Tuning jammed frictionless disk packings from isostatic to hyperstatic

Rigidity transition of a highly compressible granular medium

A wide range of disordered materials, from biological to geological assemblies, feature discrete elements undergoing large shape changes. How significant geometrical variations at the microscopic scale affect the response of the assembly, in particular rigidity transitions, is an ongoing challenge in soft matter physics. However, the lack of a model granular-like experimental system featuring large and versatile particle deformability impedes advances. Here, we explore the oscillatory shear response of a sponge-like granular assembly composed of highly compressible elastic rings. We highlight a progressive rigidity transition, switching from a yielded phase to a solid one by increasing density or decreasing shear amplitude. The rearranging yielded state consists of crystal clusters separated by melted regions; in contrast, the solid state remains amorphous and absorbs all imposed shear elastically. We rationalize this transition by uncovering an effective, attractive shear force between rings that emerges from a friction-geometry interplay. If friction is sufficiently high, the extent of the contacts between rings, captured analytically by elementary geometry, controls the rigidity transition.

Selecting relevant structural features for glassy dynamics by information imbalance

We numerically investigate the identification of relevant structural features that contribute to the dynamical heterogeneity in a model glass-forming liquid. By employing the recently proposed information imbalance technique, we select these features from a range of physically motivated descriptors. This selection process is performed in a supervised manner (using both dynamical and structural data) and an unsupervised manner (using only structural data). We then apply the selected features to predict future dynamics using a machine learning technique. One of the advantages of the information imbalance technique is that it does not assume any model a priori, i.e., it is a non-parametric method. Finally, we discuss the potential applications of this approach in identifying the dominant mechanisms governing the glassy slow dynamics.

Exceptionally dense and resilient critically jammed polydisperse disk packings

Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are protocol dependent. Here, we demonstrate that this variability can be systematically traced to structural measures of packing, as well as to energy measures inside the jammed regime. A novel generalized simultaneous particle swap algorithm constructs overjammed states of desired energy, which upon decompression lead to predictable critical packing fractions. Thus, for a given set of particle sizes, states with extraordinarily high critical packing fractions can be found efficiently, which sustain substantial shear strain and preserve their special structure over the entire jammed domain. The close relation revealed here between the energy landscape of overjammed soft-particle packings and the behavior near the jamming transition points towards new ways of understanding and constructing disordered materials with exceptional properties.

Connecting polymer collapse and the onset of jamming

Previous studies have shown that the interiors of proteins are densely packed, reaching packing fractions that are as large as those found for static packings of individual amino-acid-shaped particles. How can the interiors of proteins take on such high packing fractions given that amino acids are connected by peptide bonds and many amino acids are hydrophobic with attractive interactions? We investigate this question by comparing the structural and mechanical properties of collapsed attractive disk-shaped bead-spring polymers to those of three reference systems: static packings of repulsive disks, of attractive disks, and of repulsive disk-shaped bead-spring polymers. We show that the attractive systems quenched to temperatures below the glass transition T≪T_{g} and static packings of both repulsive disks and bead-spring polymers possess similar interior packing fractions. Previous studies have shown that static packings of repulsive disks are isostatic at jamming onset, i.e., the number of interparticle contacts N_{c} matches the number of degrees of freedom, which strongly influences their mechanical properties. We find that repulsive polymer packings are hypostatic at jamming onset (i.e., with fewer contacts than degrees of freedom) but are effectively isostatic when including stabilizing quartic modes, which give rise to quartic scaling of the potential energy with displacements along these modes. While attractive disk and polymer packings are often considered hyperstatic with excess contacts over the isostatic number, we identify a definition for interparticle contacts for which they can also be considered as effectively isostatic. As a result, we show that the mechanical properties (e.g., scaling of the potential energy with excess contact number and low-frequency contribution to the density of vibrational modes) of weakly attractive disk and polymer packings are similar to those of isostatic repulsive disk and polymer packings. Our results demonstrate that static packings generated via attractive collapse or compression of repulsive particles possess similar structural and mechanical properties.

