Showing papers on "Boltzmann constant published in 1983"
TL;DR: In this paper, the ion distribution function is calculated for the E and the F regions of the auroral latitudes, where the plasma is weakly ionized and there exist convective electric fields which may attain very significant intensities.
38 citations
TL;DR: In this paper, the Boltzmann collision operator for the hard-sphere cross section of a gas initially non-maxwellian and anisotropic is considered, and a discrete ordinate method is used to calculate the time eigenvalues of the collision operator.
36 citations
TL;DR: The papers exchanged by Boltzmann and Ernst Zermelo concerning the recurrence paradox are summarized in this paper, where the historical context of the paradox, Zermel's proof of the Paradox, his opinions of its consequences, Boltzman's reply, and the ensuing discussion are described.
Abstract: The papers exchanged by Ludwig Boltzmann and Ernst Zermelo concerning the recurrence paradox are summarized. The historical context of the paradox, Zermelo’s proof of the paradox, his opinions of its consequences, Boltzmann’s reply, and the ensuing discussion are described.
29 citations
TL;DR: In this paper, the nonuniform Percus-Yevick equation is solved by using the method introduced by Lado to study two dimensional fluids, and the adsorption of hard spheres on solids interacting according to potentials whose Boltzmann functions contain a δ-function.
Abstract: We study the adsorption of hard spheres on solids interacting according to potentials whose Boltzmann functions contain a δ-function. The nonuniform Percus-Yevick equation is solved by using the method introduced by Lado to study two dimensional fluids.
27 citations
TL;DR: In this article, several derivations of the Burnett and higher order in the gradients equation of classical hydrodynamics are critically examined, and it is clearly pointed out that the two available phenomenological derivations and Grad's kinetic derivation are compatible with the local equilibrium assumption and the entropy balance equation.
Abstract: Several derivations of the Burnett and higher order in the gradients equation of classical hydrodynamics are critically examined. It is clearly pointed out that the two available phenomenological derivations and Grad's kinetic derivation are compatible with the local equilibrium assumption and the entropy balance equation. Furthermore, the failure to fulfill these requirements when such equations are obtained from the Chapman-Enskog method for solving Boltzmann's equation is accounted for. A comparison with other more microscopic methods to obtain these equations is also provided.
18 citations
TL;DR: In this article, the authors derived the diffusion constant of muons in metals at low temperatures from the muon Boltzmann equation under the assumption that electron-muon scattering dominates, and a T-1 behavior was obtained.
Abstract: The diffusion constant of muons in metals at low temperatures is derived from the muon Boltzmann equation under the assumption that electron-muon scattering dominates, and a T-1 behaviour is obtained. This temperature dependence compares favorably with the experimental result that the diffusion constant is proportional to T-0.6 for positive muons in aluminium. However, the calculated absolute value of the diffusion constant around 1K is still in severe disagreement with experiment.
16 citations
01 May 1983
16 citations
TL;DR: In this paper, it was shown that far-from-equilibrium chemical systems can respond very sensitively to gravity by selection of possible structures or in the formation of propagating bands, where the sensitivity is characterized by the factor (E g /kT) 1 n, where n=2 or 3, eg the interaction energy, k the Boltzmann constant and T, the temperature.
15 citations
TL;DR: In this paper, a reanalysis of the correction to the Boltzmann conductivity due to maximally crossed graphs for degenerate bands explains why the conductivity scale in many-valley semiconductors is an order of magnitude higher than Mott's "minimum metallic conductivity."
Abstract: A reanalysis of the correction to the Boltzmann conductivity due to maximally crossed graphs for degenerate bands explains why the conductivity scale in many-valley semiconductors is an order of magnitude higher than Mott's "minimum metallic conductivity." With the use of a reasonable assumption for the Boltzmann mean free path, the lowest-order perturbation theory is seen to give a remarkably good, semiquantitative, description of the conductivity variation in both uncompensated doped semiconductors and amorphous alloys.
13 citations
01 Jan 1983
TL;DR: The Avogadro's number has the numerical value NA = 6.025 × 1023 as mentioned in this paper, which is the largest number known to exist in the physical world, and it has been determined by a dozen independent methods.
Abstract: The kinetic theory of gases, founded in the 18th century by Daniel Bernoulli, was further developed during the 19th century by Clausius and Maxwell, and crowned by the achievements of Ludwig Boltzmann’s statistical mechanics. At the time Boltzmann was developing his method, the hypothesis of the discontinuous structure of matter, i.e., of the existence of atoms and molecules, was becoming increasingly a matter of certainty for physicists. Boltzmann’s colleague at the University of Vienna, Joseph Loschmidt, indicated in the year 1865 a method for determining the number of molecules in a mole (the so-called Avogadro’s number NA) and the order of magnitude of atomic sizes (1 A = 10-8 cm). We know today that Avogadro’s number— determined by a dozen independent methods—has the numerical value NA = 6.025 × 1023, an enormously large number.
