Force networks and the dynamic approach to jamming in sheared granular media

Diverging correlation lengths on either side of the jamming transition are used to formulate a rheological model of granular shear flow, based on the propagation of stress through force chain networks. The model predicts three distinct flow regimes, characterized by the shear rate dependence of the stress tensor, that have been observed in both simulations and experiments. The boundaries separating the flow regimes are quantitatively determined and testable. In the limit of jammed granular solids, the model predicts the observed anomalous scaling of the shear modulus and a new relation for the shear strain at yield

The jamming transition and new percolation universality classes in particulate systems with attraction

We numerically study the jamming transition in particulate systems with attraction by investigating their mechanical response at zero temperature. We find three regimes of mechanical behavior separated by two critical transitions--connectivity and rigidity percolation. The transitions belong to different universality classes than their lattice counterparts, due to force balance constraints. We also find that these transitions are unchanged at low temperatures and resemble gelation transitions in experiments on colloidal and silica gels.Comment: 4 pages, 2 figures, 2 table

A percolation model for slow dynamics in glass-forming materials

We identify a link between the glass transition and percolation of mobile regions in configuration space. We find that many hallmarks of glassy dynamics, for example stretched-exponential response functions and a diverging structural relaxation time, are consequences of the critical properties of mean-field percolation. Specific predictions of the percolation model include the range of possible stretching exponents $1/3 \leq \beta \leq 1$ and the functional dependence of the structural relaxation time $\tau_\alpha$ and exponent $\beta$ on temperature, density, and wave number.Comment: 4 pages, 1 figur

Long Range Correlation in Granular Shear Flow II: Theoretical Implications

Numerical simulations are used to test the kinetic theory constitutive relations of inertial granular shear flow. These predictions are shown to be accurate in the dilute regime, where only binary collisions are relevant, but underestimate the measured value in the dense regime, where force networks of size $\xi$ are present. The discrepancy in the dense regime is due to non-collisional forces that we measure directly in our simulations and arise from elastic deformations of the force networks. We model the non-collisional stress by summing over all paths that elastic waves travel through force networks. This results in an analytical theory that successfully predicts the stress tensor over the entire inertial regime without any adjustable parameters

Reliable protein folding on non-funneled energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant or pH, are adjusted to induce folding. A theory based on this insight predicts that (1) proteins with non-funneled energy landscapes can fold reliably to their native state, (2) reliable folding can occur as an equilibrium or out-of-equilibrium process, and (3) reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.Comment: 13 pages, 9 figure