Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids

Hyperuniform disordered solids with crystal-like stability

Hyperuniform disordered solids, characterised by unusually suppressed density fluctuations at low wavenumbers (q), are of great interest due to their potentially distinct properties as a unique glass state. From the jamming perspective, there is ongoing debate about the relationship between hyperuniformity and the jamming transition, as well as whether hyperuniformity persists above the jamming point. Here, we successfully generate over-jammed disordered solids exhibiting the strongest class of hyperuniformity, characterised by a power-law density spectrum (qα with α = 4). By decompressing both hyperuniform and conventional over-jammed packings to their respective marginally jammed states, we identify protocol-independent exponents: α ≈ 0.25 for density hyperuniformity and α ≈ 2 for contact-number hyperuniformity, both associated with the jamming transition. Although both marginally jammed and conventional over-jammed packings exhibit marginal stability, we demonstrate that hyperuniform over-jammed packings possess exceptional stability across vibrational, kinetic, thermodynamic, and mechanical properties-similar to crystals. These findings suggest that hyperuniform over-jammed packings offer crucial insights into the ideal disordered solid state and stand out as promising candidates for disordered metamaterials, uniquely combining hyperuniformity with ultrastability.

Displacement correlations in a two-dimensional colloidal liquid and their relationship with shear strain correlations

Correlations of the displacement field in a two-dimensional model colloidal liquid are studied numerically and analytically. By calculating the displacement correlations and the shear strain correlations from the numerical data of particle simulations, the displacement field is shown to have nontrivial correlations, even in liquids that are only slightly glassy with the area fraction as low as 0.5. It is suggested analytically and demonstrated numerically that the displacement correlations are more informative than the shear correlations: the former behaves logarithmically with regard to the spatial distance at shorter scales, while the corresponding information is missing from the shear correlations. The logarithmic behavior of the displacement correlations is interpreted as manifesting a long-lived aspect of the cage effect.

Structural fluctuations in active glasses

The glassy dynamics of dense active matter have recently become a topic of interest due to their importance in biological processes such as wound healing and tissue development. However, while the liquid-state properties of dense active matter have been studied in relation to the glass transition of active matter, the solid-state properties of active glasses have yet to be understood. In this work, we study the structural fluctuations in the active glasses composed of self-propelled particles. We develop a formalism to describe the solid-state properties of active glasses in the harmonic approximation limit and use it to analyze the displacement fields in the active glasses. Our findings reveal that the dynamics of high-frequency normal modes become quasi-static with respect to the active forces, and consequently, excitations of these modes are significantly suppressed. This leads to a violation of the equipartition law, suppression of particle displacements, and the apparent collective motion of active glasses. Overall, our results provide a fundamental understanding of the solid-state properties of active glasses.

Dense random packing of disks with a power-law size distribution in thermodynamic limit

The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases infinitely, while the mean density of the disk centers and the range of the size distribution are kept constant. We investigate the structure factor dependence on momentum transfer across various number of disks and extrapolate these findings to the thermodynamic limit. The fractal power-law decay of the structure factor is recovered in reciprocal space within the fractal range, which corresponds to the range of the size distribution in real space. The fractal exponent coincides with the exponent of the power-law size distribution as was shown previously by the authors of the work of Cherny et al. [J. Chem. Phys. 158(4), 044114 (2023)]. The dependence of the structure factor on density is examined. As is found, the power-law exponent remains unchanged but the fractal range shrinks when the packing fraction decreases. Additionally, the finite-size effects are studied at extremely low momenta of the order of the inverse system size. We show that the structure factor is parabolic in this region and calculate the prefactor analytically. The obtained results reveal fractal-like properties of the packing and can be used to analyze small-angle scattering from such systems.

Two-Dimensional Crystals far from Equilibrium

When driven by nonequilibrium fluctuations, particle systems may display phase transitions and physical behavior with no equilibrium counterpart. We study a two-dimensional particle model initially proposed to describe driven non-Brownian suspensions undergoing nonequilibrium absorbing phase transitions. We show that when the transition occurs at large density, the dynamics produces long-range crystalline order. In the ordered phase, long-range translational order is observed because equipartition of energy is lacking, phonons are suppressed, and density fluctuations are hyperuniform. Our study offers an explicit microscopic model where nonequilibrium violations of the Mermin-Wagner theorem stabilize crystalline order in two dimensions.

