Maxwell-Boltzmann Gas Research Articles

Gas-kinetic schemes for compressible flow of real gases

This paper extends gas-kinetic schemes to the Euler equations for real gases. In the current scheme, the maxwell-Boltzmann gas distribution function is modified to recover macroscopic flow equations. More specifically, the internal degree of freedom of the gas distribution function becomes a function of flow variables according to the general equation of state. The numerical results confirm the accuracy and robustness of the gas-kinetic approach.

Dimerization of 3He in 3He-4He dilute mixtures filling narrow channels

We consider dimerization of ${}^{3}\mathrm{He}$ in a dilute solution of ${}^{3}\mathrm{He}$ in superfluid ${}^{4}\mathrm{He}$ filling straight narrow channels that can be found in nanoscale porous media. Dimer formation is facilitated by the restricted geometry and occurs despite the fact that in bulk fluid the interparticle interaction is too weak to lead to a bound state. Dimerization results in the effective ``bosonization'' of the system: a Bose quantum fluid of ${(}^{3}\mathrm{He}{)}_{2}$ arises in place of the ${}^{3}\mathrm{He}$ Fermi component. At high temperatures, when the ${}^{3}\mathrm{He}$ impurity quasiparticles form a Maxwell-Boltzmann gas, a drastic change in the thermodynamics occurs due to the presence of dimers. The specific heat and magnetic susceptibility of the ${}^{3}\mathrm{He}$ component, which we calculate at arbitrary degrees of dimerization, show a marked deviation from behavior expected of an undimerized ${}^{3}\mathrm{He}$ component. We show that the binding energy\char22{}which depends on the channel width\char22{}is expected to be sufficiently high to make experimental observation feasible. The presence of ${(}^{3}\mathrm{He}{)}_{2}$ dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid ${}^{4}\mathrm{He},$ due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single ${}^{3}\mathrm{He}$ polymer will form over the entire length of the channel.

PAIRING IN FERMI FLUIDS IN RESTRICTED GEOMETRIES

We consider dimerization of 3 He in a dilute solution of 3 He in superfluid 4 He filling narrow channels of a kind typically found in nanoscale porous media. Dimer formation is facilitated by the one dimensional geometry and occurs despite the fact that the interparticle interaction is too weak to lead to a bound state in bulk fluid. At sufficiently low temperatures, dimerization results in the effective "bosonization" of the system: a Bose quantum fluid of (3 He )2 arises in place of the 3 He Fermi component. At sufficiently high temperatures, for which the 3 He impurity quasiparticles form a Maxwell–Boltzmann gas, the thermodynamics is significantly affected by the presence of dimers. In particular, the specific heat and magnetic susceptibility of the 3 He component show a marked deviation from behaviour expected if dimers were absent. Solution of the Schrödinger equation for a smooth cylindrical pore indicates that the binding energy in straight nanoscale channels ought to be of sufficiently high magnitude to make experimental observation feasible. The presence of (3 He )2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4 He , due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single 3 He polymer will form over the entire length of the channel.

Perturbation theory calculation of the pressure for an electron–ion system

By means of finite-temperature, many-body perturbation theory we derive through order e 4 the corrections to an ideal Fermi gas plus an ideal Maxwell–Boltzmann gas of ions. This computation is carried out for general values of the de Broglie density. The behavior of these coefficients is reported, and their implications for the ionization profile at low densities are described.

Inflation in a self-interacting gas universe

We show that a de Sitter spacetime is a solution of Einstein's field equations with the energy momentum tensor of a self-interacting, classical Maxwell-Boltzmann gas in collisional equilibrium. The self-interaction is described by a four-force which is quadratic in the (spatially projected) particle four-momenta. This force does not preserve the particle number and gives rise to an exponential increase in the comoving entropy of the universe while the temperature of the latter remains constant. These properties of a gas universe are related to the existence of a ``projector-conformal'' timelike Killing vector representing a symmetry which is ``in between'' the symmetries characterized by a Killing vector and those characterized by a conformal Killing vector.

