Theory of the positive column of a gas discharge

An attempt is made to provide a theoretical explanation of the effect of the positive column on the voltage-current characteristic of a glow or an arc discharge. Such theories have been developed before, and all are based on balancing the production and loss of charged particles and accounting for the energy supplied to the plasma by the applied electric field. Differences among the theories arise from the approximations and omissions made in selecting processes that affect the particle and energy balances. This work is primarily concerned with the deviation from the ambipolar description of the positive column caused by space charge, electron-ion volume recombination, and temperature inhomogeneities.

The presentation is divided into three parts, the first of which involved the derivation of the final macroscopic equations from kinetic theory. The final equations are obtained by taking the first three moments of the Boltzmann equation for each of the three species in the plasma. Although the method used and the equations obtained are not novel, the derivation is carried out in detail in order to appraise the validity of numerous approximations and to justify the use of data from other sources. The equations are applied to a molecular hydrogen discharge contained between parallel walls. The applied electric field is parallel to the walls, and the dependent variables—electron and ion flux to the walls, electron and ion densities, transverse electric field, and gas temperature—vary only in the direction perpendicular to the walls. The mathematical description is given by a sixth-order nonlinear two-point boundary value problem which contains the applied field as a parameter. The amount of neutral gas and its temperature at the walls are held fixed, and the relation between the applied field and the electron density at the center of the discharge is obtained in the process of solving the problem. This relation corresponds to that between current and voltage and is used to interpret the effect of space charge, recombination, and temperature inhomogeneities on the voltage-current characteristic of the discharge.

The complete solution of the equations is impractical both numerically and analytically, and in Part II the gas temperature is assumed uniform so as to focus on the combined effects of space charge and recombination. The terms representing these effects are treated as perturbations to equations that would otherwise describe the ambipolar situation. However, the term representing space charge is not negligible in a thin boundary layer or sheath near the walls, and consequently the perturbation problem is singular. Separate solutions must be obtained in the sheath and in the main region of the discharge, and the relation between the electron density and the applied field is not determined until these solutions are matched.

In Part III the electron and ion densities are assumed equal, and the complicated space-charge calculation is thereby replaced by the ambipolar description. Recombination and temperature inhomogeneities are both important at high values of the electron density. However, the formulation of the problem permits a comparison of the relative effects, and temperature inhomogeneities are shown to be important at lower values of the electron density than recombination. The equations are solved by a direct numerical integration and by treating the term representing temperature inhomogeneities as a perturbation.

The conclusions reached in the study are primarily concerned with the association of the relation between electron density and axial field with the voltage-current characteristic. It is known that the effect of space charge can account for the subnormal glow discharge and that the normal glow corresponds to a close approach to an ambipolar situation. The effect of temperature inhomogeneities helps explain the decreasing characteristic of the arc, and the effect of recombination is not expected to appear except at very high electron densities.

Eigenvalue problems associated with Korn's inequalities in the theory of elasticity

Interest in the possible applications of a priori inequalities in linear elasticity theory motivated the present investigation. Korn's inequality under various side conditions is considered, with emphasis on the Korn's constant. In the "second case" of Korn's inequality, a variational approach leads to an eigenvalue problem; it is shown that, for simply-connected two-dimensional regions, the problem of determining the spectrum of this eigenvalue problem is equivalent to finding the values of Poisson's ratio for which the displacement boundary-value problem of linear homogeneous isotropic elastostatics has a non-unique solution.

Previous work on the uniqueness and non-uniqueness issue for the latter problem is examined and the results applied to the spectrum of the Korn eigenvalue problem. In this way, further information on the Korn constant for general regions is obtained.

A generalization of the "main case" of Korn's inequality is introduced and the associated eigenvalue problem is a gain related to the displacement boundary-value problem of linear elastostatics in two dimensions.

