Nonuniform Gases Research Articles

The ω-absorption line distribution function for rank correlated SLW model prediction of radiative transfer in non-uniform gases

Unlike previous global methods, the recently developed Rank Correlated Spectral Line Weighted-sum-of-gray-gases (RC-SLW) model does not require specification of a reference gas thermodynamic state from which all other states are corrected using a correlated spectrum assumption. However, the RC-SLW approach still requires specification of an arbitrary blackbody source temperature to generate the Absorption Line Blackbody Distribution Function (ALBDF) used in construction of the spectral model. This paper reports on the development of a universal RC-SLW model that eliminates the need for the specification of a blackbody source temperature. The approach replaces the ALBDF with a new spectral distribution function, herein termed the ω-Absorption Line Distribution Function (ω-ALDF), and is based on a new spectral weighting function instead of the Planck blackbody distribution function. The ω-ALDF presented here depends only on the local gas thermodynamic state, and does not involve the blackbody source temperature used in the ALBDF. The new weighting function is determined using the well-established ALBDF, avoiding the need to generate a radically new distribution function database from the detailed gas absorption cross-section data. The ω-ALDF based RC-SLW model thus requires no user-specified parameters (no reference thermodynamic state and no blackbody source temperature). Further, only minor modification of the conventional RC-SLW model is needed to implement the new approach. Development of this new distribution function is only possible within the theoretical framework of the Rank Correlated SLW model. This work presents the theoretical development of the ω-ALDF, and demonstrates the use and accuracy of this new universal RC-SLW model.

Surface plasmon polaritons enhanced random lasing and weak localization of light in un- and ZnSe-coated Nd3+ doped (Pb,La)(Zr,Ti)O3 ceramics

In this work, we demonstrated the formation of nonuniform two-dimensional electron gases (2DEGs) with visible surface plasmon polaritons' (SPPs) supportiveness in un- and ZnSe-coated Nd3+ doped (Pb,La)(Zr,Ti)O3 ceramics (Nd:PLZT), and its enhancement effect on random lasing and weak localization of light. Firstly, charge density distribution in the modified ZnSe film was calculated, revealing the formation of nonuniform 2DEGs, namely, a very thin metallized layer. In bulk samples, the excitation of SPPs contributes to the transformation from conventional lasing to random lasing, as evidenced by the dynamics. The optical whisper-gallery-like pattern was observed in a cylinder shaped Nd:PLZT, demonstrating convincingly SPPs propagating along the border owing to the polarity discontinuity. Based on this, Nd:PLZT was processed into powdered forms to increase the surface-volume ratio. Furthermore, the powdered specimen was coated with ZnSe film to further strengthen plasmonic impact. A 7.6 × enhancement in random lasing at 589 nm and three-fold reduction in threshold of weak localization of light at 684 nm were observed in the ZnSe/Nd:PLZT, by comparing to the bare Nd:PLZT. This work opens an avenue leading to SPPs’ implementation without any metal parts involved and hence presents a promising candidate for serving as nanolaser for nanophotonic circuits.

Improvement of osteogenesis by a uniform PCL coating on a magnesium screw for biodegradable applications

A polymer coating as polycaprolactone (PCL) is applied to improve the initial corrosion resistance of biodegradable magnesium. In addition, plasma electrolytic oxidation (PEO) is performed to increase adhesion between the polymer and the metal. However, when a complex-shaped material such as a screw is implanted in a bone, the surface coatings are locally damaged, and the protective role of the coating is not sufficiently maintained. In this study, the optimal conditions for producing a polymer coating on a screw were determined by varying the concentration of the PCL and the coating cycles, and were examined in vitro and in vivo. Among various the PCL coating conditions of 2∼6 cycles with 5∼7 wt.% concentrations, the 6 wt.% + 4 cycles group was applied uniformly to the screw thread. In the case of the non-uniform PCL layers, oxides and gases were present between the Mg and the PCL layer because internal magnesium corrosion and the layer peel off. The 6 wt.% + 4 cycles group had a high corrosion resistance due to the low wear on the thread. Denser and thicker bone formed around the PCL-coated screw in rat femur. This difference was due to the high corrosion resistance, which provided sufficient time for bone healing and promoting new bone growth.