Ideal gas sources for the Lemaître-Tolman-Bondi metrics

New exact solutions emerge by replacing the dust source of the Lemaître-Tolman-Bondi metrics with a viscous fluid satisfying the monatomic gas equation of state. The solutions have a consistent thermodynamical interpretation. The most general transport equation of extended irreversible thermodynamics is satisfied, with phenomenological coefficients bearing a close resemblance to those characterizing a non-relativistic Maxwell-Boltzmann gas.

The Classical Gases in the Tsallis Statistics Using the Generalized Riemann Zeta Functions

In the last few years an increasing interest has been paid to fractal inspired statistics. Our aim is to describe some new insight obtained using Tsallis statistics. In the framework of the generalized statistics we described some properties of the Maxwell-Boltzmann gases. The behavior of the occupation numbers with respect to the temperature indicates similarities with Fermi gases. Using the Nernst theorem we also determine the fractal index of statistics.

Collisional equilibrium, particle production, and the inflationary universe.

Particle production processes in the expanding universe are described within a simple kinetic model. The equilibrium conditions for a Maxwell-Boltzmann gas with variable particle number are investigated. We find that radiation and nonrelativistic matter may be in equilibrium at the same temperature provided the matter particles are created at a rate that is half the expansion rate. Using the fact that the creation of particles is dynamically equivalent to a nonvanishing bulk pressure we calculate the back reaction of this process on the cosmological dynamics. It turns out that the `adiabatic' creation of massive particles with an equilibrium distribution for the latter necessarily implies power-law inflation. Exponential inflation in this context is shown to become inconsistent with the second law of thermodynamics after a time interval of the order of the Hubble time.

The Maxwell-Boltzmann behavior of a quon gas

A model gas of quons whose operators obey the minimally deformed commutators a ia j † − qa j †a i = δ ij (−1 ≤ q ≤ 1) is studied in two dimensions. While interpolating between the boson limit ( q → 1) and the fermion limit ( q → −1), the gas behaves like a Maxwell-Boltzmann gas when q = 0 at any temperature.

Thermodynamic variables of a relativisitic gas in collision-dominated equilibrium

The thermodynamic variables of a relativistic gas in collision-dominated equilibrium are investigated as functions of the particle number density n and the entropy per unit volume s. Two first-order linear partial differential equations are derived for the absolute temperature T(n,s) and the chemical potential per particle K(n,s). The equations depend on the pressure p that has to be specified through an equation of state. General solutions for T(n,s), K(n,s), and the total energy density μ(n,s) are obtained for a relativistic Maxwell–Boltzmann gas for which the perfect gas law p=nkT must hold, where k is Boltzmann’s constant, and for gases with equations of state p=(γ−1)μ(1≤γ≤2) and μ=ρ+[p/(γ−1)](1<γ≤2) where γ is a constant and ρ is the rest-mass density. It is shown that if p=(γ−1)μ then T is a homogeneous function of degree γ−1 in n and s, which extends from γ=2 to 1≤γ≤2 a result established by Oliver and Davis [Ann. Inst. H. Poincaré 30, 339 (1979)]. The modification of this result for the equation of state μ=ρ+p/(γ−1) is determined. For a relativistic Maxwell–Boltzmann gas for which both p=nkT and either p=(γ−1)μ or μ=ρ+p/(γ−1) are satisfied, T(n,s), K(n,s), and μ(n,s) are determined up to an arbitrary constant.

The production spectrum of a relativistic Maxwell-Boltzmann gas

view Abstract Citations (45) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The production spectrum of a relativistic Maxwell-Boltzmann gas Dermer, C. D. Abstract A formula is derived for use in the calculation of the spectrum of particles or photons produced through particle collisions in a Maxwell-Boltzmann gas. The result is valid for all temperatures and for the general case when the gas contains different mass particles. It is written in terms of a double integral over the cross section differential in the energy of the produced particles (or photons) in the center-of-momentum system of two colliding particles. Analytic expressions for the reaction rate and luminosity are also derived and reproduce the findings of previous work. Application to the problem of the annihilation spectrum from a relativistic Maxwell-Boltzmann electron-positron gas is made. Agreement is found between the present work and previous numerical and analytical studies. Publication: The Astrophysical Journal Pub Date: May 1984 DOI: 10.1086/161999 Bibcode: 1984ApJ...280..328D Keywords: Cosmic Gases; Electron Gas; Maxwell-Boltzmann Density Function; Relativistic Particles; Kinematics; Particle Production; Positron Annihilation; Astrophysics full text sources ADS |