The complex angular momentum theory of the production of three particles in collisions of two strongly interacting particles at high energy

The problem of the continuation to complex values of the angular momentum of the partial wave amplitude is examined for the simplest production process, that of two particles → three particles. The presence of so-called "anomalous singularities" complicates the procedure followed relative to that used for quasi two-body scattering amplitudes. The anomalous singularities are shown to lead to exchange degenerate amplitudes with possible poles in much the same way as "normal" singularities lead to the usual signatured amplitudes. The resulting exchange-degenerate trajectories would also be expected to occur in two-body amplitudes.

The representation of the production amplitude in terms of the singularities of the partial wave amplitude is then developed and applied to the high energy region, with attention being paid to the emergence of "double Regge" terms. Certain new results are obtained for the behavior of the amplitude at zero momentum transfer, and some predictions of polarization and minima in momentum transfer distributions are made. A calculation of the polarization of the ρ^o meson in the reaction π ^- p → π ^- ρ^op at high energy with small momentum transfer to the proton is compared with data taken at 25 Gev by W. D. Walker and collaborators. The result is favorable, although limited by the statistics of the available data.

I. The effect of droplet solidification upon two-phase flow in a rocket nozzle. II. A kinetic theory investigation of some condensation-evaporation phenomena by a moment method

Part I:

The perturbation technique developed by Rannie and Marble is used to study the effect of droplet solidification upon two-phase flow in a rocket nozzle. It is shown that under certain conditions an equilibrium flow exists, where the gas and particle phases have the same velocity and temperature at each section of the nozzle. The flow is divided into three regions: the first region, where the particles are all in the form of liquid droplets; a second region, over which the droplets solidify at constant freezing temperature; and a third region, where the particles are all solid. By a perturbation about the equilibrium flow, a solution is obtained for small particle slip velocities using the Stokes drag law and the corresponding approximation for heat transfer between the particle and gas phases. Singular perturbation procedure is required to handle the problem at points where solidification first starts and where it is complete. The effects of solidification are noticeable.

Part II:

When a liquid surface, in contact with only its pure vapor, is not in the thermodynamic equilibrium with it, a net condensation or evaporation of fluid occurs. This phenomenon is studied from a kinetic theory viewpoint by means of moment method developed by Lees. The evaporation-condensation rate is calculated for a spherical droplet and for a liquid sheet, when the temperatures and pressures are not too far removed from their equilibrium values. The solutions are valid for the whole range of Knudsen numbers from the free molecule to the continuum limit. In the continuum limit, the mass flux rate is proportional to the pressure difference alone.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

Estimating reflectivity values from wind turbines for analyzing the potential impact on weather radar services

Locate full-text(opens in a new window)|View at Publisher| Export | Download | More... Atmospheric Measurement Techniques Volume 8, Issue 5, 27 May 2015, Pages 2183-2193 Estimating reflectivity values from wind turbines for analyzing the potential impact on weather radar services (Article) Angulo, I.a, Grande, O.a, Jenn, D.b, Guerra, D.a, De La Vega, D.a a University of the Basque Country (UPV/EHU), Bilbao, Spain b Naval Postgraduate School, Monterey, United States View references (28) Abstract The World Meteorological Organization (WMO) has repeatedly expressed concern over the increasing number of impact cases of wind turbine farms on weather radars. Current signal processing techniques to mitigate wind turbine clutter (WTC) are scarce, so the most practical approach to this issue is the assessment of the potential interference from a wind farm before it is installed. To do so, and in order to obtain a WTC reflectivity model, it is crucial to estimate the radar cross section (RCS) of the wind turbines to be built, which represents the power percentage of the radar signal that is backscattered to the radar receiver.

For the proposed model, a representative scenario has been chosen in which both the weather radar and the wind farm are placed on clear areas; i.e., wind turbines are supposed to be illuminated only by the lowest elevation angles of the radar beam.

