The rheology of dense, polydisperse granular fluids under shear

The solution of the Enskog equation for the one-body velocity distribution of a moderately dense, arbitrary mixture of inelastic hard spheres undergoing planar shear flow is described. A generalization of the Grad moment method, implemented by means of a novel generating function technique, is used so as to avoid any assumptions concerning the size of the shear rate. The result is illustrated by using it to calculate the pressure, normal stresses and shear viscosity of a model polydisperse granular fluid in which grain size, mass and coefficient of restitution varies amoungst the grains. The results are compared to a numerical solution of the Enskog equation as well as molecular dynamics simulations. Most bulk properties are well described by the Enskog theory and it is shown that the generalized moment method is more accurate than the simple (Grad) moment method. However, the description of the distribution of temperatures in the mixture predicted by Enskog theory does not compare well to simulation, even at relatively modest densities.Comment: 8 postscript figures Replaced with new version correcting an error in the SME calculations and misc. small corrections. Second replacement with final correction of SME calculation

Solitary and compact-like shear waves in the bulk of solids

We show that a model proposed by Rubin, Rosenau, and Gottlieb [J. Appl. Phys. 77 (1995) 4054], for dispersion caused by an inherent material characteristic length, belongs to the class of simple materials. Therefore, it is possible to generalize the idea of Rubin, Rosenau, and Gottlieb to include a wide range of material models, from nonlinear elasticity to turbulence. Using this insight, we are able to fine-tune nonlinear and dispersive effects in the theory of nonlinear elasticity in order to generate pulse solitary waves and also bulk travelling waves with compact support

Scale separation in granular packings: stress plateaus and fluctuations

It is demonstrated, by numerical simulations of a 2D assembly of polydisperse disks, that there exists a range (plateau) of coarse graining scales for which the stress tensor field in a granular solid is nearly resolution independent, thereby enabling an `objective' definition of this field. Expectedly, it is not the mere size of the the system but the (related) magnitudes of the gradients that determine the widths of the plateaus. Ensemble averaging (even over `small' ensembles) extends the widths of the plateaus to sub-particle scales. The fluctuations within the ensemble are studied as well. Both the response to homogeneous forcing and to an external compressive localized load (and gravity) are studied. Implications to small solid systems and constitutive relations are briefly discussed.Comment: 4 pages, 4 figures, RevTeX 4, Minor corrections to match the published versio

Cardiac assist devices: Cognitive and behavioral factors among patients awaiting cardiac transplantation

Cognitive functioning and quality of life are salient factors in predicting mortality and morbidity in end-stage heart failure patients receiving cardiac assist devices while awaiting cardiac transplantation. This study focused on cognitive functioning and selfreported quality of life, neurological impairment, and depressive symptoms. Of 103 candidates for cardiac assist devices (HeartMate ThermoCardiosystems, Inc. [TCI] Left Ventricular Devices [LVAD] or Abiomed Biventricular Assist System [Abiomed]) as a bridge to cardiac transplantation at Hahnemann University Hospital, a total of 53 patients completed neuropsychological evaluations. Cognitive factors included visual-spatial andverbal memories, motor speed, grip strength, and cognitive processing speed. Inaddition, a total of 298 end-stage heart failure (ESHF) inpatients completed the same cognitive measures over the past decade. Overall, cognitive functioning for both groups was within the normal range. Not surprisingly, a series of t-tests revealed that ESHF inpatients performed better than MCAD candidates on most cognitive measures. However, MCAD candidates performed better than ESHF inpatients on the Mental Status Exam, Visual Reproduction Immediate subtest of the Wechsler Memory Scale, and grip strength task with the nondominant hand.A total of 23 cardiac assist device candidates completed self-report measures ofgeneral and disease-specific quality of life, depressive symptoms, memory, and selfreported neuropsychological symptoms. Results did not support the hypothesis that depression would mediate the relationship between cognitive functioning and quality of life. There were significant differences in quality of life between the three groups: ESHF, MCAD, and OHT warranting a discussion of the implications of various definitions of quality of life. There were no significant gender differences. Major behavioral findings were 1) these patients are resilient in comparison to the general population; their cognitive functioning was not impaired and they were not depressed and 2) there was a strong relationship between self-report depressive symptoms and self-reportedneurological impairment.Ph.D., Clinical Psychology -- Drexel University, 200

