissipation and nucleation processes in off-equilibrium supercooled liquids which leads to a natural definition of the complexity. From the absence of coarsening growth we can derive an entropy based fluctuation formula which relates the free energy dissipation rate in the glass with the nucleation rate of the largest cooperative regions. As by-product we obtain a new phenomenological relation between the …
We analyze differences in dynamics and in properties of the sampled potential energy landscape between different equilibrium trajectories, for a system of rigid water molecules interacting with a two body potential. On entering in the supercooled region, differences between different realizations enhance and survive even when particles have diffused several time their average distance. We observe a strong correlation between the mean square displacement of the individual trajectories and the average energy of the sampled landscape.
Large scale molecular dynamics simulations are used to investigate the structural and dynamical modifications of supercooled water when confined inside an hydrophilic nanopore. We then investigate the evolution of the auto-organization of the most and the least mobile molecules (dynamical heterogeneity and string-like cooperative motions) when supercooled water is confined. Our calculations use the recent TIP5P intermolecular potential for water. We observe a strong slowing down of the dynamical properties when the liquid is confined, although the liquid structure is found to remain unchanged …
Computer simulations of a model glass-forming system are presented, which are particularly sensitive to the correlation between the dynamics and the topography of the potential energy landscape. This analysis clearly reveals that in the supercooled regime the dynamics is strongly influenced by the presence of deep valleys in the energy landscape, corresponding to long-lived metastable amorphous states. We explicitly relate non-exponential relaxation effects and dynamic heterogeneities to these metastable states and thus to the specific topography of the energy landscape.
We propose a dynamic Kerr effect experiment for the distinction between dynamic heterogeneous and homogeneous relaxation in glassy systems. The possibility of this distinction is due to the inherent nonlinearity of the Kerr effect signal. We model the slow reorientational molecular motion in supercooled liquids in terms of non-inertial rotational diffusion. The Kerr effect response, consisting of two terms, is calculated for heterogeneous and for homogeneous variants of the stochastic model. It turns out that the experiment is able to distinguish between the two scenarios. We furthermore show …
We find that the hierarchical organization of the potential energy landscape in a model supercooled liquid can be related to a change in the spatial distribution of soft normal modes. For groups of nearby minima, between which fast relaxation processes typically occur, the localization of the soft modes is very similar. The spatial distribution of soft regions changes, instead, for minima between which transitions relevant to structural relaxation occur. This may be the reason why the soft modes are able to predict spatial heterogeneities in the dynamics. Nevertheless, the very softest modes a…
We conduct molecular dynamics simulations of a bidisperse Kob-Andersen (KA) glass former, modified to add in additional polydispersity. The original KA system is known to exhibit dynamical heterogeneity. Prior work defined propensity, the mean motion of a particle averaged over simulations reconstructing the initial positions of all particles but with randomized velocities. The existence of propensity shows that structure and dynamics are connected. In this paper, we study systems which mimic problems that would be encountered in measuring propensity in a colloidal glass former, where particle…
We numerically study the interplay between heterogeneous dynamics and properties of negatively curved regions of the potential energy surface in a model glassy system. We find that the unstable modes of saddles and quasi-saddles undergo a localization transition close to the Mode-Coupling critical temperature. We also find evidence of a positive spatial correlation between clusters of particles having large displacements in the unstable modes and dynamical heterogeneities.