TL;DR: The relativistic canonical formalism was used to construct the kinetic equations for a gas in a gravitational field, whose particles interact with one another via numerous inelastic collisions.
Abstract: The relativistic canonical formalism is used to construct the kinetic equations for a gas in a gravitational field, whose particles interact with one another via numerous inelastic collisions. Boltzmann's H-theorem is proved for T-invariant interactions.
TL;DR: In this article, a spectral algorithm, conservative with respect to mass flow, is proposed for solving the homogeneous relaxation problem in the method of splitting into physical processes for Boltzmann's kinetic equation with Maxwell interaction potential.
Abstract: A spectral algorithm, conservative with respect to mass flow, is proposed for solving the homogeneous relaxation problem in the method of splitting into physical processes for Boltzmann's kinetic equation with Maxwell interaction potential. It is shown that, by realizing the algorithm by a numerical fast Fourier transformation procedure, the amount of calculation can be greatly reduced. The computational scope of the method is studies for the Cauchy problem for the non-linear kinetic equation with velocity space R 1 .
TL;DR: In this article, the bipolar charge distribution of chain aggregates composed of uniform primary spheres was derived from a previously described theory, expressed as Boltzmann distributions for an equivalent length sphere having a diameter equal to the length of the straight chain.
TL;DR: In this article, a rigorous derivation of the reactive quantum Boltzmann equations is presented for systems where breakup and recombination are excluded, and the use of an arrangement channel space representation allows an exact decomposition of the N particle density matrix into components for different chemical compositions and an exact definition of reduced species density matrices.
Abstract: A rigorous derivation of the reactive quantum Boltzmann equations is presented for systems where breakup and recombination are excluded. The use of an arrangement channel space representation allows an exact decomposition of the N particle density matrix into components for different chemical compositions and an exact definition of reduced species density matrices (as opposed, e.g., to standard projection operator techniques). This necessitates the use of the combinatorially complex arrangement channel BBGKY hierarchy which, however, avoids the need for the usual heuristic specification of collision terms. Another advantage is that scattering equations generated for the reactive and nonreactive many body T matrices appearing in the Boltzmann equations have ‘‘well‐behaved’’ kernels (unlike the corresponding Lippmann–Schwinger equations). From the derived equations we readily obtain, e.g., reaction‐diffusion equations and nonequilibrium expressions for the chemical reaction rates.
TL;DR: In this article, a unified formulation of both transport and fluctuations in a low density nonequilibrium gas is described based on an analysis of a generating functional for fluctuations of the single particle phase space density.
Abstract: A unified formulation of both transport and fluctuations in a low density nonequilibrium gas is described. The method is based on an analysis of a generating functional for fluctuations of the single particle phase space density. It is shown that the first functional derivative obeys an inhomogeneous nonlinear Boltzmann equation, from which the dynamics of multi-space and -time fluctuations may be obtained by suitable functional differentiation. In particular, the equations for two-time and equal time fluctuations are obtained to illustrate the method. In this way, the description of nonequilibrium fluctuations in a low density gas is put on the same theoretical basis as the usual Boltzmann kinetic theory. A hydrodynamic theory of fluctuations also may be derived from the kinetic theory; the procedure and results are indicated.
TL;DR: In this article, a two-state Boltzmann distribution model was proposed to explain the temperature dependence of the thickness of the smectic-A layers observed with polar single-tailed mesogens.
Abstract: Assuming a head to head and side by side association of the molecules, a two-state Boltzmann distribution model is proposed which explains the temperature dependence of the thickness of the smectic-A layers observed with polar single-tailed mesogens.
TL;DR: The covariant partition function method for ideal Boltzmann and Bose gases was developed within quantum field theory as mentioned in this paper, which is a basis to described the statistical and thermodynamical properties of the gases in canonical, grand canonical and pressure ensembles in an arbitrary inertial system.
TL;DR: In this paper, the eigenvalues of the hard sphere Boltzmann collision operator using discrete matrix methods yields discrete eigen values, a large fraction of which are unconverged and lie in th...
Abstract: The calculation of the eigenvalues of the hard sphere Boltzmann collision operator using discrete matrix methods yields discrete eigenvalues, a large fraction of which are unconverged and lie in th...