Energetic and Structural Characterizations of the PET-Water Interface as a Key Step in Understanding Its Depolymerization

We report molecular simulations of the interaction between poly(ethylene terephthalate) (PET) surfaces and water molecules with a short-term goal to better evaluate the different energy contributions governing the enzymatic degradation of amorphous PET. After checking that the glass transition temperature, density, entanglement mass, and mechanical properties of an amorphous PET are well reproduced by our molecular model, we extend the study to the extraction of a monomer from the bulk surface in different environments, i.e., water, vacuum, dodecane, and ethylene glycol. We complete this energetic characterization by the calculation of the work of adhesion of PET surfaces with water and dodecane molecules and by the determination of the contact angle of water droplets. These calculations are compared with experiments and should help us to better understand the enzymatic degradation of PET from both the thermodynamic and molecular viewpoints.

Transport through Amorphous Photonic Materials with Localization and Bandgap Regimes

We propose a framework that unifies the description of light transmission through three-dimensional amorphous dielectric materials that exhibit both localization and a photonic bandgap. We argue that direct, coherent reflection near and in the bandgap attenuates the generation of diffuse or localized photons. Using the self-consistent theory of localization and considering the density of states of photons, we can quantitatively describe the total transmission of light for all transport regimes: transparency, light diffusion, localization, and bandgap. Comparison with numerical simulations of light transport through hyperuniform networks supports our theoretical approach.

Geometrical properties of mechanically annealed systems near the jamming transition

Geometrical properties of two-dimensional mixtures near the jamming transition point are numerically investigated using harmonic particles under mechanical training. The configurations generated by the quasi-static compression and oscillatory shear deformations exhibit anomalous suppression of the density fluctuations, known as hyperuniformity, below and above the jamming transition. For the jammed system trained by compression above the transition point, the hyperuniformity exponent increases. For the system below the transition point under oscillatory shear, the hyperuniformity exponent also increases until the shear amplitude reaches the threshold value. The threshold value matches with the transition point from the point-reversible phase where the particles experience no collision to the loop-reversible phase where the particles' displacements are non-affine during a shear cycle before coming back to an original position. The results demonstrated in this paper are explained in terms of neither of universal criticality of the jamming transition nor the nonequilibrium phase transitions.

Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

The disordered and hyperuniform structures of densely packed spheres near and at jamming are characterized by vanishing of long-wavelength density fluctuations, or equivalently by long-range power-law decay of the direct correlation function (DCF). We focus on previous simulation results that exhibit the degradation of hyperuniformity in jammed structures while maintaining the long-range nature of the DCF to a certain length scale. Here we demonstrate that the field-theoretic formulation of stochastic density functional theory is relevant to explore the degradation mechanism. The strong-coupling expansion method of stochastic density functional theory is developed to obtain the metastable chemical potential considering the intermittent fluctuations in dense packings. The metastable chemical potential yields the analytical form of the metastable DCF that has a short-range cutoff inside the sphere while retaining the long-range power-law behavior. It is confirmed that the metastable DCF provides the zero-wavevector limit of the structure factor in quantitative agreement with the previous simulation results of degraded hyperuniformity. We can also predict the emergence of soft modes localized at the particle scale by plugging this metastable DCF into the linearized Dean-Kawasaki equation, a stochastic density functional equation.

Quantifying the long-range structure of foams and other cellular patterns with hyperuniformity disorder length spectroscopy

We investigate the local and long-range structure of several space-filling cellular patterns: bubbles in a quasi-two-dimensional foam, and Voronoi constructions made around points that are uncorrelated (Poisson patterns), low discrepancy (Halton patterns), and displaced from a lattice by Gaussian noise (Einstein patterns). We study local structure with distributions of quantities including cell areas and side numbers. The former is the widest for the bubbles making foams the most locally disordered, while the latter show no major differences between the cellular patterns. To study long-range structure, we begin by representing the cellular systems as patterns of points, both unweighted and weighted by cell area. For this, foams are represented by their bubble centroids and the Voronoi constructions are represented by the centroids as well as the points from which they are created. Long-range structure is then quantified in two ways: by the spectral density, and by a real-space analog where the variance of density fluctuations for a set of measuring windows of diameter D is made more intuitive by conversion to the distance h(D) from the window boundary where these fluctuations effectively occur. The unweighted bubble centroids have h(D) that collapses for the different ages of the foam with random Poissonian fluctuations at long distances. The area-weighted bubble centroids and area-weighted Voronoi points all have constant h(D)=h_{e} for large D; the bubble centroids have the smallest value h_{e}=0.084sqrt[〈a〉], meaning they are the most uniform. Area-weighted Voronoi centroids exhibit collapse of h(D) to the same constant h_{e}=0.084sqrt[〈a〉] as for the bubble centroids. A similar analysis is performed on the edges of the cells and the spectra of h(D) for the foam edges show h(D)∼D^{1-ε} where ε=0.30±0.15.