Local inhomogeneities in a Robertson-Walker background. III - Elementary growth rates in a flat background with a relativistic equation of state

view Abstract Citations (4) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Local inhomogeneities in a Robertson-Walker background. III - Elementary growth rates in a flat background with a relativistic equation of state Helaby, C. ; Lake, K. Abstract An examination is undertaken of a class of inhomogeneities, embedded in a spatially flat Robertson-Walker background, which is restricted by the simplifying assumption that isotropic pressure equals local energy flux. Both a noninteracting mixture of blackbody photons and dust, and a baryon-conserving equilibrium mixture of blackbody photons and a neutral, two-component, relativistic Maxwell-Boltzmann gas, are used to describe the background. It is demonstrated through a comparison of the resultant mass of the inhomogeneities with the Jeans and particle horizon mass scales that varying the initial photon-to-baryon ratio in the background has a critical effect on all masses. Publication: The Astrophysical Journal Pub Date: December 1981 DOI: 10.1086/159480 Bibcode: 1981ApJ...251..429H Keywords: Background Radiation; Cosmology; Inhomogeneity; Relativity; Baryons; Black Body Radiation; Dust; Equations Of State; Photons; Astrophysics full text sources ADS |

Measurement of the velocity distribution of sputtered Na atoms from NaCl by Doppler shift laser fluorescence

The velocity distribution of sputtered Na atoms from NaCl during 15 keV, Ar+ bombardment was measured by a Doppler shift laser fluorescence technique. Contrary to other measurements, the sputtered Na atoms were found to have a velocity distribution identical to that of a three-dimensional Maxwell–Boltzmann gas.

The theory of pulsed Fourier transform microwave spectroscopy carried out in a Fabry–Perot cavity: Static gas

A semiclassical theory has been developed to describe pulsed Fourier transform microwave spectroscopy carried out in a Fabry–Perot cavity. A density matrix formalism is used to study the interaction of a two-level quantum system with a classical standing wave electric field, appropriate for the Fabry–Perot cavity. Equations describing the polarization of, and subsequent emission of radiation by arbitrary distributions of molecules in the cavity are derived. The specific problem of a static Maxwell–Boltzmann gas is studied in detail, both theoretically and experimentally. The static gas line shape in the power-broadened limit is described by an ordinary Doppler and pressure broadened envelope. Sensitivities of the ordinary waveguide cell and Fabry–Perot cavity pulsed Fourier transform spectrometers using static gas samples are compared.

Boundary effects in fluid flow. Application to quantum liquids

The effect of boundaries on the flow of rarefied gases is considered. For an excitation gas of arbitrary statistics and energy-momentum relationship we determine the magnitude of the slip length and the flow between parallel plates mostly by variational methods. Our approximate method avoids the need to solve integral equations numerically and yields in the stationary case better than 1% agreement with known exact results for the classical Maxwell-Boltzmann gas. Our general results are primarily applied to normal and superfluid Fermi liquids. We calculate the surface impedance of an oscillating plate and determine the frequency-dependent slip length for frequencies ranging from the hydrodynamic to the collisionless limit. Our results are applied to the analysis of viscosity measurements based on a torsional oscillator or a vibrating wire. The slip effects are shown to be very important for realistic experimental parameters, especially at low temperatures in the superfluid B phase of liquid 3He.

Comments on the orbital magnetic susceptibility of electrons confined by smooth potentials

Jennings and Bhaduri have recently derived an expression for the zero-field limit of the orbital magnetic susceptibility for a Maxwell-Boltzmann gas of electrons confined by a smooth potential. Their expression for the susceptibility, which represents the two lowest-order terms in its expansion in powers of Planck's constant, is shown to be, for a certain class of potentials, the two lowest-order terms in its high-temperature expansion as well.