Spatial constraints and stochastic seeding subvert microbial arms race

Surface attached communities of microbes grow in a wide variety of environments. Often, the size of these microbial community is constrained by their physical surroundings. However, little is known about how size constraints of a colony impact the outcome of microbial competitions. Here, we use individual-based models to simulate contact killing between two bacterial strains with different killing rates in a wide range of community sizes. We found that community size has a substantial impact on outcomes; in fact, in some competitions the identity of the most fit strain differs in large and small environments. Specifically, when at a numerical disadvantage, the strain with the slow killing rate is more successful in smaller environments than in large environments. The improved performance in small spaces comes from finite size effects; stochastic fluctuations in the initial relative abundance of each strain in small environments lead to dramatically different outcomes. However, when the slow killing strain has a numerical advantage, it performs better in large spaces than in small spaces, where stochastic fluctuations now aid the fast killing strain in small communities. Finally, we experimentally validate these results by confining contact killing strains of Vibrio cholerae in transmission electron microscopy grids. The outcomes of these experiments are consistent with our simulations. When rare, the slow killing strain does better in small environments; when common, the slow killing strain does better in large environments. Together, this work demonstrates that finite size effects can substantially modify antagonistic competitions, suggesting that colony size may, at least in part, subvert the microbial arms race.

Jammed disks of two sizes and weights in a channel: Alternating sequences

Disks of two sizes and weights in alternating sequence are confined to a long and narrow channel. The axis of the channel is horizontal and its plane vertical. The channel is closed off by pistons that freeze jammed microstates out of loose disk configurations subject to moderate pressure, gravity, and random agitations. Disk sizes and channel width are such that under jamming no disk remains loose and all disks touch one wall. We present exact results for the characterization of jammed macrostates including volume and entropy. The rigorous analysis divides the disk sequences of jammed microstates into overlapping tiles from which we construct a small number of species of statistically interacting particles. Jammed macrostates depend on dimensionless control parameters inferred from ratios between measures of expansion work against the pistons, gravitational potential energy, and intensity of random agitations. These control parameters enter the configurational statistics via the activation energies prior to jamming of the particles. The range of disk weights naturally divides into regimes where qualitatively different features come into play. We sketch a path toward generalizations that include random sequences under a modified jamming protocol.

Microscopic Theory for the Rheology of Jammed Soft Suspensions

We develop a constitutive model allowing for the description of the rheology of two-dimensional soft dense suspensions above jamming. Starting from a statistical description of the particle dynamics, we derive, using a set of approximations, a nonlinear tensorial evolution equation linking the deviatoric part of the stress tensor to the strain-rate and vorticity tensors. The coefficients appearing in this equation can be expressed in terms of the packing fraction and of particle-level parameters. This constitutive equation rooted in the microscopic dynamic qualitatively reproduces a number of salient features of the rheology of jammed soft suspensions, including the presence of yield stresses for the shear component of the stress and for the normal stress difference. More complex protocols like the relaxation after a preshear are also considered, showing a smaller stress after relaxation for a stronger preshear.

Contact network changes in ordered and disordered disk packings

We investigate the mechanical response of packings of purely repulsive, frictionless disks to quasistatic deformations. The deformations include simple shear strain at constant packing fraction and at constant pressure, "polydispersity" strain (in which we change the particle size distribution) at constant packing fraction and at constant pressure, and isotropic compression. For each deformation, we show that there are two classes of changes in the interparticle contact networks: jump changes and point changes. Jump changes occur when a contact network becomes mechanically unstable, particles "rearrange", and the potential energy (when the strain is applied at constant packing fraction) or enthalpy (when the strain is applied at constant pressure) and all derivatives are discontinuous. During point changes, a single contact is either added to or removed from the contact network. For repulsive linear spring interactions, second- and higher-order derivatives of the potential energy/enthalpy are discontinuous at a point change, while for Hertzian interactions, third- and higher-order derivatives of the potential energy/enthalpy are discontinuous. We illustrate the importance of point changes by studying the transition from a hexagonal crystal to a disordered crystal induced by applying polydispersity strain. During this transition, the system only undergoes point changes, with no jump changes. We emphasize that one must understand point changes, as well as jump changes, to predict the mechanical properties of jammed packings.

