Gas In Thermodynamic Equilibrium Research Articles

Classical and quantum warm dense electron gas dynamic characteristics: analytic predictions

We apply a novel 9-moment variational version of the self-consistent non-perturbative method of moments to study how the temperature affects the dynamic response of the electron gas in thermodynamic equilibrium. The theoretical results are obtained with the only input being the static structure factor. Comparison is carried out with the data obtained in the random-phase and the effective static local-field (ESA) (1) approximations. A quite satisfactory agreement is achieved with the system dynamic structure factor evaluated within the ESA interpolation scheme. We analyze the system properties for the temperature values (1 ≤ T/TF ≤ 4) chosen in the range where the electron gas starts to undergo a transition from the degenerate to classical behaviour. The extension of the method to a broader range of temperatures and densities is straightforward and is left for future studies. Nevertheless, we demonstrate a systematic way to investigate the gradual transition from degenerate to classical systems.

Stability condition for strong shocks in flows over an infinite planar wedge satisfying the Lopatinski condition

We study the classical problem for a flow of uniform inviscid non-heat-conducting gas in thermodynamical equilibrium moving onto a planar infinite wedge. As it is known, theoretically this problem has solutions of two types. Solutions of the first type correspond to a strong shock when the gas velocity behind the shock front is less than the sound speed whereas solutions of the second type correspond to the case of a weak shock when the gas velocity behind the shock front is greater than the sound speed. The shock fronts are attached to the wedge vertex. We consider the linear problem for a strong shock wave provided that the Lopatinski condition holds (in a weak sense) on the shock front and the initial data are compactly, i.e. supports of the initial data are separated from the coordinate axes. Under some additional conditions on the initial data we find a solution of the generalized problem. In contrast to the previously studied case when the uniform Lopatinski condition holds on the shock front, this solution contains plane waves. The stability of the found solution is thus justified on the linear level what gives a principle possibility to realize the flow regime containing a strong shock as time increases.

On the distribution of dark matter in galaxies: Quantum treatments

The problem of modeling the distribution of dark matter in galaxies in terms of equilibrium configurations of collisionless self-gravitating quantum particles is considered. We first summarize the pioneering model of a Newtonian self-gravitating Fermi gas in thermodynamic equilibrium developed by Ruffini and Stella (1983), which is shown to be the generalization of the King model for fermions. We further review the extension of the former model developed by Gao, Merafina and Ruffini (1990), done for any degree of fermion degeneracy at the center ($\theta_0$), within general relativity. Finally, we present here for the first time the solutions of the density profiles and rotation curves corresponding to the Gao et. al. model, which have a definite mass $M_h$ and circular velocity $v_h$, at the halo radius $r_h$ of the configurations, typical of spiral galaxies. This treatment allow us to determine a novel core-halo morphology for the dark matter profiles, as well as a novel particle mass bound associated with them.

Stability of a supersonic flow over a wedge containing a weak shock wave satisfying the Lopatinski condition

We study the stability problem for a stationary supersonic flow of inviscid non-heat-conducting gas in thermodynamical equilibrium moving onto a planar infinite wedge. As it is known, this problem has two solutions: a solution with a strong shock wave (when the velocity behind the front of the shock wave is subsonic) and a solution with a weak shock wave (when the velocity behind the front of the shock wave is supersonic). We consider the case of a weak shock wave and we prove that if the Lopatinski condition for the shock wave holds (in a weak sense), then the corresponding linearized initial boundary-value problem is well-posed. We thus find a classical solution to this problem. Unlike the case when the uniform Lopatinski condition holds, additional plane waves appear. For compactly supported initial data we show that the solution of the linearized problem converges to the zero solution as time tends to infinity. Therefore, for the case of a weak shock wave and when the Lopatinski condition holds in a weak sense, these results complete the proof of the well-known Courant–Friedrichs' conjecture that the strong shock wave solution is unstable whereas the weak shock wave solution is stable.