An analysis of the symmetry issue in the ℓ-distribution method of gas radiation in non-uniform gaseous media

The recently proposed ℓ-distribution/ICE (Iterative Copula Evaluation) method of gas radiation suffers from symmetry issues when applied in highly non-isothermal and non-homogeneous gaseous media. This problem is studied in a detailed theoretical way. The objective of the present paper is: 1/to provide a mathematical analysis of this problem of symmetry and, 2/to suggest a decisive factor, defined in terms of the ratio between the narrow band Planck and Rosseland mean absorption coefficients, to handle this issue. Comparisons of model predictions with reference LBL calculations show that the proposed criterion improves the accuracy of the intuitive ICE method for applications in highly non-uniform gases at high temperatures.

Two-color absorption spectroscopy strategy for measuring the column density and path average temperature of the absorbing species in nonuniform gases

A two-color absorption spectroscopy strategy has been developed for measuring the column density and density-weighted path-average temperature of the absorbing species in nonuniform gases. This strategy uses two transitions with strengths that scale nearly linearly with temperature. In addition, measured lineshapes are used to accurately model absorbance spectra. As a result, the column density and density-weighted path-average temperature of the absorbing species can be inferred from a comparison of signals measured across a nonuniform line of sight (LOS) with simulated signals calculated using a uniform LOS. This strategy is demonstrated with simulations of water-vapor absorption across a nonuniform LOS with temperature and composition gradients comparable to those in hydrogen-air diffusion flames. In this demonstration, both the column density and density-weighted path-average temperature of water vapor are recovered to within 0.5%.

Dynamic behavior of non-uniform granular gases system with the fractal characteristic in one dimension

A one-dimensional dynamic model of polydisperse granular mixture with a power-law size distribution is presented, in which the particles are subject to inelastic mutual collisions and driven by Gaussian white noise. The particle size distribution of the mixture has the fractal characteristic, and a fractal dimension D as a measurement of the inhomogeneity of the particle size distribution is introduced. We define the global granular temperature and the kinetic pressure of the mixture, and obtain their expressions. By molecular dynamics simulations, we have mainly investigated how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the steady-state dynamic properties of the system, focusing on the global granular temperature, kinetic pressure, velocity distribution and distribution of interparticle spacing. Some novel results are found that, with the increase of the fractal dimension D, the global granular temperature and the kinetic pressure decrease, the velocity distribution deviates more obviously from the Gaussian one and the particles cluster more pronouncedly at the same value of the restitution coefficient e (0< e<1). On the other hand, as the restitution coefficient e decreases, the dynamic behavior has the similar evolution as above at the fixed fractal dimension D. The dynamic behavior changing with e and D is, respectively, presented.

Transport coefficients for binary Yukawa mixtures: theory and molecular dynamic simulations

We present the generalization to the binary Yukawa mixture of equilibrium molecular dynamic computations of the transport coefficients of the Yukawa one-component plasma (Salin and Caillol 2002 Phys. Rev. Lett. 88 065002, Salin and Caillol 2000 J. Chem. Phys. 113 10459–63). The simulations were performed within periodic boundary conditions, and Ewald sums were implemented for the potentials, the forces and for all the currents which enter the Kubo formulae. Results include shear and bulk viscosities, ionic thermal conductivity, as in the one-component case, but also diffusion and interdiffusion coefficients. We will present the different coefficients and examples of simulations. We shall also compare our simulation results for large screening parameters with Chapman–Enskog theory (Chapman and Cowling 1970 The Mathematical Theory of Non-Uniform Gases 3rd edn (Cambridge: Cambridge University Press)).