Hidden Order Beyond Hyperuniformity in Critical Absorbing States

Disordered hyperuniformity is a description of hidden correlations in point distributions revealed by an anomalous suppression in fluctuations of local density at various coarse-graining length scales. In the absorbing phase of models exhibiting an active-absorbing state transition, this suppression extends up to a hyperuniform length scale that diverges at the critical point. Here, we demonstrate the existence of additional many-body correlations beyond hyperuniformity. These correlations are hidden in the higher moments of the probability distribution of the local density and extend up to a longer length scale with a faster divergence than the hyperuniform length on approaching the critical point. Our results suggest that a hidden order beyond hyperuniformity may generically be present in complex disordered systems.

Microscopic ergodicity breaking governs the emergence and evolution of elasticity in glass-forming nanoclay suspensions

We report a study combining x-ray photon correlation spectroscopy (XPCS) with in situ rheology to investigate the microscopic dynamics and mechanical properties of aqueous suspensions of the synthetic hectorite clay Laponite, which is composed of charged, nanometer-scale, disk-shaped particles. The suspensions, with particle concentrations ranging from 3.25 to 3.75 wt %, evolve over time from a fluid to a soft glass that displays aging behavior. The XPCS measurements characterize the localization of the particles during the formation and aging of the soft-glass state. The fraction of localized particles, f_{0}, increases rapidly during the early formation stage and grows more slowly during subsequent aging, while the characteristic localization length r_{loc} steadily decreases. Despite the strongly varying rates of aging at different concentrations, both f_{0} and r_{loc} scale with the elastic shear modulus G^{'} in a manner independent of concentration. During the later aging stage, the scaling between r_{loc} and G^{'} agrees quantitatively with a prediction of naive mode coupling theory. Breakdown of agreement with the theory during the early formation stage indicates the prevalence of dynamic heterogeneity, suggesting the soft solid forms through precursors of dynamically localized clusters.

Hyperuniformity and density fluctuations at a rigidity transition in a model of biological tissues

The suppression of density fluctuations at different length scales is the hallmark of hyperuniformity. Here, we explore the presence of this hidden order in a manybody interacting model of biological tissue, known to exhibit a transition, or sharp crossover, from a solid to a fluid like phase. We show that the density fluctuations in the rigid phase are only suppressed up to a finite lengthscale. This length scale monotonically increases and grows rapidly as we approach the fluid phase reminiscent to divergent behavior at a critical point, such that the system is effectively hyperuniform in the fluid phase. Furthermore, complementary behavior of the structure factor across the critical point also indicates that hyperuniformity found in the fluid phase is stealthy.

Can a Large Packing be Assembled from Smaller Ones?

We consider zero temperature packings of soft spheres that undergo a jamming to unjamming transition as a function of packing fraction. We compare differences in the structure, as measured from the contact statistics, of a finite subsystem of a large packing to a whole packing with periodic boundaries of an equivalent size and pressure. We find that the fluctuations of the ensemble of whole packings are smaller than those of the ensemble of subsystems. Convergence of these two quantities appears to occur at very large systems, which are usually not attainable in numerical simulations. Finding differences between packings in two dimensions and three dimensions, we also consider four dimensions and mean-field models, and find that they show similar system size dependence. Mean-field critical exponents appear to be consistent with the 3D and 4D packings, suggesting they are above the upper critical dimension. We also find that the convergence as a function of system size to the thermodynamic limit is characterized by two different length scales. We argue that this is the result of the system being above the upper critical dimension.

Two Diverging Length Scales in the Structure of Jammed Packings

At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, ξ_{Z}, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, ξ_{f}, is associated with contact-number fluctuations in subsystems of different sizes. On scales below ξ_{f}, the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of ξ_{Z} and ξ_{f} are different and appear to be different in two and three dimensions.

Absence of Hyperuniformity in Amorphous Hard-Sphere Packings of Nonvanishing Complexity

We relate the structure factor S(k→0) in a system of jammed hard spheres of number density ρ to its complexity per particle Σ(ρ) by the formula S(k→0)=-1/[ρ^{2}Σ^{″}(ρ)+2ρΣ^{'}(ρ)]. We have verified this formula for the case of jammed disks in a narrow channel, for which it is possible to find Σ(ρ) and S(k) analytically. Hyperuniformity, which is the vanishing of S(k→0), will therefore not occur if the complexity is nonzero. An example is given of a jammed state of hard disks in a narrow channel which is hyperuniform when generated by dynamical rules that produce a nonextensive complexity.