TL;DR: A numerical analysis of the asymmetric part of electon-electron collision integral is presented in this article, where the results are given in the form of graphs for two commonly considered plasma situations: the collision-dominated case and the field-dominated one.
Abstract: A numerical analysis of the asymmetric part of electon-electron collision integral is presented. The results are given in the form of graphs for two commonly considered plasma situations: the collision-dominated case (symmetric part of electron disribution is Maxwellian) and the field-dominated case (symmetric part of electron distribution is Druyvesteynian). The importance of the asymmetric part of e-e collision integral in the Boltzmann equation is also discussed.
01 Jan 1983
TL;DR: A submitted manuscript is the author's version of the article upon submission and before peer-review as discussed by the authors, and the final published version features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
TL;DR: In this article, an expression for the generation of entropy in the problem of external flow past a body was obtained using the kinetic approach, using the linear Boltzmann equation and the boundary conditions satisfying the reciprocity conditions.
Abstract: Using the kinetic approach, an expression is obtained for the generation of entropy in the problem of external flow past a body. Using the linear Boltzmann equation and the boundary conditions satisfying the reciprocity conditions, the symmetry (the Onsager principle) of the kinetic coefficients in flows is proved.
TL;DR: In this article, the authors look for closed stationary solutions of nonlinear transport equations of the stochastic Boltzmann type in (1+1) dimensions (velocity v and position x).
Abstract: The authors look for closed stationary solutions of nonlinear transport equations of the stochastic Boltzmann type in (1+1) dimensions (velocity v and position x). These solutions, mainly written as the product of an exponential by a polynomial in z=xlambda v2, have the quasi similarity property. As a consequence of their polynomial character, they violate the positivity requirement; however, the authors think that they are the dominant term of infinite series solutions which might have the desired positivity property. Calculations are greatly simplified by using sum rules analogous to conservation of mass and energy.
TL;DR: In this paper, the global solutions of the spatially homogeneous Boltzmann equation, for a classical gas of identical point particles in the presence of an external constant force, are extended to the case of velocity-dependent external forces.
Abstract: A previous result of G. di Blasio, concerning the global solutions of the spatially homogeneous Boltzmann equation, for a classical gas of identical point particles in the presence of an external constant force, is extended to the case of velocity-dependent external forces.
TL;DR: In this article, the stationary solutions of the non-linear Kac model of spatially nonhomogeneous Boltzmann equations are studied and closed quasi-similarity solutions can exist.
TL;DR: In this paper, it is suggested that long-range correlation in a rarefied gas can be described by a hierarchy of generalized Boltzmann equations which, unlike either the Liouville equation or the BBGKY hierarchy, take the rarefaction of the gas into account and are presumably easier to handle.
Abstract: It is suggested that long-range correlation in a rarefied gas can be described by a hierarchy of generalized Boltzmann equations which, unlike either the Liouville equation or the BBGKY hierarchy, take the rarefaction of the gas into account and are presumably easier to handle The equations are postulated, and compatibility criteria for their truncation as well as a class of truncations are proposed The work presented here can be regarded as a further step toward a kinetic theory of turbulence (for rarefied gases) along the lines of Zhigulev and Tsuge
TL;DR: In this paper, the Boltzmann transport equation is used to describe a beam of ions of atomic species 1 (1-atom) bombarding a target modelled as an amorphous mixture of 2-atoms and 3-atom.
Abstract: The Boltzmann transport equation is used to describe a beam of ions of atomic species 1 (1-atoms) bombarding a target modelled as an amorphous mixture of 2-atoms and 3-atoms. In a manner familiar in nuclear reactor theory, the method of characteristics is used to integrate the resulting transport equations. An exact expression for the migration flux J3 of 3-atoms is obtained in closed form. This expression can be evaluated in terms of a power series in a distance parameter s. For the case of slowly varying density N3 of 3-atoms, Fick’s law, relating J3 to the gradient of N3, is derived from this expression; it is given by the lowest order term of the power series. J3 is shown to be proportional to the bombarding flux. Concomittantly, a closed expression for the mixing parameter in Fick’ s law is obtained, which allows a calculation of this quantity for realistic interatomic potentials. A model Kinchin-Pease displacement cascade is proposed, which is expected to allow a reasonable first approximation calculation of the mixing parameter in Fick’s law. It is deduced that the mixing parameter will depend sensitively on the lattice displacement energy. This dependence constitutes a physical mechanism for chemical effect in cascade mixing, as well as for fluence and temperature dependence of cascade mixing.