Kinetic approach to one-dimensional non-uniform granular gases

We present a model of polydisperse granular mixture with a power-law size distribution subjected to Brownian forces. The driven inelastic mixture which has n components can be regarded as 'granular gas'. The stationary state where the mixture reaches is the result of the balance between the dissipation and random forces which inject energies. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time tau of the driving Brownian process is greater than the mean collision time tau(c), the velocity probability distribution strongly deviates from the Gaussian one and the system has a strong spatial clustering. We define the partial granular temperature and the global granular temperature of the multi-component mixture. The partial granular temperature is the average kinetic energy per particle of the same component and the global one is the statistic average value per partial granular temperature of the mixture. One of the most useful properties of the temperature, i.e., the independence from the thermal substance, is lost. We introduce a fractal dimension D as a measurement of the inhomogeneity of the size distribution of the mixture. Our simulations represent that the deviation and clusterization become more and more pronounced with the increasing value of the fractal dimension D. The global granular temperature decreases, and dissipated energy per particle increases as D augments.

Effect of electric fields on electron thermal transport in laser-produced plasmas

Gradients in the laser-induced electric field introduce ponderomotive terms in the current flow, heat flux, and electric stress tensor. The transport coefficients, previously derived in the limit Z≫1, are obtained for an arbitrary ion charge Z using the Chapman–Enskog method [S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1970)]. It is shown that the ponderomotive terms significantly modify the thermal transport near the laser turning points and the critical surface.

A simple transport theory of non-uniform gases

Transport phenomena in non-uniform gases are studied with the diffusion velocity defined according to momentum conservation. Instead of using the Maxwellian-Boltzmann distribution function, the mass weighted transport fluxes are evaluated with the partial velocity introduced. The modified Eucken correction may be derived from the simple theory. The new algorithms obtained may be used to calculate the transport coefficients in terms of molecular structure, without considering the intermolecular forces or potentials. The agreements with experiments are generally good for the gases with weak or no polar momenta.

Damping in dilute Bose gases: A mean-field approach

Damping in a dilute Bose gas is investigated using a mean-field approximation which describes the coupled oscillations of condensate and non-condensate atoms in the collisionless regime. Explicit results for both Landau and Beliaev damping rates are given for non-uniform gases. In the case of uniform systems we obtain results for the damping of phonons both at zero and finite temperature. The isothermal compressibility of a uniform gas is also discussed.

Vortex formation in sheared flow driven fluctuations in nonuniform magnetized dusty gases

The linear and nonlinear properties of low-frequency (in comparison with the ion gyrofrequency) electrostatic and electromagnetic waves in nonuniform, magnetized dusty plasmas with sheared plasma flows are examined. For this purpose, the multifluid dusty plasma model is employed to derive the relevant nonlinear equations for the modified dust-convective cells as well as for the coupled dust Alfv\'en waves and dust-convective cells. In the linear limit, we obtain dispersion relations which exhibit instabilities of both the electrostatic and electromagnetic waves. In the nonlinear case, it is shown that the newly derived dynamical equations for weakly coupled waves admit various types of vortex solutions. The results can have relevance to the understanding of the salient features of nonthermal fluctuations and coherent vortex structures in nonuniform dusty magnetoplasmas such as those in the Earth's ionosphere as well as in cometary tails and interstellar clouds.

Landau damping in dilute Bose gases

Landau damping in weakly interacting Bose gases is investigated by means of perturbation theory. Our approach points out the crucial role played by Bose-Einstein condensation and yields an explicit expression for the decay rate of elementary excitations in both uniform and non-uniform gases. Systematic results are derived for the phonon width in homogeneous gases interacting with repulsive forces. Special attention is given to the low and high temperature regimes.

Energy-diffusion calculation of the electron-swarm distribution function.