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.

Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres

We investigate the glass and the jamming transitions of hard spheres in finite dimensions d, through a revised cell theory, that combines the free volume and the Random First Order Theory (RFOT). Recent results show that in infinite dimension the ideal glass transition and jamming transitions are distinct, while based on our theory we argue that they indeed coincide for finite d. As a consequence, jamming results into a percolation transition described by RFOT, with a static length diverging with exponent ν = 2/d, which we verify through finite size scaling, and standard critical exponents α = 0, β = 0 and γ = 2 independent on d.

Characterizing pixel and point patterns with a hyperuniformity disorder length

We introduce the concept of a "hyperuniformity disorder length" h that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of particles within a distance h from the boundary of the window. We first compute special expectations and bounds in d dimensions, and then illustrate the range of behavior of h versus window size L by analyzing several different types of simulated two-dimensional pixel patterns-where particle positions are stored as a binary digital image in which pixels have value zero if empty and one if they contain a particle. The first are random binomial patterns, where pixels are randomly flipped from zero to one with probability equal to area fraction. These have long-ranged density fluctuations, and simulations confirm the exact result h=L/2. Next we consider vacancy patterns, where a fraction f of particles on a lattice are randomly removed. These also display long-range density fluctuations, but with h=(L/2)(f/d) for small f, and h=L/2 for f→1. And finally, for a hyperuniform system with no long-range density fluctuations, we consider "Einstein patterns," where each particle is independently displaced from a lattice site by a Gaussian-distributed amount. For these, at large L,h approaches a constant equal to about half the root-mean-square displacement in each dimension. Then we turn to gray-scale pixel patterns that represent simulated arrangements of polydisperse particles, where the volume of a particle is encoded in the value of its central pixel. And we discuss the continuum limit of point patterns, where pixel size vanishes. In general, we thus propose to quantify particle configurations not just by the scaling of the density fluctuation spectrum but rather by the real-space spectrum of h(L) versus L. We call this approach "hyperuniformity disorder length spectroscopy".

Large-scale structure of randomly jammed spheres

We numerically analyze the density field of three-dimensional randomly jammed packings of monodisperse soft frictionless spherical particles, paying special attention to fluctuations occurring at large length scales. We study in detail the two-point static structure factor at low wave vectors in Fourier space. We also analyze the nature of the density field in real space by studying the large-distance behavior of the two-point pair correlation function, of density fluctuations in subsystems of increasing sizes, and of the direct correlation function. We show that such real space analysis can be greatly improved by introducing a coarse-grained density field to disentangle genuine large-scale correlations from purely local effects. Our results confirm that both Fourier and real space signatures of vanishing density fluctuations at large scale are absent, indicating that randomly jammed packings are not hyperuniform. In addition, we establish that the pair correlation function displays a surprisingly complex structure at large distances, which is however not compatible with the long-range negative correlation of hyperuniform systems but fully compatible with an analytic form for the structure factor. This implies that the direct correlation function is short ranged, as we also demonstrate directly. Our results reveal that density fluctuations in jammed packings do not follow the behavior expected for random hyperuniform materials, but display instead a more complex behavior.

Static structural signatures of nearly jammed disordered and ordered hard-sphere packings: Direct correlation function

The nonequilibrium process by which hard-particle systems may be compressed into disordered, jammed states has received much attention because of its wide utility in describing a broad class of amorphous materials. While dynamical signatures are known to precede jamming, the task of identifying static structural signatures indicating the onset of jamming have proven more elusive. The observation that compressing hard-particle packings towards jamming is accompanied by an anomalous suppression of density fluctuations (termed "hyperuniformity") has paved the way for the analysis of jamming as an "inverted critical point" in which the direct correlation function c(r), rather than the total correlation function h(r), diverges. We expand on the notion that c(r) provides both universal and protocol-specific information as packings approach jamming. By considering the degree and position of singularities (discontinuities in the nth derivative) as well as how they are changed by the convolutions found in the Ornstein-Zernike equation, we establish quantitative statements about the structure of c(r) with regards to singularities it inherits from h(r). These relations provide a concrete means of identifying features that must be expressed in c(r) if one hopes to reproduce various details in the pair correlation function accurately and provide stringent tests on the associated numerics. We also analyze the evolution of systems of three-dimensional monodisperse hard spheres of diameter D as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) molecular dynamics and Torquato-Jiao (TJ) sequential linear programming algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling c(r)∝-1/r as r→0 that accompanies the formation of the delta function at c(D) that indicates the formation of contacts in all cases, and show that this scaling behavior is, in this case, a consequence of the growing long rangedness in c(r), e.g., c∝-1/r^{2} as r→∞ for disordered packings. At densities in the vicinity of the freezing density, we find striking qualitative differences in the structure factor S(k) as well as c(r) between TJ- and LS-generated configurations, including the early formation of a delta function at c(D) in the TJ algorithm's packings, indicating the early formation of clusters of particles in near contact. Both algorithms yield structure factors that tend towards zero in the low-wave-number limit as jamming is approached. Correspondingly, we observe the expected power-law decay in c(r) for large r, in agreement with previous theoretical work. Our work advances the notion that static signatures are exhibited by hard-particle packings as they approach jamming and underscores the utility of the direct correlation function as a sensitive means of monitoring for the appearance of an incipient rigid network.

Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids

As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, a displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the analytical calculation is to relate the displacement correlation tensor, which is a kind of four-point space-time correlation, to the Lagrangian two-time correlation of the deformation gradient tensor. Tensorial treatment of the statistical quantities, including the displacement correlation itself, allows capturing the vortical structure of the cooperative motion. The calculated displacement correlation also implies a negative long-time tail in the velocity autocorrelation, which is a manifestation of the cage effect. Both the longitudinal and transverse components of the displacement correlation are found to be expressible in terms of a similarity variable, suggesting that the cages are nested to form a self-similar structure in the space-time.

Role of Short-Range Order and Hyperuniformity in the Formation of Band Gaps in Disordered Photonic Materials

We study photonic band gap formation in two-dimensional high-refractive-index disordered materials where the dielectric structure is derived from packing disks in real and reciprocal space. Numerical calculations of the photonic density of states demonstrate the presence of a band gap for all polarizations in both cases. We find that the band gap width is controlled by the increase in positional correlation inducing short-range order and hyperuniformity concurrently. Our findings suggest that the optimization of short-range order, in particular the tailoring of Bragg scattering at the isotropic Brillouin zone, are of key importance for designing disordered PBG materials.

Critical slowing down and hyperuniformity on approach to jamming

Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming (mechanical rigidity) and (effective or exact) hyperuniformity in frictionless hard-particle packings. However, in doing so, one must necessarily study very large packings in order to access the long-ranged behavior and to ensure that the packings are truly jammed. We modify the rigorous linear programming method of Donev et al. [J. Comput. Phys. 197, 139 (2004)JCTPAH0021-999110.1016/j.jcp.2003.11.022] in order to test for jamming in putatively collectively and strictly jammed packings of hard disks in two dimensions. We show that this rigorous jamming test is superior to standard ways to ascertain jamming, including the so-called "pressure-leak" test. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes of N≈10^{3} bidisperse disks in two dimensions; importantly, these packings have a high reduced pressure that persists over extended amounts of time, meaning that they appear to be jammed by conventional tests, though rigorous jamming tests reveal that they are not. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming of the numerical protocols to generate exactly jammed configurations as a result of a type of "critical slowing down" as the packing's collective rearrangements in configuration space become locally confined by high-dimensional "bottlenecks" from which escape is a rare event. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for disordered packings with rattlers, we find that when jamming is ensured, our packings are very nearly hyperuniform, and deviations from hyperuniformity correlate with an inability to ensure jamming, suggesting that strict jamming and hyperuniformity are indeed linked. This raises the possibility that the ideal MRJ packings have no rattlers. Our work provides the impetus for the development of packing algorithms that produce large disordered strictly jammed packings that are rattler free, which is an outstanding, challenging task.

Finite-temperature mechanical instability in disordered lattices

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as G∼T(1/2), whereas the square lattice shows G∼T(2/3). We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.

Experimental study of the relationship between local particle-size distributions and local ordering in random close packing

We experimentally study the structural properties of a sediment of size distributed colloids. By determining each particle size using a size estimation algorithm, we are able to investigate the relationship between local environment and local ordering. Our results show that ordered environments of particles tend to generate where the local particle-size distribution is within 5%. In addition, we show that particles whose size is close to the average size have 12 coordinate neighbors, which matches the coordination number of the fcc and hcp crystals. On the other hand, bcc structures are observed around larger particles. Our results represent experiments to show a size dependence of the specific ordering in colloidal systems.

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.