arXiv subjects

James W. Dufty

Publications and source records attributed to James W. Dufty.

At least 37 records · Page 2Linked to original sources

arXiv2006

Strong breakdown of equipartition in uniform granular mixtures

A binary mixture made of heavy and light inelastic hard spheres in the free cooling state is considered. First, the regions in the parameter space where the partial granular temperature of the heavy species is larger (or smaller) than that of the light species are analyzed. Next, the asymptotic behavior of the mean square velocity ratio in the disparate-mass limit is investigated, assuming different scaling laws for the parameters of the mixture. It is seen that two general classes of states are possible: a "normal" state and an "ordered" state, the latter representing a strong breakdown of energy equipartition.

cond-mat.stat-mech↗

arXiv2006

Mass and heat fluxes for a binary granular mixture at low-density

The Navier--Stokes order hydrodynamic equations for a low density granular mixture obtained previously from the Chapman--Enskog solution to the Boltzmann equation are considered further. The six transport coefficients associated with mass and heat flux in a binary mixture are given as functions of the mass ratio, size ratio, composition, and coefficients of restitution. Their quantitative variation across this parameter set is demonstrated using low order Sonine polynomial approximations to solve the exact integral equations. The results are also used to quantify the violation of the Onsager reciprocal relations for a granular mixture. Finally, the stability of the homogeneous cooling state is discussed.

cond-mat.stat-mech↗

arXiv2005

Multiscale Modeling of Materials - Concepts and Illustration

The approximate representation of a quantum solid as an equivalent composite semi-classical solid is considered for insulating materials. The composite is comprised of point ions moving on a potential energy surface. In the classical bulk domain this potential energy is represented by pair potentials constructed to give the same structure and elastic properties as the underlying quantum solid. In a small local quantum domain the potential is determined from a detailed quantum calculation of the electronic structure. The primary new ingredients are 1) a determination of the pair potential from quantum data for equilibrium and strained structures, 2) development of pseudo-atoms for a realistic treatment of charge densities where bonds have been broken to define the quantum domain, and 3) inclusion of polarization effects on the quantum domain due to its environment. This formal structure is illustrated in detail for an silica nanorod. For each configuration considered, the charge density of the entire solid is calculated quantum mechanically to provide the reference by which to judge the accuracy of the modeling.It is then shown that the quantum rod, the rod constructed from the classical pair potentials, and the composite classical/quantum rod all have the same equilibrium structure and response to elastic strain. The accuracy of the modeling is shown to apply for two quite different quantum chemical methods for the underlying quantum mechanics: transfer Hamiltonian and density functional methods.

cond-mat.mtrl-sci↗

arXiv2005

Hard Sphere Dynamics for Normal and Granular Fluids

A fluid of N smooth, hard spheres is considered as a model for normal (elastic collisions) and granular (inelastic collisions) fluids. The potential energy is discontinuous for hard spheres so the pairwise forces are singular and the usual forms of Newtonian and Hamiltonian mechanics do not apply. Nevertheless, particle trajectories in the N particle phase space are well defined and the generators for these trajectories can be identified. The first part of this presentation is a review of the generators for the dynamics of observables and probability densities. The new results presented in the second part refer to applications of these generators to the Liouville dynamics for granular fluids. A set of eigenvalues and eigenfunctions of the generator for this Liouville dynamics is identified in a special "stationary representation". This provides a class of exact solutions to the Liouville equation that are closely related to hydrodynamics for granular fluids.

cond-mat.soft↗

arXiv2005

Constructing A Small Strain Potential for Multi-Scale Modeling

For problems relating to fracture, a consistent embedding of a quantum (QM) domain in its classical (CM) environment requires that the classical system should yield the same structure and elastic properties as the QM domain for states near equilibrium. It is proposed that an appropriate classical potential can be constructed using ab initio data on the equilibrium and weakly strained configurations calculated from the quantum description, rather than the more usual approach of fitting to a wide range of empirical data. The scheme is illustrated in detail for a model system, silica nanorod that has the proper stiochiometric ratio of Si:O as observed in real silica. The potential is chosen to be pairwise additive, with the same pair potential functional form as familiar phenomenological TTAM potential. Here, the parameters are determined using a genetic algorithm with force data obtained directly from a quantum calculation. The resulting potential gives excellent agreement with properties of the reference quantum calculations both for structure (bond lengths, bond angles) and elasticity (Young's modulus). The proposed method for constructing the classical potential is carried out for two different choices for the quantum mechanical description: a transfer Hamiltonian method (NDDO with coupled cluster parameterization) and density functional theory (with plane wave basis set and PBE exchange correlation functional). The quality of the potentials obtained in both cases is quite good, although the two quantum rods have significant differences.

physics.comp-ph↗

arXiv2004

Study of charge-charge coupling effects on dipole emitter relaxation within a classical electron-ion plasma description

