Gregg Lois

Numerical tests of constitutive laws for dense granular flows

We numerically and theoretically study the macroscopic properties of dense, sheared granular materials. In this process we first consider an invariance in Newtons equations, explain how it leads to Bagnolds scaling, and discuss how it relates to the dynamics of granular temperature. Next we implement numerical simulations of granular materials in two different geometries--simple shear and flow down an incline--and show that measurements can be extrapolated from one geometry to the other. Then we observe nonaffine rearrangements of clusters of grains in response to shear strain and show that fundamental observations, which served as a basis for the shear transformation zone (STZ) theory of amorphous solids [M. L. Falk and J. S. Langer, Phys. Rev. E. 57, 7192 (1998); M.R.S. Bull 25, 40 (2000)], can be reproduced in granular materials. Finally we present constitutive equations for granular materials as proposed by Lemaître [Phys. Rev. Lett. 89, 064303 (2002)], based on the dynamics of granular temperature and STZ theory, and show that they match remarkably well with our numerical data from both geometries.

Non-random-coil Behavior as a Consequence of Extensive PPII Structure in the Denatured State

Unfolded proteins may contain a native or nonnative residual structure, which has important implications for the thermodynamics and kinetics of folding, as well as for misfolding and aggregation diseases. However, it has been universally accepted that residual structure should not affect the global size scaling of the denatured chain, which obeys the statistics of random coil polymers. Here we use a single-molecule optical technique--fluorescence correlation spectroscopy--to probe the denatured state of a set of repeat proteins containing an increasing number of identical domains, from 2 to 20. The availability of this set allows us to obtain the scaling law for the unfolded state of these proteins, which turns out to be unusually compact, strongly deviating from random coil statistics. The origin of this unexpected behavior is traced to the presence of an extensive nonnative polyproline II helical structure, which we localize to specific segments of the polypeptide chain. We show that the experimentally observed effects of polyproline II on the size scaling of the denatured state can be well-described by simple polymer models. Our findings suggest a hitherto unforeseen potential of nonnative structure to induce significant compaction of denatured proteins, significantly affecting folding pathways and kinetics.

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 (T=0). 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.

Emergence of multi-contact interactions in contact dynamics simulations of granular shear flows

We examine two basic assumptions of kinetic theory-- binary collisions and molecular chaos-- using numerical simulations of sheared granular materials. We investigate a wide range of densities and restitution coefficients and demonstrate that kinetic theory breaks down at large density and small restitution coefficients. In the regimes where kinetic theory fails, there is an associated emergence of clusters of spatially correlated grains.

Percolation model for slow dynamics in glass-forming materials.

We identify a link between the glass transition and percolation of regions of mobility 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< or =beta< or =1 and the functional dependence of the structural relaxation time tau_{alpha} and exponent beta on temperature, density, and wave number.

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.

Spatial force correlations in granular shear flow. I. Numerical evidence

We investigate the emergence of correlations in granular shear flow. By increasing the density of a simulated granular flow, we observe a transition from a dilute regime, where interactions are dominated by binary collisions, to a dense regime characterized by large force networks and collective motions. With increasing density, interacting grains tend to form networks of simultaneous contacts due to the dissipative nature of collisions. We quantify the size of these networks by measuring two-point force correlations and find dramatic changes in the statistics of contact forces as the size of the networks increases.

Spatial force correlations 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.

Momentum transport in granular flows

We investigate the error induced by considering only binary collisions in the momentum transport of hard-sphere granular materials, as is done in kinetic theories. In this process, we first present a general microscopic derivation of the momentum transport equation and compare it to the kinetic theory derivation, which relies on the binary collision assumption. These two derivations yield different microscopic expressions for the stress tensor, which we compare by using numerical simulations. This provides a quantitative bound on the regime where binary collisions dominate momentum transport and reveals that most realistic granular flows occur in the region of phase space where the binary collision assumption does not apply.

Reliable Protein Folding on Complex 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 complex 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.