New insights into phase separation in colloidal suspensions are provided via a new dynamical theory based on the Polydisperse Lattice-Gas model. The model gives a simplified description of polydisperse colloids, incorporating a hard-core repulsion combined with polydispersity in the strength of the attraction between neighbouring particles. Our mean-field equations describe the local concentration evolution for each of an arbitrary number of species, and for an arbitrary overall composition of the system. We focus on the predictions for the dynamics of colloidal gas-liquid phase separation aft…
We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are carried out for the supercooled states of various prototype models of glass-forming liquids such as binary Kob-Andersen, Wahnstrom, soft-sphere, and network-forming liquids. First, we quantify the length scale of the dynamic heterogeneities utilizing the four-point correlation function. The growth of the dynamic length scale with decreasing temperature is chara…
We analyze the slow, glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory of the glass transition (MCT). Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multi-component calculation, but qualitative disagreement at small $q$ when the system is treated as effectively monodisperse. The origin of the different small-$q$ behaviour is…
Slow relaxation and plastic deformation in disordered materials such as metallic glasses and supercooled liquids occur at dynamical heterogeneities, or neighboring particles that rearrange in a correlated, cooperative manner. Dynamical heterogeneities have historically been described by a four-point, time-dependent density correlation function $χ_4 (r, t)$. In this paper, we posit that $χ_4 (r, t)$ contains essentially the same information about medium-range order as the Van Hove correlation function $G(r, t)$. In other words, medium-range order is the origin of spatially correlated regions of…
Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liquids and glasses. The conundrum: close to the glass transition, the dynamics slow down dramatically and become heterogeneous while the structure appears largely unperturbed. Largely unperturbed, however, is not the same as unperturbed, and many studies have attempted to identify "slow" local structures by exploiting dynamical information. Nonetheless, the question remains open: is the key to the slow dynamics imprinted in purely structural information?…
Size-polydisperse liquids have become standard models for avoiding crystallization, thereby enabling studies of supercooled liquids and glasses formed, e.g., by colloidal systems. Purely \textit{energy} polydisperse liquids have been studied much less, but provide an interesting alternative. We here study numerically the difference in structure and dynamics obtained by introducing these two kinds of polydispersity into systems of particles interacting via the Lennard-Jones and EXP pair potentials. To a very good approximation, the average pair structure and dynamics are unchanged even for stro…
We investigate the translational and rotational relaxation dynamics of a crowded two-dimensional system of monodisperse Penrose kites, in which crystallization, quasi-crystallization, and nematic ordering are suppressed, from low to high area fractions along the metastable ergodic fluid branch. First, we demonstrate a decoupling between both the translational and the rotational diffusion coefficients and the relaxation time: the diffusivities are not inversely proportional to the relaxation time, neither in the low-density normal liquid regime nor in the high-density supercooled regime. Our si…
Most of the liquid-state theories, including glass-transition theories, are constructed on the basis of two-body density correlations. However, we have recently shown that many-body correlations, in particular bond orientational correlations, play a key role in both the glass transition and the crystallization transition. Here we show, with numerical simulations of supercooled polydisperse hard spheres systems, that the lengthscale associated with any two-point spatial correlation function does not increase toward the glass transition. A growing lengthscale is instead revealed by considering m…
Computer simulations give precious insight into the microscopic behavior of supercooled liquids and glasses, but their typical time scales are orders of magnitude shorter than the experimentally relevant ones. We recently closed this gap for a class of models of size polydisperse fluids, which we successfully equilibrate beyond laboratory time scales by means of the swap Monte Carlo algorithm. In this contribution, we study the interplay between compositional and geometric local orders in a model of polydisperse hard spheres equilibrated with this algorithm. Local compositional order has a wea…
We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance epsilon from continuous second-order glass transitions. We find that the dynamical correlation length xi behaves generically as epsilon^{-1/3} and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where xi grows with time as [ln(t)]^2 exactly at criticality. All these results suggest a deep analogy between the glassy behaviour of attractive colloids or randomly pinned supercooled liquids and that of the Random F…
We study the dynamics of water confined between hydrophobic flat surfaces at low temperature. At different pressures, we observe different behaviors that we understand in terms of the hydrogen bonds dynamics. At high pressure, the formation of the open structure of the hydrogen bond network is inhibited and the surfaces can be rapidly dehydrated by decreasing the temperature. At lower pressure the rapid ordering of the hydrogen bonds generates heterogeneities that are responsible for strong non-exponential behavior of the correlation function, but with no strong increase of the correlation tim…
We study a dense colloidal suspension confined between two quasiparallel glass plates as a model system for a supercooled liquid in confined geometries. We directly observe the three-dimensional Brownian motion of the colloidal particles using laser scanning confocal microscopy. The particles form dense layers along the walls, but crystallization is avoided as we use a mixture of two particle sizes. A normally liquid-like sample, when confined, exhibits slower diffusive motion. Particle rearrangements are spatially heterogeneous, and the shapes of the rearranging regions are strongly influence…
An alternative scenario for the glass transition based on the cooperative nature of nucleation processes and the role of entropic effects is presented. The new ingredient is to relate the dissipation during the relaxation process to the release of strain energy driven by the nucleation of progressively larger cooperative spatial regions. Using an equiprobability hypothesis for the transition between different metastable configurations, we obtain a relation between the free energy dissipation rate and the size of the largest cooperative regions. Th is leads to a new phenomenological relation be…
We use molecular dynamics computer simulations to investigate the coupling/decoupling between translational and rotational dynamics in a glass-forming liquid of dumbbells. This is done via a careful analysis of the $α$-relaxation time $τ_{q^{*}}^{\rm C}$ of the incoherent center-of-mass density correlator at the structure factor peak, the $α$-relaxation time $τ_{2}$ of the reorientational correlator, and the translational ($D_{t}$) and rotational ($D_{r}$) diffusion constants. We find that the coupling between the relaxation times $τ_{q^{*}}^{\rm C}$ and $τ_{2}$ increases with decreasing tempe…
We use molecular dynamic simulations to investigate the relation between the presence of packing defects in a glass-former and the spontaneous cooperative motions called dynamic heterogeneity. For that purpose we use a simple diatomic glass-former and add a small number of larger or smaller diatomic probes. The diluted probes modify locally the packing, inducing structural defects in the liquid, while we find that the number of defects is small enough not to disturb the average structure. We find that a small packing modification around a few molecules can deeply influence the dynamics of the …
Molecular Dynamics (MD) computer simulations of a polydisperse soft-sphere model under shear are presented. Starting point for these simulations are deeply supercooled samples far below the critical temperature, $T_c$, of mode coupling theory. These samples are fully equilibrated with the aid of the swap Monte Carlo technique. For states below $T_c$, we identify a life time $τ_{\rm lt}$ that measures the time scale on which the system can be considered as an amorphous solid. The temperature dependence of $τ_{\rm lt}$ can be well described by an Arrhenius law. The existence of transient amorpho…
We present a detailed investigation of the wave vector dependence of collective atomic motion in Au49Cu26.9Si16.3Ag5.5Pd2.3 and Pd42.5Cu27Ni9.5P21 supercooled liquids close to the glass transition temperature. Using x-ray photon correlation spectroscopy in a precedent uncovered spatial range of only few interatomic distances, we show that the microscopic structural relaxation process follows in phase the structure with a marked slowing down at the main average inter-particle distance. This behavior is accompanied by dramatic changes in the shape of the intermediate scattering functions which s…
We present the relaxation dynamics of glass-forming glycerol mixed with 1.1 nm sized polyhedral oligomeric silsesquioxane (POSS) molecules using dielectric spectroscopy (DS) and two different neutron scattering (NS) techniques. Both, the reorientational dynamics as measured by DS and the density fluctuations detected by NS reveal a broadening of the alpha relaxation when POSS molecules are added. Moreover, we find a significant slowing down of the alpha-relaxation time. These effects are in accord with the heterogeneity scenario considered for the dynamics of glasses and supercooled liquids. T…
When a liquid is cooled below its melting temperature, if crystallization is avoided, it forms a glass. This phenomenon, called glass transition, is characterized by a marked increase of viscosity, about 14 orders of magnitude, in a narrow temperature interval. The microscopic mechanism behind the glass transition is still poorly understood. However, recently, great advances have been made in the identification of cooperative rearranging regions, or dynamical heterogeneities, i.e. domains of the liquid whose relaxation is highly correlated. The growth of the size of these domains is now believ…
The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. U.S.A., 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder char…
Thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) particles of a nearly constant swelling ratio and with polydispersity indices (PDIs) varying over a wide range (7.4% - 48.9%) are synthesized to study the effects of polydispersity on the dynamics of suspensions of soft PNIPAM colloidal particles. The PNIPAM particles are characterized using dynamic light scattering (DLS) and scanning electron microscopy (SEM). The zero shear viscosity ($η_{0}$) data of these colloidal suspensions, estimated from rheometric experiments as a function of the effective volume fraction $ϕ_{eff}$ of the suspensi…
We study the appearance of large-scale dynamical heterogeneities in a simplified model of a driven, dissipative granular system. Simulations of steady-state gravity-driven flows of inelastically colliding hard disks show the formation of large-scale linear structures of particles with a high collision frequency. These chains can be shown to carry much of the collisional stress in the system due to a dynamical correlation that develops between the momentum transfer and time between collisions in these "frequently-colliding" particles. The lifetime of these dynamical stress heterogeneities is se…
As approaching the glass transition, particle motion in liquids becomes highly heterogeneous and regions with virtually no mobility coexist with liquid-like domains. This complex dynamics is believed to be responsible for different phenomena including non-exponential relaxation and the breakdown of Stokes-Einstein relation. Understanding the relationships between dynamical heterogeneities and local structure in metallic liquids and glasses is a major scientific challenge. Here we use classical molecular dynamics simulations to study the atomic dynamics and microscopic structure of $\mbox{Cu}_{…
The violation of Stokes--Einstein (SE) relation $D\sim (η/T)^{-1}$ between the shear viscosity $η$ and the translational diffusion constant $D$ at temperature $T$ is of great importance for characterizing anomalous dynamics of supercooled water. Determining which time scales play key roles in the SE violation remains elusive without the measurement of $η$. Here we provide comprehensive simulation results of the dynamic properties involving $η$ and $D$ in TIP4P/2005 supercooled water. This enabled the thorough identification of the appropriate time scales for SE relation $Dη/T$. In particular, …
The dynamics of glass-forming liquids display several outstanding features, such as two-step relaxation and dynamic heterogeneities, which are difficult to predict quantitatively from first principles. In this work, we revisit a simple theoretical model of the $β$-relaxation, i.e., the first step of the relaxation dynamics. The model, first introduced by Cavagna et al., describes the dynamics of the system in the neighborhood of a saddle point of the potential energy surface. We extend the model to account for density-density correlation functions and for the 4-point dynamic susceptibility. We…
Concentrated suspensions of Brownian hard-spheres in water are an epitome for understanding the glassy dynamics of both soft materials and supercooled molecular liquids. From an experimental point of view, such systems are especially suited to perform particle tracking easily, and, therefore, are a benchmark for novel optical techniques, applicable when primary particles cannot be resolved. Differential Variance Analysis (DVA) is one such novel technique that simplifies significantly the characterization of structural relaxation processes of soft glassy materials, since it is directly applicab…
The binary Voronoi mixture is a fluid model whose interactions are local and many-body. Here we perform molecular-dynamics (MD) simulations of an equimolar mixture that is weakly polydisperse and additive. For the first time we study the structural relaxation of this mixture in the supercooled-liquid regime. From the simulations we determine the time- and temperature-dependent scattering functions for a large range of wave vectors, as well as the mean-square displacements of both particle species. We perform a detailed analysis of the dynamics by comparing the MD results with the first-princip…
Theories of the Glass Transition Based on Local Excitations
Nanyang Technological University（南洋理工大学）；Consiglio Nazionale delle Ricerche（意大利国家研究委员会）；Roskilde University（罗斯基勒大学）；University of Amsterdam（阿姆斯特丹大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；EPFL（洛桑联邦理工学院）
We analyze one thousand independent equilibrium trajectories of a system of 155 Lennard Jones particles to separate in a model-free approach the role of temperature and the role of the explored potential energy landscape basin depth in the particle dynamics. We show that the diffusion coefficient $D$ can be estimated as a sum over over contributions of the sampled basins, establishing a connection between thermodynamics and dynamics in the potential energy landscape framework. We provide evidence that the observed non-linearity in the relation between local diffusion and basin depth is respons…
The emergence of glassy dynamics and the glass transition in dense disordered systems is still not fully understood theoretically. Mode-coupling theory (MCT) has shown to be effective in describing some of the non-trivial features of glass formation, but it cannot explain the full glassy phenomenology due to the strong approximations on which it is based. Generalized mode-coupling theory (GMCT) is a hierarchical extension of the theory, which is able to outclass MCT by carefully describing the dynamics of higher order correlations in its generalized framework. Unfortunately, the theory has so …
We investigate the static and dynamic properties of a weakly polydisperse hard sphere system in the deeply supercooled state, i.e. at densities higher than that corresponding to the mode-coupling transition. The structural analysis reveals the emergence of icosahedral locally favoured structures, previously only found in trace quantities. We present a new approach to probe the shape of dynamically heterogeneous regions, which is insensitive to particle packing effects that can hamper such analysis. Our results indicate that the shape of the dynamically heterogeneous regions changes only weakly…
Supercooled liquids and dense colloids exhibit anomalous behaviour known as "spatially heterogeneous dynamics" (SHD), which becomes increasingly pronounced with approach to the glass transition. Recently, SHD has been observed in confined granular packings under slow shear near the onset of jamming, bolstering speculation that the two transitions are related. Here, we report measurements of SHD in a system of air-driven granular beads, as a function of both density and effective temperature. On approach to jamming, the dynamics become progressively slower and more spatially heterogeneous. The …