Studies of charge-charge (ion-ion, ion-electron, and electron-electron) coupling properties for ion impurities in an electron gas and for a two component plasma are carried out on the basis of a regularized electron-ion potential without short-range Coulomb divergence. This work is motivated in part by questions arising from recent spectroscopic measurements revealing discrepancies with present theoretical descriptions. Many of the current radiative property models for plasmas include only single electron-emitter collisions and neglect some or all charge-charge interactions. A molecular dynamics simulation of dipole relaxation is proposed here to allow proper account of many electron-emitter interactions and all charge-charge couplings. As illustrations, molecular dynamics simulations are reported for the cases of a single ion imbedded in an electron plasma and for a two-component ion-electron plasma. Ion-ion, electron-ion, and electron-electron coupling effects are discussed for hydrogen-like Balmer alpha lines.

physics.plasm-ph↗

arXiv2004

Origins of Hydrodynamics for a Granular Gas

The basis for a hydrodynamic description of granular gases is discussed for a low density gas of smooth, inelastic hard spheres. The more fundamental mesoscopic description is taken to be the nonlinear Boltzmann kinetic equation. Two arguments are presented in favor of a hydrodynamics for granular gases. The first one is the concept of a "normal" solution and its explicit approximate construction via the Chapman-Enskog method. The second is the demonstration of hydrodynamic modes in the spectrum of the generator for the dynamics of small spatial perturbations of the homogeneous reference state. In the first case, a derivation of the nonlinear hydrodynamic equations is given to Navier-Stokes order, with explicit expressions for the transport coefficients. The approach is formal and the context of the derivation is left unspecified, although internal mathematically consistency is demonstrated. The second method is more restricted, leading only to linearized hydrodynamics, but with the potential to define more sharply the context of hydrodynamics.

cond-mat.stat-mech↗

arXiv2004

Hydrodynamics for a granular gas from an exactly solvable kinetic model

A simple exactly solvable kinetic model for the non-linear inelastic hard sphere Boltzmann equation is used to explore the relevance of hydrodynamics for a granular gas. The equation predicts a non-trivial homogeneous cooling state (HCS), including algebraic decay at large velocities. The linearized kinetic equation for small perturbations about the HCS is solved exactly. It is shown that the hydrodynamic excitations exist in this linearized dynamics, and their detailed form is shown to agree with results from the Chapman-Enskog method up through Navier-Stokes order. The existence of the hydrodynamic modes at short wavelengths, far beyond Navier-Stokes order is demonstrated as well. Finally, the precise sense in which the hydrodynamic excitations dominate the dynamics at long times is described.

cond-mat.soft↗

arXiv2004

An Application of Transfer Hamiltonian Quantum Mechanics to Multi-Scale Modeling

In quantum/classical (QM/CM) partitioning methods for multi-scale modeling, one is often forced to introduce uncontrolled phenomenological effects of the environment (CM) in the quantum (QM) domain as ab initio quantum calculations are computationally too intensive to be applied to the whole sample. We propose a method, in which two qualitatively different components of the information about the state of the CM region are incorporated into the QM calculations. First, pseudoatoms constructed to describe the chemistry of the nearest neighbor exchange interactions replace the atoms at the boundary of the CM and the QM regions. Second, the remaining effect of the CM bulk environment due to long-range Coulombic interactions is modeled in terms of dipoles. We have tested this partitioning method in a silica nanorod and a 3-membered silica ring for which ab initio quantum data for the whole system is available to assess the quality of the proposed partitioning method.

physics.chem-ph↗

arXiv2004

Electron Dynamics at a Positive Ion

The dynamics of electrons in the presence of a positive ion is considered for conditions of weak electron-electron couping but strong electron-ion coupling. The equilibrium electron density and electric field time correlation functions are evaluated for semi-classical conditions using a classical statistical mechanics with a regularized electron-ion interaction for MD simulation. The theoretical analysis for the equilibrium state is obtained from the corresponding nonlinear Vlasov equation. Time correlation functions for the electrons are determined from the linearized Vlasov equation. The resulting electron dynamics is described in terms of a distribution of single electron-ion trajectories screened by an inhomogeneous electron gas dielectric function. The results are applied to calculation of the autocorrelation function for the electron electric field at the ion for $ 0\leq Z\leq 40$, including conditions of strong electron-ion coupling. The electron stopping power and self-diffusion coefficient are determined from these results, and all properties calculated are compared with those obtained from semi-classical molecular dynamics simulation. The agreement with semi-classical MD simulation is found to be reasonable. The theoretical description provides an instructive interpretation for the strong electron-ion results.

cond-mat.stat-mech↗

arXiv2004

Exact Short Time Dynamics for Steeply Repulsive Potentials

The autocorrelation functions for the force on a particle, the velocity of a particle, and the transverse momentum flux are studied for the power law potential $v(r)=ε(σ/r)^ν$ (soft spheres). The latter two correlation functions characterize the Green-Kubo expressions for the self-diffusion coefficient and shear viscosity. The short time dynamics is calculated exactly as a function of $ν$. The dynamics is characterized by a universal scaling function $S(τ)$, where $τ=t/τ_ν$ and $ τ_ν$ is the mean time to traverse the core of the potential divided by $ν$. In the limit of asymptotically large $ν$ this scaling function leads to delta function in time contributions in the correlation functions for the force and momentum flux. It is shown that this singular limit agrees with the special Green-Kubo representation for hard sphere transport coefficients. The domain of the scaling law is investigated by comparison with recent results from molecular dynamics simulation for this potential.