Prediction of strong shock structure using the bimodal distribution function

A modified Mott-Smith method for predicting the one-dimensional shock wave solution at very high Mach numbers is constructed by developing a system of fluid dynamic equations. The predicted shock solutions in a gas of Maxwell molecules, a hard sphere gas and in argon using the newly proposed formalism are compared with the experimental data, direct-simulation Monte Carlo (DSMC) solution and other solutions computed from some existing theories for Mach numbers M<50. In the limit of an infinitely large Mach number, the predicted shock profiles are also compared with the DSMC solution. The density, temperature and heat flux profiles calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutionsComment: 22 pages, 9 figures, Accepted for publication in Physical Review

Stability in constrained temperature-rate-dependent thermoelasticity

In an anisotropic temperature-rate-dependent thermoelastic material four plane harmonic waves may propagate in any direction, all dispersive and attenuated, and all stable in the sense that their amplitudes remain bounded in the direction of travel. In this paper, the material is additionally assumed to suffer an internal constraint of the deformation-temperature type, i.e. the temperature is a prescribed function of the deformation gradient. In this constrained thermoelastic material four waves continue to propagate but instabilities are now found. Constrained temperature-rate-dependent thermoelasticity is then combined with generalized thermoelasticity in which the rate of change of heat flux also appears in the heat conduction equation. Four waves again propagate but instabilities are found as before. Anisotropic and isotropic materials are both considered

Stretching and folding versus cutting and shuffling: An illustrated perspective on mixing and deformations of continua

We compare and contrast two types of deformations inspired by mixing applications -- one from the mixing of fluids (stretching and folding), the other from the mixing of granular matter (cutting and shuffling). The connection between mechanics and dynamical systems is discussed in the context of the kinematics of deformation, emphasizing the equivalence between stretches and Lyapunov exponents. The stretching and folding motion exemplified by the baker's map is shown to give rise to a dynamical system with a positive Lyapunov exponent, the hallmark of chaotic mixing. On the other hand, cutting and shuffling does not stretch. When an interval exchange transformation is used as the basis for cutting and shuffling, we establish that all of the map's Lyapunov exponents are zero. Mixing, as quantified by the interfacial area per unit volume, is shown to be exponentially fast when there is stretching and folding, but linear when there is only cutting and shuffling. We also discuss how a simple computational approach can discern stretching in discrete data.Comment: REVTeX 4.1, 9 pages, 3 figures; v2 corrects some misprints. The following article appeared in the American Journal of Physics and may be found at http://ajp.aapt.org/resource/1/ajpias/v79/i4/p359_s1 . Copyright 2011 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the AAP

On the 3D steady flow of a second grade fluid past an obstacle

We study steady flow of a second grade fluid past an obstacle in three space dimensions. We prove existence of solution in weighted Lebesgue spaces with anisotropic weights and thus existence of the wake region behind the obstacle. We use properties of the fundamental Oseen tensor together with results achieved in \cite{Koch} and properties of solutions to steady transport equation to get up to arbitrarily small \ep the same decay as the Oseen fundamental solution

Comment on the calculation of forces for multibody interatomic potentials

The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles interact via pair or embedded-atom potentials. However in literature both definitions are used in order to determine Cauchy stress tensor. A simplest example of the linear pure shear of perfect square lattice is analyzed. It is shown that, Hardy's definition for the stress tensor gives different results depending on the radius of localization function. The differences strongly depend on the way of the force definition.Comment: 9 pages, 2 figure

Power-law velocity distributions in granular gases

We report a general class of steady and transient states of granular gases. We find that the kinetic theory of inelastic gases admits stationary solutions with a power-law velocity distribution, f(v) ~ v^(-sigma). The exponent sigma is found analytically and depends on the spatial dimension, the degree of inelasticity, and the homogeneity degree of the collision rate. Driven steady-states, with the same power-law tail and a cut-off can be maintained by injecting energy at a large velocity scale, which then cascades to smaller velocities where it is dissipated. Associated with these steady-states are freely cooling time-dependent states for which the cut-off decreases and the velocity distribution is self-similar.Comment: 11 pages, 9 figure