An approximate treatment of the Boltzmann collision integral for electrons in a gas, valid for small fractional average energy loss, is studied. It is essentially a Fokker-Planck expansion in energy space, including mean energy loss (dynamical friction) and energy straggling (coefficient of diffusion). When applied to electron swarms in weakly ionized gases, treating angle variables in the two-term Legendre series, there results a useful, physically meaningful, differential equation for the time evolution of the energy spectrum in a time-dependent electric field. Elastic scattering, and inelastic and superelastic energy-transfer collisions are included. The time-independent solution in a constant field is a simple approximate expression for the steady-state energy spectrum of swarm electrons. The physical meaning of its functional form is made clear by showing its relation to ordinary diffusion-convection theory. Previous spectra by Pidduck [Proc. R. Soc. London Ser. A 88, 296 (1913); Proc. London Math. Soc. 15, 89 (1916); Q. J. Math. 7, 199 (1936)]; Druyvesteyn [Physica 10, 61 (1930)]; Davydov [Phys. Z. Sowjetunion 8, 59 (1935)]; Morse, Allis, and Lamar [Phys. Rev. 48, 412 (1935)]; Chapman and Cowling [The Mathematical Theory of Non-Uniform Gases, 2nd ed. (Cambridge University Press, Cambridge, 1952), p. 350]; and Wannier [Am. J. Phys. 39, 281 (1971)] are special cases.The reasons for the inadequacy of the continuous-slowing-down approximation (CSDA) become apparent. The new spectrum is exact in the limit of small quantum transition energies. It is further shown that the CSDA violates detailed balance. Consequences of detailed balance on the loss function and related functions are investigated, and the Boltzmann H theorem is studied. During non-steady-state behavior, collisions may increase or decrease the swarm entropy, but the effect of the electric field is always to increase entropy. The spectrum is used with experimental cross sections to compute transport coefficients in ${\mathrm{O}}_{2}$ and ${\mathrm{N}}_{2}$, in both of which fractional average energy loss is acceptably small over most energy ranges. Agreement with compiled swarm data is excellent over more than four orders of magnitude in E/N for most coefficients, except at certain energies in ${\mathrm{N}}_{2}$ that strain the approximation's validity. In the absence of an electric field, the inclusion of energy straggling provides a treatment of spectral relaxation valid for arbitrary energies that is an improvement over common mean-stopping-power formulas.

Kinetic theory of field effects in nonuniform molecular gases

Effects of magnetic and electric fields on transport phenomena in dilute polyatomic gases are reviewed within the framework of first order Enskog theory. The established technique of approximate operator inversion is used to give first order approximations of the transport coefficients. Instead of the customary expansion of polarization into orthogonal polynomials a more general treatment is chosen here so as to accomodate recent experimental observations. The polarizations produced by macroscopic fluxes are assumed to be eigenfunctions of the collision operator within the subspace of functions anisotropic in angular momentum. The formalism is extended to mixtures in a way to let the final expressions assume the same form as for pure gases. The obtained transport coefficients obey several symmetry relations and inequalities. Additional inequalities are now also derived for the matrix describing the saturated field effects.

Intermolecular Forces: Their Origin and Determination

Introduction Theoretical calculation of intermolecular forces Gas imperfections Molecular collisions The kinetic theory of non-uniform dilute gases The transport properties of gases and intermolecular forces Spectroscopic measurements Condensed phases Intermolecular forces: The present position Appendices Substance index Index.

Techniques for producing uniform linear filamentary laser sparks

Experimental techniques are discussed for producing uniform linear filamentary laser sparks suitable for use as an imaging probe of nonuniform gases and other applications. A new technique is described which is based on controlling the laser flux as the breakdown front propagates through a focus. Several methods of initiating the filaments are described.

