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. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Its accuracy in the warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated T. Pressure shifts for hot electrons in compressed static fcc Al and for low-density Al demonstrate the combined magnitude of thermal and gradient effects handled well by this functional over a wide T range.

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. This provides a theoretical context for the current DFT-related approach, the Kubo-Greenwood model, while showing the nature of its corrections. The method is to calculate the short-time dynamics in the single-electron subspace for a given configuration of the ions. This differs from the usual kinetic theory approach in which an average over the ions is performed as well. In this way the effective ion-electron interaction includes strong Coulomb coupling and is shown to be determined from DFT. The correlation functions have the form of the random-phase approximation for an inhomogeneous system but with renormalized ion-electron and electron-electron potentials. The dynamic structure function, density response function, and electrical conductivity are calculated as examples. The static local field corrections in the dielectric function are identified in this way. The current analysis is limited to semiclassical electrons (quantum statistical potentials), so important quantum conditions are excluded. However, a quantization of the kinetic theory is identified for broader application while awaiting its detailed derivation.

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. Keyword searches were carried out, utilising MeSH terms and free text. English language articles primarily were included, with key foreign language (French and German) articles included where possible from the 1900s to the present day. RESULTS: Necrotising ulcerative gingivitis is a rare disease (prevalence <1%), with an acute, painful and destructive presentation. It is an opportunistic bacterial infection which is predominantly associated with spirochetes. Treatment of NUG must be provided on a case-by-case basis, tailored to what the individual can tolerate and the extent of the infection. CONCLUSION: Although there is low prevalence of NUG, its importance should not be underestimated as one of the most severe responses to the oral biofilm. Risk factors must be investigated and addressed. Treatment should consist of gentle superficial debridement, oral hygiene instruction and prescription of mouthwash and antibiotics in severe cases.

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. The analysis extends from the classical strong Coulomb coupling conditions of dusty plasmas to the opposite limit of low temperatures and large densities characteristic of "warm, dense matter."

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. The thermal diffusion factor characterizing conditions for segregation is calculated without the usual restriction to Navier-Stokes hydrodynamics. Integral equations for the coefficients in this hydrodynamic description are calculated approximately within a Sonine polynomial expansion. Molecular dynamics simulations are reported, confirming the existence of this idealized Fourier state. Good agreement is found for the predicted and simulated thermal diffusion coefficient, while only qualitative agreement is found for the temperature ratio.

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. Explicit expressions for the cooling rate, pressure, and transport coefficients are given and compared with the corresponding expressions for a system of elastic hard spheres. The scope of the results for further analytical explorations and possible numerical evaluation is discussed.

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. An expansion in the wave vector to second order allows identification of all phenomenological susceptibilities and transport coefficients through Navier-Stokes order in terms of appropriate time correlation functions. The transport coefficients in this representation are the generalization to granular fluids of the familiar Helfand and Green-Kubo relations for normal fluids. The analysis applies to a variety of collision rules. Important differences in both the analysis and results from those for normal fluids are identified and discussed. A scaling limit is described corresponding to the conditions under which idealized inelastic hard sphere models can apply. Further details and interpretation are provided in the paper following this one, by specialization to the case of smooth, inelastic hard spheres with constant coefficient of restitution.

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. The electron stopping power and self-diffusion coefficient are determined from these results. Interpretation is provided by a theoretical analysis using the nonlinear Vlasov equation for the equilibrium structure, and a corresponding linear Vlasov equation for time correlation functions. The agreement of a simple mean field model with the semiclassical MD simulation is found to be quite good except for one state condition.

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. In a small local quantum domain the potential is determined from a detailed quantum calculation of the electronic structure. The new features of this well-studied problem are (1) a clearly stated theoretical context in which approximations leading to the model are introduced, (2) the representation of the classical domain by potentials focused on reproducing the specific quantum response being studied, (3) development of "pseudoatoms" for a realistic treatment of charge densities where bonds have been broken to define the environment of the quantum domain, and (4) inclusion of polarization effects on the quantum domain due to its distant bulk environment. This formal structure is illustrated in detail for a SiO(2) nanorod. More importantly, each component of the proposed modeling is tested quantitatively for this case, verifying its accuracy as a faithful multiscale model of the original quantum solid. To do so, the charge density of the entire nanorod is calculated quantum mechanically to provide the reference by which to judge the accuracy of the modeling. The construction of the classical potentials, the rod, the pseudoatoms, and the multipoles is discussed and tested in detail. It is then shown that the quantum rod, the rod constructed from the classical potentials, and the composite classical/quantum rod all have the same equilibrium structure and response to elastic strain. In more detail, the charge density and forces in the quantum subdomain are accurately reproduced by the proposed modeling of the environmental effects even for strains beyond the linear domain. The accuracy of the modeling is shown to apply for two quite different choices for the underlying quantum chemical method: transfer Hamiltonian and density functional methods.

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. Within this context of small gradients, the theory is applicable to a wide range of restitution coefficients and densities. The resulting integral-differential equations for the zeroth- and first-order approximations of the distribution functions are given in exact form. An approximate solution to these equations is required for practical purposes in order to cast the constitutive quantities as algebraic functions of the macroscopic variables; this task is described in the companion paper.

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. The results hold for arbitrary degree of inelasticity and are not limited to specific values of the parameters of the mixture. Finally, a detailed comparison between the derivation of the current theory and previous theories for mixtures is made, with attention paid to the implication of the various treatments employed to date.

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.

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. 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 embedded in an electron plasma and for a two-component ion-electron plasma. Charge-charge coupling effects are discussed for hydrogen-like Balmer alpha lines at weak coupling conditions.

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. The conditions for the hydrodynamic excitations to dominate all other excitations are discussed.

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. 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 system 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.

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. For a given degree of inelasticity, the complete nonlinear dependence of the shear viscosity on the shear rate requires the analysis of the unsteady hydrodynamic behavior. The relationship to the Chapman-Enskog method to derive hydrodynamics is clarified using an approximate Grad's solution of the Boltzmann kinetic equation.

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 overpopulation at large velocities, are reproduced 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.