Session Z43: Invited Session: Applications of Jamming

Shocks in fragile matter

Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they unjam, these fragile and disordered solids exhibit vanishing elastic moduli and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are continuously compressed, and demonstrate that the resulting excitations are strongly nonlinear shocks, rather than linear waves. We capture the full dependence of the shock speed on pressure and compression speed by a surprisingly simple analytical model. We also treat shear shocks within a simplified viscoelastic model of nearly-isostatic random networks comprised of harmonic springs. In this case, anharmonicity does not originate locally from nonlinear interactions between particles, as in granular media; instead, it emerges from the global architecture of the network. As a result, the diverging width of the shear shocks bears a nonlinear signature of the diverging isostatic length associated with the loss of rigidity in these floppy networks.   

Controlling the jamming transition of sheared hard spheres

Many applications require understanding how disordered materials flow under an external load such as a shear stress. Since external loads drive systems out of equilibrium, their behavior cannot be described solely in terms of equilibrium parameters like temperature and pressure. However, simulations and experiments show that sheared spherical particles possess an \textit{effective} temperature that relates low-frequency fluctuations of various observable quantities to their associated response functions. Here, we show that the mobility of a mixture of sheared hard spheres is largely controlled by the dimensionless ratio of effective temperature to pressure, $T_{\rm eff}/p\sigma^3$, where $\sigma$ is the sphere diameter. We define the effective temperature as the consistent value that relates the amplitudes of low-frequency shear stress and density fluctuations to their associated response functions. We find that the relaxation time $\tau$ characterizing the mobility depends on $T_{\rm eff}/p\sigma^3$ according to two distinct mechanisms in two distinct regimes. In the \textit{solid response} regime, the behavior at fixed packing fraction $\phi$ satisfies $\tau\dot\gamma\propto \exp(-cp\sigma^3/T_{\rm eff})$, where $\dot\gamma$ is the strain rate and $c$ depends weakly on $\phi$, suggesting that the effective temperature controls the average local yield strain. In the \textit{fluid response} regime, $\tau$ depends on $T_{\rm eff}/p\sigma^3$ as it depends on $T/p\sigma^3$ in equilibrium. This regime comprises a large part of the hard-sphere jamming phase diagram including both near-equilibrium conditions where $T_{\rm eff}$ is similar to the kinetic temperature $T_{\rm kin}$ and far-from-equilibrium conditions where $T_{\rm eff} \ne T_{\rm kin}$. In particular, the dynamic jamming transition is largely controlled by the fluid-response mechanism; like equilibrium hard spheres, sheared hard spheres can flow only if low-frequency fluctuations are large enough compared to the pressure. By presenting our results in terms of the dimensionless jamming phase diagram, we show how these mechanisms likely apply to systems with soft repulsive interactions.   

Density-Temperature-Softness Scaling of the Dynamics of Glass-forming Soft-sphere Liquids

We employ the principle of dynamic equivalence between soft-sphere and hard-sphere fluids [Phys. Rev. E {\bf 68}, 011405 (2003); Phys. Rev. Lett. {\bf 107}, 155701 (2011)] to describe the interplay of the effects of varying the density $n$, the temperature $T$, and the softness (characterized by a softness parameter $\nu^{-1}$) on the dynamics of glass-forming soft-sphere liquids in terms of simple scaling rules. The main prediction is the existence of a dynamic universality class associated with the hard sphere fluid, constituted by the soft-sphere systems whose dynamic parameters, such as the $\alpha$-relaxation time and the long-time self-diffusion coefficient, depend on $n,\ T$, and $\nu$ only through the reduced density $n^*\equiv n \sigma_{HS}^3(n,T,\nu)$, where the effective hard-sphere diameter $\sigma_{HS}(n,T,\nu)$ is determined by the Andersen-Weeks-Chandler condition for soft-sphere--hard-sphere structural equivalence. A number of scaling properties observed in recent experiments and simulations involving glass-forming fluids with repulsive short range interactions are found to be a direct manifestation of this general dynamic equivalence principle. The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E {\bf 76}, 041504, 062502 (2007)] is shown to accurately capture these scaling rules. The non-equilibrium extension of this theory [Phys. Rev. E {\bf 82}, 061503, 061504 (2010)] is employed to describe the manifestation of this scaling on the aging of instantaneously-quenched soft-sphere liquids.   

Active Jamming: Self-propelled particles at high density

What determines the mechanical properties of dense collections of active particles? The answer to this question is highly relevant to a wide range of physical and biological phenomena from tissue formation to the dynamics of vibrated granular layers. We present a numerical study of the phases and dynamics of a dense collection of self-propelled particles with soft repulsive interactions and polar alignment in a two-dimensional confined geometry. The phase diagram consists of a polar liquid phase at low packing fraction and high self-propulsion speed, and an active jammed phase at high density and low self-propulsion speed. The liquid phase exhibits local alignment and giant number fluctuations typical of the Vicsek class of models. The dynamics of the jammed phase is dominated by oscillations along the low frequency modes of the underlying packing. We show analytically that at long times the energy is carried entirely by the lowest available excitations of the system. Recent experiments on epithelial cell monolayers using force traction microscopy have revealed stress distributions that resemble those observed in granular materials. We measure and compare the local stresses in our active system, with added attraction, to both granular materials and the tissue experiments.