Classical relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated reference frame

A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using these methods explicit expressions for the particle, energy and entropy density distributions are obtained, which are found to be in agreement with the well-known results of the relativistic formulation of Boltzmann's kinetic theory. Explicit expressions for the total entropy, total energy and rest mass of the gas are obtained. The position of the center of mass of the gas in equilibrium is found. The non-relativistic and ultrarelativistic approximations are also considered. The phase space volume of the system is calculated explicitly in the ultrarelativistic approximation.

PAKAL: A THREE-DIMENSIONAL MODEL TO SOLVE THE RADIATIVE TRANSFER EQUATION

We present a new numerical model called "Pakal" intended to solve the radiative transfer equation in a three-dimensional (3D) geometry, using the approximation for a locally plane-parallel atmosphere. Pakal uses pre-calculated radial profiles of density and temperature (based on hydrostatic, hydrodynamic, or MHD models) to compute the emission from 3D source structures with high spatial resolution. Then, Pakal solves the radiative transfer equation in a set of (3D) ray paths, going from the source to the observer. Pakal uses a new algorithm to compute the radiative transfer equation by using an intelligent system consisting of three structures: a cellular automaton; an expert system; and a program coordinator. The code outputs can be either two-dimensional maps or one-dimensional profiles, which reproduce the observations with high accuracy, giving detailed physical information about the environment where the radiation was generated and/or transmitted. We present the model applied to a 3D solar radial geometry, assuming a locally plane-parallel atmosphere, and thermal free–free radio emission from hydrogen–helium gas in thermodynamic equilibrium. We also present the convergence test of the code. We computed the synthetic spectrum of the centimetric–millimetric solar emission and found better agreement with observations (up to 104 K at 20 GHz) than previous models reported in the literature. The stability and convergence test show the high accuracy of the code. Finally, Pakal can improve the integration time by up to an order of magnitude compared against linear integration codes.

Stability of a supersonic flow about a wedge with weak shock wave

It is known that the problem of finding the streamlines of a stationary supersonic flow of a nonviscous nonheat-conducting gas in thermodynamical equilibrium past an infinite plane wedge (with a sufficiently small angle at the vertex) in theory has two solutions: a strong shock wave solution (the velocity behind the front of the shock wave is subsonic) and a weak shock wave solution (the velocity behind the front of the shock wave is generally speaking supersonic). In the present paper it is shown for a linear approximation to this problem that the weak shock wave solution is asymptotically stable in the sense of Lyapunov. Moreover, it is shown that for initial data with compact support the solution of the mixed linear problem converges in finite time to the zero solution. In the case of linear approximation these results complete the verification of the well-known Courant-Friedrichs conjecture that the strong shock wave solution is unstable, whereas the weak shock wave solution is asymptotically stable in the sense of Lyapunov.Bibliography: 39 titles.

Quantum boundary layer: a non-uniform density distribution of an ideal gas in thermodynamic equilibrium

Density distribution of an ideal Maxwellian gas confined in a finite domain is not uniform even in thermodynamic equilibrium. Near to the boundaries, there is a layer in which the density goes to zero. Existence of this boundary layer explains the shape and size dependence of the thermodynamic quantities in nano scale.

On the Statistics of an Ideal Gas with Mass Fluctuations and the Boltzman Ergodic Theorem: The Combined Boltzman–Tsallis Statistics

In this letter, we evaluate the effective velocities probability distribution associated to a classical ideal gas in thermodynamical equilibrium, but in the presence of fluctuations of the (inertial) mass parameter of the molecules. We obtain in the context of linear response theory of the mass fluctuations and the usual Boltzman framework the combined statistics of Boltzman and Tsallis as an outcome of the study for our effective Fractal gas distribution probability. This result explains from first principles the Tsallis-inverse power law distribution previously only speculated on in the literature. Finally, we give a new mathematical proof of the Boltzman ergodic theorem in classical statistics mechanics.