The G schemes of approximations to the thermal diffusion factors of Lorentzian and non-Lorentzian mixtures

In the Chapman–Enskog mathematical theory of nonuniform gases, the thermal diffusion factors are found from the solution of an infinite set of linear equations. Two methods of obtaining successive approximations to the solution of these equations have been developed, one by Chapman and Cowling, and the other by Kihara. The Kihara method is somewhat difficult to exactly interpret since it is too much based on a peculiar model, the so-called Maxwellian one. On the other hand, it is well known that the Chapman–Cowling series of approximation exhibits a rather poor convergence. So, a new scheme of approximation has been recently introduced in order to interpret plasma measurements previously reported. This scheme (the so-called G scheme) has been first developed in an almost-Lorentzian mixture, a situation too particular to make it really interesting unless it could be generalized and used for non-Lorentzian mixtures. This paper is concerned with such a generalization. The two first approximations to the thermal diffusion factors in an He/K gaseous mixture in the Chapman–Cowling and in the G schemes are computed, and results are discussed. The advantages of the G schemes are pointed out.

A simple theory of the motion of small particles suspended in nonuniform gases.

A simple theory of the motion of small particles suspended in nonuniform gases.

The Linearized Boltzmann Collision Operator for Cut-Off Potentials

Previous article Next article The Linearized Boltzmann Collision Operator for Cut-Off PotentialsHans Birger DrangeHans Birger Drangehttps://doi.org/10.1137/0129054PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractBoundedness and compactness of integral operators arising from the linearized Boltzmann collision operator are investigated for a wide class of angular and radial cut-off potentials.[1] C. Cercignani, On Boltzmann equation with cut-off potentials, Phys. Fluids, 10 (1967), 2097–2104 10.1063/1.1762004 CrossrefISIGoogle Scholar[2] Sydney Chapman and , T. G. Cowling, The mathematical theory of non-uniform gases. An account of the kinetic theory of viscosity, thermal conduction and diffusion in gases, Third edition, prepared in co-operation with D. Burnett, Cambridge University Press, London, 1970xxiv+423 MR0258399 Google Scholar[3] Harold Grad, J. A. Laurmann, Asymptotic theory of the Boltzmann equation. IIRarefied Gas Dynamics (Proc. 3rd Internat. Sympos., Palais de l'UNESCO, Paris, 1962), Vol. I, Academic Press, New York, 1963, 26–59 MR0156656 Google Scholar[4] G. H. Hardy, , J. E. Littlewood and , G. Pólya, Inequalities, Cambridge University Press, London, 1967 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Convergence Analysis of Grad's Hermite Expansion for Linear Kinetic EquationsNeeraj Sarna, Jan Giesselmann, and Manuel TorrilhonSIAM Journal on Numerical Analysis, Vol. 58, No. 2 | 13 April 2020AbstractPDF (762 KB)Spectral Properties of the Linearized Boltzmann Operator in L p for 1≤p≤∞Journal of Statistical Physics, Vol. 153, No. 6 | 7 November 2013 Cross Ref On the Relativistic BGK-Boltzmann Model: Asymptotics and HydrodynamicsJournal of Statistical Physics, Vol. 149, No. 2 | 26 September 2012 Cross Ref The Linearized Collision OperatorMathematical Methods in Kinetic Theory | 1 Jan 1990 Cross Ref Stationary solutions of the non-linear Boltzmann equation in a bounded spatial domainMathematical Methods in the Applied Sciences, Vol. 11, No. 4 | 1 Jul 1989 Cross Ref On the linearized relativistic Boltzmann equationCommunications in Mathematical Physics, Vol. 115, No. 4 | 1 Dec 1988 Cross Ref Existence and Uniqueness Theorems for the Boltzmann EquationKinetic Theory and Gas Dynamics | 1 Jan 1988 Cross Ref Existence problems of the non-linear Boltzmann equationTrends and Applications of Pure Mathematics to Mechanics | 3 June 2005 Cross Ref On the Boltzmann Equation with External ForcesHans Birger DrangeSIAM Journal on Applied Mathematics, Vol. 34, No. 3 | 12 July 2006AbstractPDF (1500 KB) Volume 29, Issue 4| 1975SIAM Journal on Applied Mathematics571-787 History Submitted:26 November 1973Published online:12 July 2006 InformationCopyright © 1975 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0129054Article page range:pp. 665-676ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics