Jammed solids with pins: Thresholds, force networks, and elasticity.

The role of fixed degrees of freedom in soft or granular matter systems has broad applicability and theoretical interest. Here we address questions of the geometrical role that a scaffolding of fixed particles plays in tuning the threshold volume fraction and force network in the vicinity of jamming. Our two-dimensional simulated system consists of soft particles and fixed "pins," both of which harmonically repel overlaps. On the one hand, we find that many of the critical scalings associated with jamming in the absence of pins continue to hold in the presence of even dense pin latices. On the other hand, the presence of pins lowers the jamming threshold in a universal way at low pin densities and a geometry-dependent manner at high pin densities, producing packings with lower densities and fewer contacts between particles. The onset of strong lattice dependence coincides with the development of bond-orientational order. Furthermore, the presence of pins dramatically modifies the network of forces, with both unusually weak and unusually strong forces becoming more abundant. The spatial organization of this force network depends on pin geometry and is described in detail. Using persistent homology, we demonstrate that pins modify the topology of the network. Finally, we observe clear signatures of this developing bond-orientational order and broad force distribution in the elastic moduli which characterize the linear response of these packings to strain.

Universal scaling in the aging of the strong glass former SiO2.

We show that the aging dynamics of a strong glass former displays a strikingly simple scaling behavior, connecting the average dynamics with its fluctuations, namely, the dynamical heterogeneities. We perform molecular dynamics simulations of SiO2 with van Beest-Kramer-van Santen interactions, quenching the system from high to low temperature, and study the evolution of the system as a function of the waiting time tw measured from the instant of the quench. We find that both the aging behavior of the dynamic susceptibility χ4 and the aging behavior of the probability distribution P(fs,r) of the local incoherent intermediate scattering function fs,r can be described by simple scaling forms in terms of the global incoherent intermediate scattering function C. The scaling forms are the same that have been found to describe the aging of several fragile glass formers and that, in the case of P(fs,r), have been also predicted theoretically. A thorough study of the length scales involved highlights the importance of intermediate length scales. We also analyze directly the scaling dependence on particle type and on wavevector q and find that both the average and the fluctuations of the slow aging dynamics are controlled by a unique aging clock, which is not only independent of the wavevector q, but is also the same for O and Si atoms.

Slow and long-ranged dynamical heterogeneities in dissipative fluids.

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

Strong dynamical heterogeneity and universal scaling in driven granular fluids.

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

Temperature-dependent defect dynamics in the network glass SiO2.

We investigate the long time dynamics of a strong glass former, SiO(2), below the glass transition temperature by averaging single-particle trajectories over time windows which comprise roughly 100 particle oscillations. The structure on this coarse-grained time scale is very well defined in terms of coordination numbers, allowing us to identify ill-coordinated atoms, which are called defects in the following. The most numerous defects are O-O neighbors, whose lifetimes are comparable to the equilibration time at low temperature. On the other hand, SiO and OSi defects are very rare and short lived. The lifetime of defects is found to be strongly temperature dependent, consistent with activated processes. Single-particle jumps give rise to local structural rearrangements. We show that in SiO(2) these structural rearrangements are coupled to the creation or annihilation of defects, giving rise to very strong correlations of jumping atoms and defects.

Microscopic picture of aging in SiO2.

We investigate the aging dynamics of amorphous SiO(2) via molecular dynamics simulations of a quench from a high temperature T(i) to a lower temperature T(f). We obtain a microscopic picture of aging dynamics by analyzing single particle trajectories, identifying jump events when a particle escapes the cage formed by its neighbors, and determining how these jumps depend on the waiting time t(w), the time elapsed since the temperature quench to T(f). We find that the only t(w)-dependent microscopic quantity is the number of jumping particles per unit time, which decreases with age. Similar to previous studies for fragile glass formers, we show here for the strong glass former SiO(2) that neither the distribution of jump lengths nor the distribution of times spent in the cage are t(w) dependent. We conclude that the microscopic aging dynamics is surprisingly similar for fragile and strong glass formers.

Hydrodynamic correlation functions of a driven granular fluid in steady state.

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

Heterogeneities in the glassy state.

We study heterogeneities in a binary Lennard-Jones system below the glass transition using molecular dynamics simulations. We identify mobile and immobile particles and measure their distribution of vibrational amplitudes. For temperatures near the glass transition the distribution of vibrational amplitudes obeys scaling and compares reasonably well with a mean-field theory for the amorphous solid state. To investigate correlations among the immobile and mobile particles we identify clusters and analyze their size and shape. For a fixed number of immobile particles we observe that the immobile particles cluster more strongly together as the temperature is increased which allows the particles to block each other more effectively and to therefore stay immobile. For the mobile particles, on the other hand, the clustering is most pronounced at low temperatures, indicating that mobility at low temperatures can only be sustained in cooperative motion.