Statistical mechanics of the self-gravitating gas: II. Local physical magnitudes and fractal structures

We complete our study of the self-gravitating gas by computing the fluctuations around the saddle point solution for the three statistical ensembles (grand canonical, canonical and microcanonical). Although the saddle point is the same for the three ensembles, the fluctuations change from one ensemble to the other. The zeroes of the small fluctuations determinant determine the position of the critical points for each ensemble. This yields the domains of validity of the mean field approach. Only the S-wave determinant exhibits critical points. Closed formulae for the S- and P-wave determinants of fluctuations are derived. The local properties of the self-gravitating gas in thermodynamic equilibrium are studied in detail. The pressure, energy density, particle density and speed of sound are computed and analyzed as functions of the position. The equation of state turns out to be locally p( r → )=Tρ V( r → ) as for the ideal gas. Starting from the partition function of the self-gravitating gas, we prove in this microscopic calculation that the hydrostatic description yielding locally the ideal gas equation of state is exact in the N=∞ limit. The dilute nature of the thermodynamic limit ( N∼ L→∞ with N/ L fixed) together with the long range nature of the gravitational forces play a crucial role in obtaining such ideal gas equation. The self-gravitating gas being inhomogeneous, we have PV/[ NT]= f( η)⩽1 for any finite volume V. The inhomogeneous particle distribution in the ground state suggests a fractal distribution with Haussdorf dimension D, D is slowly decreasing with increasing density, 1< D<3. The average distance between particles is computed in Monte Carlo simulations and analytically in the mean field approach. A dramatic drop at the phase transition is exhibited, clearly illustrating the properties of the collapse.

Effect of exciton-carrier thermodynamics on the GaAs quantum well photoluminescence.

In order to explain the power-dependent temporal behavior of the photoluminescence from free excitons in a GaAs quantum well following a short optical pulse, we consider the excitons and free carriers to be a nearly ideal gas in thermodynamic equilibrium. The temperature of the gas, which decreases in time after the pulse due to cooling by phonon emission, can be measured experimentally from the free-carrier recombination luminescence. Because only excitons with near-zero kinetic energy can luminesce, the photoluminescence intensity depends on the excitonic-gas temperature. Due to the law of mass action between excitons and free carriers, the photoluminescence intensity of excitons also depends on the density of the gas, which decays in time. Using the known binding energy of excitons, we find that the density-dependent temporal behavior of the photoluminescence is consistent with a simple thermodynamic equilibrium between excitons and free carriers. \textcopyright{} 1996 The American Physical Society.

Probability distribution function in the gas of paramagnetic particles.

In this paper we consider a system of noninteracting paramagnetic particles with a spin S in a dc magnetic field. The exact expression for the probability distribution function of a transverse spin component is obtained for the gas in thermodynamic equilibrium. Dependences of the probability on the thermofield parameter \ensuremath{\beta}\ensuremath{\mu}H (\ensuremath{\beta} is the inverse temperature, \ensuremath{\mu} is the Bohr magneton, H is a field strength) and S are investigated. It is shown that this distribution reflects the quantum nature of the spin and both the spin-wave and the classical approximation formulas are obtained.

SURVIVAL OF J/Ψ IN HADRONIC MATTER AT HIGH ENERGY DENSITY?

The collision rate of massive strings representing J/Ψ mesons has been determined by numerical simulation, modelling the surrounding hadronic matter as an ideal string gas in thermodynamical equilibrium. The survival time of the J/Ψ string tends to zero at the Hagedorn temperature. Whether the final state J/Ψ-nucleon scattering accounts for a major part of the observed J/Ψ suppression, depends on the value of the J/Ψ-nucleon cross section.

Correlation functions of one-dimensional Bose gas in thermodynamic equilibrium

Correlation functions of one-dimensional Bose gas in thermodynamic equilibrium

Relativistic generalization of the Einstein-Milne relations

The Einstein-Milne relations for the continuum are generalized to a nondegenerate relativistic gas in thermodynamic equilibrium, using the relativistic ionization equation which has been recently established by us [J. Phys. A 16, 2347 (1983)] and which must replace the Saha equation at temperatures above ${10}^{8}$ K. The macroscopic continuum opacity and emissivity of this gas are also derived.

Lattice gas models for chemisorption on stepped surfaces

We consider the theory of chemisorption on stepped surfaces for systems for which a lattice gas in thermodynamic equilibrium is an appropriate model. Using statistical mechanics we demonstrate that by comparing LEED (Low Energy Electron Diffraction) results for overlayer features on flat and stepped substrates one can determine the change in adsorption energy at terrace edges. Thus one can answer the important question for whether adatoms bind more or less strongly at this kind of defect site. We also examine some new and interesting features of LEED spot shapes and integrated intensity behavior for adsorption on stepped substrates when the overlayer is partially disordered. In a companion paper, we consider O on a certain stepped W(110) surface. We demonstrate there, via Monte Carlo calculations, that the binding energy is less strong on either terrace edge for this particular adsorbate, surface and defect.

Chemisorption on stepped surfaces: O/stepped W(110)

In a previous study we have developed a general theory of chemisorption on certain stepped surfaces; namely those for which a lattice gas in thermodynamic equilibrium is an appropriate model. We showed there that a comparison of LEED (Low Energy Electron Diffraction) results for flat and stepped substrates can determine the change in adsorption energy at terrace edge sites. In the present work we demonstrate this via detailed Monte Carlo calculations for O on a certain stepped W(110) surface. We use oxygen adatom-adatom (AA) interaction energies previously determined by experimental and theoretical studies on flat W(110). By comparison with experimental results for the stepped surface system we find that the O binding energy is less strong at either terrace edge for this particular surface and defect.

Lattice gas models for chemisorption on stepped surfaces

Abstract We consider the theory of chemisorption on stepped surfaces for systems for which a lattice gas in thermodynamic equilibrium is an appropriate model. Using statistical mechanics we demonstrate that by comparing LEED (Low Energy Electron Diffraction) results for overlayer features on flat and stepped substrates one can determine the change in adsorption energy at terrace edges. Thus one can answer the important question for whether adatoms bind more or less strongly at this kind of defect site. We also examine some new and interesting features of LEED spot shapes and integrated intensity behavior for adsorption on stepped substrates when the overlayer is partially disordered. In a companion paper, we consider O on a certain stepped W(110) surface. We demonstrate there, via Monte Carlo calculations, that the binding energy is less strong on either terrace edge for this particular adsorbate, surface and defect.

Chemisorption on stepped surfaces: O/stepped W(110)

Abstract In a previous study we have developed a general theory of chemisorption on certain stepped surfaces; namely those for which a lattice gas in thermodynamic equilibrium is an appropriate model. We showed there that a comparison of LEED (Low Energy Electron Diffraction) results for flat and stepped substrates can determine the change in adsorption energy at terrace edge sites. In the present work we demonstrate this via detailed Monte Carlo calculations for O on a certain stepped W(110) surface. We use oxygen adatom-adatom (AA) interaction energies previously determined by experimental and theoretical studies on flat W(110). By comparison with experimental results for the stepped surface system we find that the O binding energy is less strong at either terrace edge for this particular surface and defect.

On the integration of Riemann's compatibility condition in one-dimensional unsteady flow of a gas in thermodynamic equilibrium

Riemann's compatibility condition, valid along the characteristics of a nonviscous, one-dimensional, unsteady flow of a gas in thermodynamic equilibrium is discussed. That part of it, that containes variables of state, is shown to be a path dependant integral. Its integration is carried out for flows, in which one variable of state remains constant. For multi-isentropic flow of a calorically perfect gas an ansatz is given, that approximates the path of integration of the Riemann condition as if the law of thermodynamic change along a characteristic were uniform for one step of the calculation.