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Statistical mechanics theory for gas transport phenomena, obtaining Enskog equation from generalization of Boltzmann equation approximation of Liouville equation
Proton mobility in ice when limited by lattice scattering calculated, using Boltzmann transport equation
Epitaxial layers with varying donor concentration profiles were grown on silicon substrate wafers using chemical vapor deposition (CVD) techniques, and solid state photomultiplier (SSPM) devices were fabricated from the wafers. Representative detectors were tested in a low background photon flux, low temperature environment to determine the device characteristics for comparison to NASA goals for astronomical applications. The SSPM temperatures varied between 6 and 11 K with background fluxes in the range from less than 5 x 10 to the 6th power to 10 to the 13th power photons/square cm per second at wavelengths of 3.2 and 20 cm. Measured parameters included quantum efficiency, dark count rate and bias current. Temperature for optimal performance is 10 K, the highest ever obtained for SSPMs. The devices exhibit a combination of the lowest dark current and highest quantum efficiency yet achieved. Experimental data were reduced, analyzed and used to generate recommendations for future studies. The background and present status of the microscopic theory of SSPM operation were reviewed and summarized. Present emphasis is on modeling of the avalanche process which is the basis for SSPM operation. Approaches to the solution of the Boltzmann transport equation are described and the treatment of electron scattering mechanisms is presented. The microscopic single-electron transport theory is ready to be implemented for large-scale computations.
Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.
Closed form solution for conductivity tensor for magnetic field strength obtained from linearized Boltzmann equation for electron conduction distribution function
The structure of a strong plane shock wave in a monatomic rarefied perfect gas is one of the simplest problems able to be posed in kinetic theory, and one of the hardest to solve. Its simplicity lies in the absence of solid boundaries, geometrical complications, or internal molecular energy. Its difficulty arises from the great departure of the gas from equilibrium within the shock, which invalidates many of the techniques used successfully elsewhere in kinetic theory. In addition to this theoretical challenge, the modern development of ballistics and hypersonic flight has helped to stimulate extensive theoretical and experimental interest in the shock problem. The experimenters in turn have encountered great difficulties on account of the very small physical dimensions of shocks. In fact, until very recently indeed, any close comparisons of theoretical and experimental shock structure results have been rather unprofitable due to the inadequacies of both theory and experiment. During the last few years this situation has been appreciably improved by development of the Monte Carlo method. This allows idealized 'experiments' to be performed on large computers instead of in wind tunnels, using a known intermolecular force law. The most developed of these methods has been shown to be equivalent theoretically to the Boltzmann equation and to give results which agree extremely closely with measurements of high accuracy. Thus Monte Carlo results not only form the soundest basis for our present theoretical knowledge of shock wave structure, but, for purposes of developing other theories, can also be considered a very valuable experimental resource. However, such results remain very expensive to obtain. In this thesis we develop more economical kinetic theory methods for the approximate prediction of shock structure, and compare our results with those of the Monte Carlo method.
Possible initial perturbations development into galaxies with dissipative effects associated with transport processes treated via Boltzmann equation
It is shown that the distribution function assumed by Mott-Smith determines a unique relation between heat flux, stress, and fluid velocity given by q = (3/2) tau u - i.e., it provides a constitutive relation for heat flux, and it also determines a simple expression for the ratio of third-order central moments. These expressions allow the equation of transfer for (C sub x) squared to be cast in a form that yields a nonlinear constitutive relation for stress. The results obtained from the Mott-Smith ansatz are compared with the theory of Baganoff and Nathenson (1970) and results from a numerical solution of the Boltzmann equation for shock-wave structure obtained by Hicks et al. (1972).
The thermalization of particle kinetic motion by binary collisions is considered for a plasma with a Boltzmann constant-temperature product approximately equal to 10 to 100 times the product of the electron mass with the square of the speed of light. At this temperature, the principal mechanism for relaxation of electron motion is via radiationless electron-electron collisions (Moller scattering). Ions are nonrelativistic, but are energetic enough so that their Coulomb scattering can be treated in the Born approximation. Relaxation times are computed and Boltzmann-equation Fokker-Planck operators are derived for the various binary-collision processes. The expression for the rate of kinetic energy exchange between electron and ion gases is derived for the case where the gases are at different temperatures.
An analytical theory is developed for the velocity evolution of nonaccreting planetesimal populations, based on the Boltzmann and Fokker-Planck equations. Adapting Shkarofsky's calculation of plasma viscosities, the rate of increase in random velocities due to gravitational encounters between planetesimals of equal mass is found to be one-third to one-half Safronov's result. Comparison with Wetherill's numerical experiments suggests that the Fokker-Planck equation underestimates the effectiveness of encounters and that Safronov's value is approximately correct. For populations of nonuniform sizes, the Fokker-Planck equation indicates an efficient redistribution of energy from the largest bodies to the smaller ones. By conserving angular momentum, the rate of radial spreading of orbits is also derived.
The relaxation times for electronic excitation due to electron bombardment of atoms was found to be quite short, so that electron kinetic temperature (T sub e) and the electron excitation temperature (T asterisk) should equilibrate quickly whenever electrons are present. However, once equilibrium has been achieved, further energy to the excited electronic states and to the kinetic energy of free electrons must be fed in by collisions with heavy particles that cause vibrational and electronic state transitions. The rate coefficients for excitation of electronic states produced by heavy particle collision have not been well known. However, a relatively simple semi-classical theory has been developed here which is analytic up to the final integration over a Boltzmann distribution of collision energies; this integral can then be evaluated numerically by quadrature. Once the rate coefficients have been determined, the relaxation of electronic excitation energy can be evaluated and compared with the relaxation rates of vibrational excitation. Then the relative importance of these two factors, electronic excitation and vibrational excitation by heavy particle collision, on the transfer of energy to free electron motion, can be assessed.
Collisional theory of longitudinal wave propagation for two fluid viscous ionized plasmas formulated from coupled Maxwell and Boltzmann equations
A simple momentum-transfer theory for the composition dependence of ion mobilities and diffusion coefficients in gas mixtures at arbitrary field strengths is corrected, extended, and compared with a similar theory based on momentum and energy transfer, and with results based on direct solution of the Boltzmann equation by Kihara's method. Final equations are recommended for predicting composition dependences, given only results on ion mobilities and diffusion coefficients in the pure component gases.
Simple momentum-transfer theory for the composition dependence of ion mobilities and diffusion coefficients in gas mixtures at arbitrary field strengths is corrected and extended, and compared with a similar theory based on momentum and energy transfer, and with results based on direct solution of the Boltzmann equation by Kihara's method. Final equations are recommended for predicting composition dependences, given only results on ion mobilities and diffusion coefficients in the pure component gases.
Data related to the development of cosmic rays are discussed. The relationship between cosmic ray production and the steady-state Boltzmann equation is analyzed. The importance of the power-law spectrum, the scattering rate, the theory of shock acceleration, anisotropic instabilities, and cosmic ray diffusion in the formation of cosmic rays is described. It is noted that spacecraft observations at the earth's bow shock are useful for studying cosmic rays and that the data support the collisionless shock-wave theory of cosmic ray origin.
Oseen equations derived for compressible flow by applying small perturbation method and Chapman- Enskog procedure to Bhatnagar-Gross-Krook model of Boltzmann equation
Experimental results are presented for the vibrational relaxation of pure carbon monoxide behind incident shock waves over the temperature range 4000 to 6300 K. The data were obtained as infrared emission from the fundamental and overtone vibrational band systems (in some of the experiments the two-band systems were recorded simultaneously). The data are consistent with present theories for the vibrational relaxation of diatomic molecules and can be interpreted in terms of an initial Boltzmann vibrational distribution relaxing toward final equilibrium via a continuous sequence of intermediate Boltzmann distributions.
This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a three-dimensional viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi's micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.