Biomedical subjects

Corey S O'Hern

Publications and source records attributed to Corey S O'Hern.

9 recordsLinked to original sources

PubMed2006

Measurements of the yield stress in frictionless granular systems.

We perform extensive molecular dynamics simulations of two-dimensional frictionless granular materials to determine whether these systems can be characterized by a single static yield shear stress. We consider boundary-driven planar shear at constant volume and either constant shear force or constant shear velocity. Under steady flow conditions, these two ensembles give similar results for the average shear stress versus shear velocity. However, near jamming it is possible that the shear stress required to initiate shear flow can differ substantially from the shear stress required to maintain flow. We perform several measurements of the shear stress near the initiation and cessation of flow. At fixed shear velocity, we measure the average shear stress Sigma(yv) in the limit of zero shear velocity. At fixed shear force, we measure the minimum shear stress Sigma(yf) required to maintain steady flow at long times. We find that in finite-size systems Sigma(yf) > Sigma(yv), which implies that there is a jump discontinuity in the shear velocity from zero to a finite value when these systems begin flowing at constant shear force. However, our simulations suggest that the difference Sigma(yf) - Sigma(yv), and thus the discontinuity in the shear velocity, tend to zero in the infinite-system-size limit. Thus, our results imply that in the large-system limit, frictionless granular systems can be characterized by a single static yield shear stress. We also monitor the short-time response of these systems to applied shear and show that the packing fraction of the system and shape of the velocity profile can strongly influence whether or not the shear stress at short times overshoots the long-time average value.

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PubMed2005

Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow.

We perform molecular dynamics simulations of model frictionless granular systems undergoing boundary-driven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time t(l) required for the velocity profiles to become linear and find that t(l) increases as a power law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.

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PubMed2005

Random close packing revisited: ways to pack frictionless disks.

We create collectively jammed (CJ) packings of 50-50 bidisperse mixtures of smooth disks in two dimensions (2D) using an algorithm in which we successively compress or expand soft particles and minimize the total energy at each step until the particles are just at contact. We focus on small systems in 2D and thus are able to find nearly all of the collectively jammed states at each system size. We decompose the probability P(phi) for obtaining a collectively jammed state at a particular packing fraction phi into two composite functions: (1) the density of CJ packing fractions rho(phi), which only depends on geometry, and (2) the frequency distribution beta(phi), which depends on the particular algorithm used to create them. We find that the function rho(phi) is sharply peaked and that beta(phi) depends exponentially on phi. We predict that in the infinite-system-size limit the behavior of P(phi) in these systems is controlled by the density of CJ packing fractions--not the frequency distribution. These results suggest that the location of the peak in P(phi) when N --> infinity can be used as a protocol-independent definition of random close packing.

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PubMed2005

Effective temperature in athermal systems sheared at fixed normal load.

We perform molecular dynamics simulations of repulsive athermal systems sheared at fixed normal load to study the effective temperature TL defined from time-dependent fluctuation-dissipation relations for density. We show that these systems possess two distinct regimes as a function of the ratio TS/V of the granular temperature to the potential energy per particle. At small TS/V, these systems are pressure controlled and TL is set by the normal load. In contrast, they behave as quasiequilibrium systems with TL approximately TS that increases with the shear rate at large TS/V. These results point out several problems with using TL in thermodynamic descriptions of slowly sheared athermal systems.

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PubMed2005

Velocity profiles in repulsive athermal systems under shear.

We conduct molecular dynamics simulations of athermal systems undergoing boundary-driven planar shear flow in two and three spatial dimensions. We find that these systems possess nonlinear mean velocity profiles when the velocity u of the shearing wall exceeds a critical value u(c). Above u(c), we also show that the packing fraction and mean-square velocity profiles become spatially dependent with dilation and enhanced velocity fluctuations near the moving boundary. In systems with overdamped dynamics, u(c) is only weakly dependent on packing fraction phi. However, in systems with underdamped dynamics, u(c) is set by the speed of shear waves in the material and tends to zero as phi approaches phi(c), which is near random close packing at small damping. For underdamped systems with phi<phi(c), u(c) is zero; thus they possess nonlinear velocity profiles at any nonzero u.

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PubMed2004

Effective temperatures in driven systems: static versus time-dependent relations.

Using simulations of glassy systems under steady-state shear, we compare effective temperatures obtained from static linear response with those from time-dependent fluctuation-dissipation relations. Although these two definitions are not expected to agree, we show that they yield the same answer over two and a half decades of effective temperature. This suggests that a more complete conceptual framework is necessary for effective temperatures in steady-state driven systems.

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PubMed2003

Jamming at zero temperature and zero applied stress: the epitome of disorder.

We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors. For each configuration, there is a unique jamming threshold phi(c) at which particles can no longer avoid each other, and the bulk and shear moduli simultaneously become nonzero. The distribution of phi(c) values becomes narrower as the system size increases, so that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close packing. In fact, our results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, point J, occurring at zero temperature and applied stress and at the random-close-packing density, has properties reminiscent of an ordinary critical point. As point J is approached from higher packing fractions, power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure, shear modulus, and excess number of overlapping neighbors. Moreover, near point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. Indeed, at point J, the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

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PubMed2002

Effective temperatures of a driven system near jamming.

Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that independently reduce to the true temperature in an equilibrium thermal system are calculated. One of the quantities is calculated up to an unknown coefficient. The other four quantities have the same value and all five have the same shear-rate dependence. These results imply that statistical mechanics is useful for the system even though it is far from thermal equilibrium.

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PubMed2002

Random packings of frictionless particles.

We conduct numerical simulations of random packings of frictionless particles at T = 0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows, and its peak approaches random close packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.

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