Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions.

Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (XC) free-energy functional accurate over a wide range of state conditions. Unlike the ground-state case, no such functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free-energy gradient expansion.

Kinetic theory for strongly coupled Coulomb systems.

The calculation of dynamical properties for matter under extreme conditions is a challenging task. The popular Kubo-Greenwood model exploits elements from equilibrium density-functional theory (DFT) that allow a detailed treatment of electron correlations, but its origin is largely phenomenological; traditional kinetic theories have a more secure foundation but are limited to weak ion-electron interactions. The objective here is to show how a combination of the two evolves naturally from the short-time limit for the generator of the effective single-electron dynamics governing time correlation functions without such limitations.

Necrotising Ulcerative Gingivitis: A Literature Review.

Purpose: The literature surrounding necrotising ulcerative gingivitis (NUG) is extensive, yet the rare nature of this disease means that there is a lack of good quality research available. This paper aims to scrutinise the literature and provide an up-to-date summary of the available information.

Materials And Methods: A literature search was performed electronically using the Cochrane Library, Ovid Medline, Embase, PubMed Clinical Queries and Google Scholar.

Finite-temperature quantum effects on confined charges.

A quantum system of N Coulomb charges confined within a harmonic trap is considered over a wide range of densities and temperatures. A recently described construction of an equivalent classical system is applied in order to exploit the rather complete classical description of harmonic confinement via liquid-state theory. Here, the effects of quantum mechanics on that representation are described with attention focused on the origin and nature of shell structure.

Accurate homogeneous electron gas exchange-correlation free energy for local spin-density calculations.

An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin polarization, is derived via thermodynamic analysis of recent restricted path integral Monte Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and low- and high-T asymptotic limits, and is well behaved beyond the range of the RPIMC data, suggestive of broad utility.

Thermal segregation of intruders in the Fourier state of a granular gas.

A low density binary mixture of granular gases is considered within the Boltzmann kinetic theory. One component, the intruders, is taken to be dilute with respect to the other, and thermal segregation of the two species is described for a special solution to the Boltzmann equation. This solution has a macroscopic hydrodynamic representation with a constant temperature gradient and is referred to as the Fourier state.

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 coupling but strong electron-ion coupling. The equilibrium electron density and the electric field time correlation functions are evaluated for semiclassical conditions using a classical statistical mechanics with a regularized electron-ion interaction for molecular dynamics simulation (MD). Results are reported for the autocorrelation function of the electron electric field at the ion for 0< or =Z< or =40 , including conditions of strong electron-ion coupling.

Transport coefficients for the hard-sphere granular fluid.

In the preceding paper, linear response methods have been applied to obtain formally exact expressions for the parameters of Navier-Stokes order hydrodynamics. The analysis there is general, applying to both normal and granular fluids with a wide range of collision rules. Those results are specialized here to the case of smooth, inelastic, hard spheres with constant coefficient of normal restitution, for further elaboration.

Linear response and hydrodynamics for granular fluids.

A formal derivation of linear hydrodynamics for a granular fluid is given. The linear response to small spatial perturbations of a homogeneous reference state is studied in detail, using methods of nonequilibrium statistical mechanics. A transport matrix for macroscopic excitations in the fluid is defined in terms of the response functions.

Multiscale modeling of materials based on force and charge density fidelity.

The approximate representation of a quantum solid as an equivalent composite semiclassical 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 potentials constructed to give the same structure and elastic properties as the underlying quantum solid.

Enskog theory for polydisperse granular mixtures. II. Sonine polynomial approximation.

The linear integral equations defining the Navier-Stokes (NS) transport coefficients for polydisperse granular mixtures of smooth inelastic hard disks or spheres are solved by using the leading terms in a Sonine polynomial expansion. Explicit expressions for all the NS transport coefficients are given in terms of the sizes, masses, compositions, density, and restitution coefficients. In addition, the cooling rate is also evaluated to first order in the gradients.

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport.

A hydrodynamic description for an s -component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In this first part of the two-part series, the macroscopic balance equations for mass, momentum, and energy are derived. Constitutive equations are calculated from exact expressions for the fluxes by a Chapman-Enskog expansion carried out to first order in spatial gradients, thereby resulting in a Navier-Stokes order theory.

Dynamics of a hard sphere granular impurity.

An impurity particle coupling to its host fluid via inelastic hard sphere collisions is considered. It is shown that the exact equation for its distribution function can be mapped onto that for an impurity with elastic collisions and an effective mass. The application of this result to the Enskog-Lorentz kinetic equation leads to several conclusions: (1) every solution in the elastic case is equivalent to a class of solutions in the granular case; (2) for an equilibrium host fluid the granular impurity approaches equilibrium at a different temperature, with a dominant diffusive mode at long times; (3) for a granular host fluid in its scaling state, the granular impurity approaches the corresponding scaling solution.

High division of the accessory nerve: a rare anatomical variation as a possible pitfall during neck dissection surgery.

A rare clinical variant found during neck dissection surgery is reported in which the spinal accessory nerve divided at a high level in the neck, before entering the sternocleidomastoid muscle. This case documents the need for meticulous technique in identification and dissection of the spinal accessory nerve in order to reduce the risk of postoperative morbidity.

Hydrodynamic modes for a granular gas from kinetic theory.

Small perturbations of the homogeneous cooling state for a low density granular gas are described by means of the linearized Boltzmann equation. The spectrum of the generator for this dynamics is shown to contain points corresponding to hydrodynamic excitations. The corresponding eigenvectors and eigenvalues are calculated to Navier-Stokes order and shown to agree with those obtained by the Chapman-Enskog method.

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 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-day 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.

Hard sphere dynamics for normal and granular fluids.

A fluid of N smooth, hard spheres is considered as a model for normal (elastic collision) and granular (inelastic collision) fluids. The potential energy is discontinuous for hard spheres so that 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.

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.

Inherent rheology of a granular fluid in uniform shear flow.

In contrast to normal fluids, a granular fluid under shear supports a steady state with uniform temperature and density since the collisional cooling can compensate locally for viscous heating. It is shown that the hydrodynamic description of this steady state is inherently non-Newtonian. As a consequence, the Newtonian shear viscosity cannot be determined from experiments or simulation of uniform shear flow.

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.

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 alpha=0.

Long-ranged correlations in sheared fluids.

The presence of long-ranged correlations in a fluid undergoing uniform shear flow is investigated. An exact relation between the density autocorrelation function and the density-momentum correlation function implies that the former must decay more rapidly than 1/r, in contrast to predictions of simple mode-coupling theory. Analytic and numerical evaluation of a nonperturbative mode-coupling model confirms a crossover from 1/r behavior at "small" r to a stronger asymptotic power-law decay.

Classical description of electron structure near a positive ion.

A single positive ion is imbedded in an electron gas with overall charge neutrality. A classical statistical mechanics is considered using an electron-ion Coulomb potential regularized at distances within the de Broglie length. The electron charge density and electric field distribution at the ion are studied as a function of ion-electron coupling using molecular dynamics simulation and theoretical models.

Diffusion in a granular fluid. II. Simulation.

The linear-response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceding 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.