cond-mat.stat-mech↗

arXiv2003

Gaussian Kinetic Model for Granular Gases

A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal "homogeneous cooling solution" after a few collisions. The homogeneous cooling solution (HCS) is studied in some detail and the exact solution is compared with known results for the hard sphere Boltzmann equation. It is shown that all qualitative features of the HCS, including the nature of over population at large velocities, are reproduced semi-quantitatively by the kinetic model. It is also shown that all the transport coefficients are in excellent agreement with those from the Boltzmann equation. Also, the model is specialized to one having a velocity independent collision frequency and the resulting HCS and transport coefficients are compared to known results for the Maxwell Model. The potential of the model for the study of more complex spatially inhomogeneous states is discussed.

cond-mat.stat-mech↗

arXiv2003

Linearized Boltzmann Equation and Hydrodynamics for Granular Gases

The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as the basis for a hydrodynamic description. Hydrodynamics is defined in terms of the spectrum of the generator for the dynamics of the linearized Boltzmann equation. The hydrodynamic eigenfunctions and eigenvalues are calculated in the long wavelength limit. The results allow identification of the hydrodynamic part of the solution to the linearized Boltzmann equation. This contribution is used to calculate the fluxes in the macroscopic balance equations, leading to the Navier-Stokes equations and associated transport coefficients. The results agree with those obtained earlier by the Chapman-Enskog method. The implications of this analysis for application of methods of linear response to granular fluids and derivation of Green-Kubo expressions for transport coefficients are discussed.

cond-mat.stat-mech↗

arXiv2003

Hydrodynamic Modes for Granular Gases

The eigenfunctions and eigenvalues of the linearized Boltzmann equation for inelastic hard spheres (d=3) or disks (d=2) corresponding to d+2 hydrodynamic modes, are calculated in the long wavelength limit for a granular gas. The transport coefficients are identified and found to agree with those from the Chapman-Enskog solution. The dominance of hydrodynamic modes at long times and long wavelengths is studied via an exactly solvable kinetic model. A collisional continuum is bounded away from the hydrodynamic spectrum, assuring a hydrodynamic description at long times. The bound is closely related to the power law decay of the velocity distribution in the reference homogeneous cooling state.

cond-mat.stat-mech↗

arXiv2002

Kinetic Temperatures for a Granular Mixture

An isolated mixture of smooth, inelastic hard spheres supports a homogeneous cooling state with different kinetic temperatures for each species. This phenomenon is explored here by molecular dynamics simulation of a two component fluid, with comparison to predictions of the Enskog kinetic theory. The ratio of kinetic temperatures is studied for two values of the restitution coefficient, $α=0.95$ and 0.80, as a function of mass ratio, size ratio, composition, and density. Good agreement between theory and simulation is found for the lower densities and higher restitution coefficient; significant disagreement is observed otherwise. The phenomenon of different temperatures is also discussed for driven systems, as occurs in recent experiments. Differences between the freely cooling state and driven steady states are illustrated.

cond-mat.stat-mech↗

arXiv2002

Diffusion in a Granular Fluid - Theory

Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic case as well. This is illustrated here for diffusion of an impurity particle in a fluid undergoing homogeneous cooling. An appropriate scaling of the Liouville equation is described such that the homogeneous cooling ensemble and associated time correlation functions map to those of a stationary state. In this form the familiar methods of linear response can be applied, leading to Green - Kubo and Einstein representations of diffusion in terms of the velocity and mean square displacement correlation functions. These correlation functions are evaluated approximately using a cumulant expansion and from kinetic theory, providing the diffusion coefficient as a function of the density and the restitution coefficients. Comparisons with results from molecular dynamics simulation are given in the following companion paper.

cond-mat.soft↗

arXiv2002

Diffusion in a Granular Fluid - Simulation

The linear response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceeding paper. The formally exact Einstein and Green-Kubo expressions for the self-diffusion coefficient are evaluated there from an approximation to the velocity autocorrelation function. These results are compared here to those from molecular dynamics simulations over a wide range of density and inelasticity, for the particular case of self-diffusion. It is found that the approximate theory is in good agreement with simulation data up to moderate densities and degrees of inelasticity. At higher density, the effects of inelasticity are stronger, leading to a significant enhancement of the diffusion coefficient over its value for elastic collisions. Possible explanations associated with an unstable long wavelength shear mode are explored, including the effects of strong fluctuations and mode coupling.

cond-mat.soft↗

arXiv2002

Green-Kubo Expressions for a Granular Gas

The transport coefficients for a gas of smooth, inelastic hard spheres are obtained from the Boltzmann equation in the form of Green-Kubo relations. The associated time correlation functions are not simply those constructed from the fluxes of conserved densities. Instead, fluxes constructed from the reference local homogeneous distribution occur as well. The analysis exposes potential problems associated with a straightforward extension of linear response methods to granular systems.

cond-mat.stat-mech↗