Structured randomness: jamming of soft discs and pins

Simulations are used to find the zero temperature jamming threshold, φj, for soft, bidisperse disks in the presence of small fixed particles, or "pins", arranged in a lattice. The presence of pins leads, as one expects, to a decrease in φj. Structural properties of the system near the jamming threshold are calculated as a function of the pin density. While the correlation length exponent remains ν = 1/2 at low pin densities, the system is mechanically stable with more bonds, yet fewer contacts than the Maxwell criterion implies in the absence of pins. In addition, as pin density increases, novel bond orientational order and long-range spatial order appear, which are correlated with the square symmetry of the pin lattice.

Robustness of mean field theory for hard sphere models

In very recent work the mean field theory of the jamming transition in infinite-dimensional hard sphere models was presented. Surprisingly, this theory predicts quantitatively the numerically determined characteristics of jamming in two and three dimensions. This is a rare and unusual finding. Here we argue that this agreement is nongeneric: only for hard sphere models does it happen that sufficiently close to the jamming density (at any temperature) the effective interactions are binary, in agreement with mean field theory, justifying the truncation of many-body interactions (which is the exact protocol in infinite dimensions). Any softening of the bare hard sphere interactions results in many-body effective interactions that are not mean field at any density, making the d=∞ results not applicable.

Response of jammed packings to thermal fluctuations

We focus on the response of mechanically stable (MS) packings of frictionless, bidisperse disks to thermal fluctuations, with the aim of quantifying how nonlinearities affect system properties at finite temperature. In contrast, numerous prior studies characterized the structural and mechanical properties of MS packings of frictionless spherical particles at zero temperature. Packings of disks with purely repulsive contact interactions possess two main types of nonlinearities, one from the form of the interaction potential (e.g., either linear or Hertzian spring interactions) and one from the breaking (or forming) of interparticle contacts. To identify the temperature regime at which the contact-breaking nonlinearities begin to contribute, we first calculated the minimum temperatures T_{cb} required to break a single contact in the MS packing for both single- and multiple-eigenmode perturbations of the T=0 MS packing. We find that the temperature required to break a single contact for equal velocity-amplitude perturbations involving all eigenmodes approaches the minimum value obtained for a perturbation in the direction connecting disk pairs with the smallest overlap. We then studied deviations in the constant volume specific heat C[over ¯]_{V} and deviations of the average disk positions Δr from their T=0 values in the temperature regime T_{C[over ¯]_{V}}<T<T_{r}, where T_{r} is the temperature beyond which the system samples the basin of a new MS packing. We find that the deviation in the specific heat per particle ΔC[over ¯]_{V}^{0}/C[over ¯]_{V}^{0} relative to the zero-temperature value C[over ¯]_{V}^{0} can grow rapidly above T_{cb}; however, the deviation ΔC[over ¯]_{V}^{0}/C[over ¯]_{V}^{0} decreases as N^{-1} with increasing system size. To characterize the relative strength of contact-breaking versus form nonlinearities, we measured the ratio of the average position deviations Δr^{ss}/Δr^{ds} for single- and double-sided linear and nonlinear spring interactions. We find that Δr^{ss}/Δr^{ds}>100 for linear spring interactions is independent of system size. This result emphasizes that contact-breaking nonlinearities are dominant over form nonlinearities in the low-temperature range T_{cb}<T<T_{r} for model jammed systems.

Elastic moduli and vibrational modes in jammed particulate packings

When we elastically impose a homogeneous, affine deformation on amorphous solids, they also undergo an inhomogeneous, nonaffine deformation, which can have a crucial impact on the overall elastic response. To correctly understand the elastic modulus M, it is therefore necessary to take into account not only the affine modulus M_{A}, but also the nonaffine modulus M_{N} that arises from the nonaffine deformation. In the present work, we study the bulk (M=K) and shear (M=G) moduli in static jammed particulate packings over a range of packing fractions φ. The affine M_{A} is determined essentially by the static structural arrangement of particles, whereas the nonaffine M_{N} is related to the vibrational eigenmodes. We elucidate the contribution of each vibrational mode to the nonaffine M_{N} through a modal decomposition of the displacement and force fields. In the vicinity of the (un)jamming transition φ_{c}, the vibrational density of states g(ω) shows a plateau in the intermediate-frequency regime above a characteristic frequency ω^{*}. We illustrate that this unusual feature apparent in g(ω) is reflected in the behavior of M_{N}: As φ→φ_{c}, where ω^{*}→0, those modes for ω<ω^{*} contribute less and less, while contributions from those for ω>ω^{*} approach a constant value which results in M_{N} to approach a critical value M_{Nc}, as M_{N}-M_{Nc}∼ω^{*}. At φ_{c} itself, the bulk modulus attains a finite value K_{c}=K_{Ac}-K_{Nc}>0, such that K_{Nc} has a value that remains below K_{Ac}. In contrast, for the critical shear modulus G_{c}, G_{Nc} and G_{Ac} approach the same value so that the total value becomes exactly zero, G_{c}=G_{Ac}-G_{Nc}=0. We explore what features of the configurational and vibrational properties cause such a distinction between K and G, allowing us to validate analytical expressions for their critical values.

Random close packing in protein cores

Shortly after the determination of the first protein x-ray crystal structures, researchers analyzed their cores and reported packing fractions ϕ ≈ 0.75, a value that is similar to close packing of equal-sized spheres. A limitation of these analyses was the use of extended atom models, rather than the more physically accurate explicit hydrogen model. The validity of the explicit hydrogen model was proved in our previous studies by its ability to predict the side chain dihedral angle distributions observed in proteins. In contrast, the extended atom model is not able to recapitulate the side chain dihedral angle distributions, and gives rise to large atomic clashes at side chain dihedral angle combinations that are highly probable in protein crystal structures. Here, we employ the explicit hydrogen model to calculate the packing fraction of the cores of over 200 high-resolution protein structures. We find that these protein cores have ϕ ≈ 0.56, which is similar to results obtained from simulations of random packings of individual amino acids. This result provides a deeper understanding of the physical basis of protein structure that will enable predictions of the effects of amino acid mutations to protein cores and interfaces of known structure.

Protocol dependence of the jamming transition

We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol. However, the probability to obtain a particular jammed packing depends on the packing-generation protocol. We predict the average shear strain required to jam initially unjammed isotropically compressed packings from the density of jammed packings, shape of their basins of attraction, and path traversed in configuration space. We compare our predictions to simulations of shear strain-induced jamming and find quantitative agreement. We also show that the packing fraction range, over which shear strain-induced jamming occurs, tends to zero in the large system limit for frictionless packings with overdamped dynamics.

Search for hyperuniformity in mechanically stable packings of frictionless disks above jamming

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction ϕ(J). For configurations with a fixed isotropic global stress tensor, we investigate the fluctuations of the local packing fraction ϕ(r) to test whether such configurations display the hyperuniformity that has been claimed to exist exactly at ϕ(J). For our configurations, generated by a rapid quench protocol, we find that hyperuniformity persists only out to a finite length scale and that this length scale appears to remain finite as the system stress decreases towards zero, i.e., towards the jamming transition. Our result suggests that the presence of hyperuniformity at jamming may be sensitive to the specific protocol used to construct the jammed configurations.

Self-assembly in a near-frictionless granular material: conformational structures and transitions in uniaxial cyclic compression of hydrogel spheres

We use a Markov transition matrix-based analysis to explore the structures and structural transitions in a three-dimensional assembly of hydrogel spheres under cyclic uniaxial compression. We apply these methods on experimental data obtained from a packing of nearly frictionless hydrogel balls. This allows an exploration of the emergence and evolution of mesoscale internal structures - a key micromechanical property that governs self-assembly and self-organization in dense granular media. To probe the mesoscopic force network structure, we consider two structural state spaces: (i) a particle and its contacting neighbours, and (ii) a particle's local minimal cycle topology summarized by a cycle vector. In both spaces, our analysis of the transition dynamics reveals which structures and which sets of structures are most prevalent and most likely to transform into each other during the compression/decompression of the material. In compressed states, structures rich in 3-cycle or triangle topologies form in abundance. In contrast, in uncompressed states, transitions comprising poorly connected structures are dominant. An almost-invariant transition set within the cycle vector space is discovered that identifies an intermediate set of structures crucial to the material's transition from weakly jammed to strongly jammed, and vice versa. Preferred transition pathways are also highlighted and discussed with respect to thermo-micro-mechanical constitutive formulations.

Inherent structures, fragility, and jamming: insights from quasi-one-dimensional hard disks

We study a quasi-one-dimensional system of hard disks confined between hard lines to explore the relationship between the inherent structure landscape, the thermodynamics, and the dynamics of the fluid. The transfer matrix method is used to obtain an exact description of the landscape, equation of state, and provide a mapping of configurations of the equilibrium fluid to their local jammed structures. This allows us to follow how the system samples the landscape as a function of occupied volume fraction ϕ. Configurations of the ideal gas map to the maximum in the distribution of inherent structures, with a jamming volume fraction ϕ(J)(*), and sample more dense basins with increasing ϕ. This suggests jammed states with a density below ϕ(J)(*) are inaccessible from the equilibrium fluid. The configurational entropy of the fluid decreases rapidly at intermediate ϕ before plateauing at a low value and going to zero as the most dense packing is approached. This leads to the appearance of a maximum in both the isobaric heat capacity and the inherent structure pressure. We also show that the system exhibits a crossover from fragile to strong fluid behavior, located at the heat capacity maximum. Structural relaxation in the fragile fluid is shown to be controlled by the presence of high order saddle points caused by neighboring defects that are unstable with respect to jamming and spontaneously rearrange to form a stable local environment. In the strong fluid, the defect concentration is low so that defects do not interact and relaxation occurs through the hopping of isolated defects between stable local packing environments.

Renaissance of Bernal's random close packing and hypercritical line in the theory of liquids

We review the scientific history of random close packing (RCP) of equal spheres, advocated by J D Bernal as a more plausible alternative to the non-ideal gas or imperfect crystal as a structural model of simple liquids. After decades of neglect, computer experiments are revealing a central role for RCP in the theory of liquids. These demonstrate that the RCP amorphous state of hard spheres can be well defined, is reproducible, and has the thermodynamic status of a metastable ground state. Further evidence from simulations of square-well model liquids indicates an extended role of RCP as an amorphous ground state that terminates a supercooled liquid coexistence line, suggesting likewise for real liquids. A phase diagram involving percolation boundaries has been proposed in which there is no merging of liquid and gas phases, and no critical singularity as assumed by van der Waals. Rather, the liquid phase continuously spans all temperatures, but above a critical dividing line on the Gibbs density surface, it is bounded by a percolation transition and separated from the gas phase by a colloidal supercritical mesophase. The colloidal-like inversion in the mesophase as it changes from gas-in-liquid to liquid-in-gas can be identified with the hypercritical line of Bernal. We therefore argue that the statistical theory of simple liquids should start from the RCP reference state rather than the ideal gas. Future experimental priorities are to (i) find evidence for an amorphous ground state in real supercooled liquids, (ii) explore the microscopic structures of the supercritical mesophase, and (iii) determine how these change from gas to liquid, especially across Bernal's hypercritical line. The theoretical priority is a statistical geometrical theory of RCP. Only then might we explain the coincident values of the RCP packing fraction with Buffon's constant, and the RCP residual entropy with Boltzmann's ideal gas constant.

Connection between the packing efficiency of binary hard spheres and the glass-forming ability of bulk metallic glasses

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio α, and number fraction x(S) of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate R(c), below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with α≳0.8 that do not demix, R(c) decreases strongly with Δϕ(J), as R(c)∼exp(-1/Δϕ(J)(2)), where Δϕ(J) is the difference between the average packing fraction of the amorphous packings and random crystal structures at R(c). Systems with α≲0.8 partially demix, which promotes crystallization, but we still find a strong correlation between R(c) and Δϕ(J). We show that known metal-metal BMGs occur in the regions of the α and x(S) parameter space with the lowest values of R(c) for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing α to increase packing efficiency, while maximizing α to prevent demixing.

Aspects of jamming in two-dimensional athermal frictionless systems

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

Disordered strictly jammed binary sphere packings attain an anomalously large range of densities

Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634≤φ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain α and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the α-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the α-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and explicit construction of binary packings with such high packing fractions could have important practical implications for granular composites where density is critical both to material properties and fabrication cost, including for solid propellants, concrete, and ceramics. The densities and structures of jammed binary packings at various α and x are also relevant to the formation of a glass phase in multicomponent metallic systems.

Athermal jamming versus thermalized glassiness in sheared frictionless particles

Numerical simulations of soft-core frictionless disks in two dimensions are carried out to study the behavior of a simple liquid as a function of temperature T, packing fraction φ, and uniform applied shear strain rate γ[over ·]. Inferring the hard-core limit from our soft-core results, we find that it depends on the two parameters φ and T/γ[over ·]. Here T/γ[over ·]→0 defines the athermal limit in which a shear-driven jamming transition occurs at a well defined φ(J) and T/γ[over ·]→∞ defines the thermalized limit where an equilibrium glass transition may take place at φ(G). This conclusion argues that athermal jamming and equilibrium glassy behavior are not controlled by the same critical point. Preliminary results suggest φ(G)<φ(J).

Inherent structure landscape connection between liquids, granular materials, and the jamming phase diagram

We provide a comprehensive picture of the jamming phase diagram by connecting the athermal, granular ensemble of jammed states and the equilibrium fluid through the inherent structure paradigm for a system of hard disks confined to a narrow channel. The J line is shown to be divided into packings that are either accessible or inaccessible from the equilibrium fluid. The J point itself is found to occur at the transition between these two sets of packings and is located at the maximum of the inherent structure distribution. We also present a general thermodynamic argument that suggests the density of the states at the maximum of the configurational entropy represents a lower bound on the J-point density in hard sphere systems. Finally, we show that the granular system, modeled using the Edwards ensemble, and the fluid sample the same set of thermodynamically accessible states over the full range of thermodynamic state points, but only occupy the same set of inherent structures, under the same thermodynamic conditions, at two points, corresponding to zero and infinite pressures, where they sample the J-point states and the most dense packing, respectively.

Jamming transition and inherent structures of hard spheres and disks

Recent studies show that volume fractions φ(J) at the jamming transition of frictionless hard spheres and disks are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate the dependence of φ(J) on the initial configurations of the parent fluid equilibrated at a volume fraction φ(eq), before compressing to generate a jammed packing. We find that φ(J) remains constant when φ(eq) is small but sharply increases as φ(eq) exceeds the dynamic transition point which the mode-coupling theory predicts. We carefully analyze configurational properties of both jammed packings and parent fluids and find that, while all jammed packings remain isostatic, the increase of φ(J) is accompanied with subtle but distinct changes of local orders, a static length scale, and an exponent of the finite-size scaling. These results are consistent with the scenario of the random first-order transition theory of the glass transition.

Structural relaxation in dense liquids composed of anisotropic particles

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in two dimensions that interact via purely repulsive contact forces. We measure the structural relaxation times obtained from the long-time α decay of the self part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction φ, temperature T, and aspect ratio α. We are able to collapse the packing-fraction and temperature-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of α, onto a universal scaling function F(±)(|φ-φ(0)|,T,α), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in three dimensions. F(±) for both the translational and rotational DOF are characterized by the α-dependent scaling exponents μ and δ and packing fraction φ(0)(α) that signals the crossover in the scaling form F(±) from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility of structural relaxation at φ(0), m(φ(0)), decreases monotonically with increasing aspect ratio for both ellipses and dimers. For α>α(p), where α(p) is the location of the peak in the packing fraction φ(J) at jamming onset, the rotational DOF are strongly coupled to the translational DOF, and the dynamic scaling exponents and φ(0) are similar for the rotational and translational DOF. For 1<α<α(p), the translational DOF become frozen at higher temperatures than the rotational DOF, and φ(0) for the rotational degrees of freedom increases above φ(J). Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic. Thus, zero-temperature contact counting arguments do not apply to structural relaxation of dense liquids of anisotropic particles near the glass transition.

Microscopic theory of the jamming transition of harmonic spheres

We develop a microscopic theory to analyze the phase behavior and compute correlation functions of dense assemblies of soft repulsive particles both at finite temperature, as in colloidal materials, and at vanishing temperature, a situation relevant for granular materials and emulsions. We use a mean-field statistical mechanical approach which combines elements of liquid state theory to replica calculations to obtain quantitative predictions for the location of phase boundaries, macroscopic thermodynamic properties, and microstructure of the system. We focus, in particular, on the derivation of scaling properties emerging in the vicinity of the jamming transition occurring at large density and zero temperature. The new predictions we obtain for pair correlation functions near contact are tested using computer simulations. Our work also clarifies the conceptual nature of the jamming transition and its relation to the phenomenon of the glass transition observed in atomic liquids.