This paper first characterizes the RCS of wind turbines in the weather radar frequency bands by means of computer simulations based on the physical optics theory and then proposes a simplified model to estimate wind turbine RCS values. This model is of great help in the evaluation of the potential impact of a certain wind farm on the weather radar operation.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.

Correcting the systematic error of the density functional theory calculation: the alternate combination approach of genetic algorithm and neural network

The alternate combinational approach of genetic algorithm and neural network (AGANN) has been presented to correct the systematic error of the density functional theory (DFT) calculation. It treats the DFT as a black box and models the error through external statistical information. As a demonstration, the AGANN method has been applied in the correction of the lattice energies from the DFT calculation for 72 metal halides and hydrides. Through the AGANN correction, the mean absolute value of the relative errors of the calculated lattice energies to the experimental values decreases from 4.93% to 1.20% in the testing set. For comparison, the neural network approach reduces the mean value to 2.56%. And for the common combinational approach of genetic algorithm and neural network, the value drops to 2.15%. The multiple linear regression method almost has no correction effect here.

Mandarin speech emotion recognition based on high dimensional geometry theory

In this paper, a novel approach for mandarin speech emotion recognition, that is mandarin speech emotion recognition based on high dimensional geometry theory, is proposed. The human emotions are classified into 6 archetypal classes: fear, anger, happiness, sadness, surprise and disgust. According to the characteristics of these emotional speech signals, the amplitude, pitch frequency and formant are used as the feature parameters for speech emotion recognition. The new method called high dimensional geometry theory is applied for recognition. Compared with traditional GSVM model, the new method has some advantages. It is noted that this method has significant values for researches and applications henceforth.

Applicability of the reaction window theory

Based on the molecular Coulombic over barrier model for description of slow ion-atom collisions, the reaction window theory related to projectile velocity is presented briefly. According to the theory, the state-selective differential cross sections of single electron capture in O8+ -H, A(8+) -H, Ar8+-He, Ne10+-He and Ar18+-He collisions at different collision velocities are calculated and compared with experimental results. Calculations are also done for single, double, and triple electron capture in N-15(7+)-Ne collisions at fixed velocity of 0.53 a.u., and are compared with experimental data. It is found that the predictions of the final electronic state distribution of captured electron(s) are in agreement with experimental data, and both theory and experiments show that the widths of the reaction window increase with the projectile velocity. The differential cross sections predicted by the theory are larger for smaller Q-values, vice versa, when compared with experimental data.

Calculations of cross sections of resonant two-photon transitions to the second excited 4f5d state in Pr3+: Y3Al5O12 using density matrix theory

The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in cm(4)s Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 x 10(-50) cm(4)s which is very close to the previous experimental value 4 x 10(-50) cm(4) s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.

Phase-separation behavior of the system PES/phenoxy: An application of the Sanchez-Lacombe lattice fluid theory

Cloud-point curves reported for the system polyethersulfone (PES)/phenoxy were calculated by means of the Sanchez-Lacombe (SL) lattice fluid theory. The one adjustable parameter epsilon(12)*/k (quantifying the interaction energy between mers of the different components) can be evaluated by comparison of the theoretical and experimental phase diagrams. The Flory-Huggins (FH) interaction parameters are computed based on the evaluated epsilon(12)*/k and are approximately a linear function of volume fraction and of inverse temperature. The calculated enthalpies of mixing of PES/phenoxy blends for different compositions are consistent with the experimental values obtained previously by Singh and Walsh [1].

Thermodynamics of blends of poly(ethylene oxide) with poly(methyl methacrylate) and poly(vinyl acetate): prediction of miscibility based on Flory solution theory modified by Hamada

Flory solution theory modified by Hamada et al. (Macromolecules, 1980, 13, 729) was used to predict the miscibility of blends of poly(ethylene oxide) with poly(methyl methacrylate) (PEO-aPMMA) and with poly(vinyl acetate) (PEO-PVAc). Interaction parameters of a PEO-aPMMA blend with the weight ratio of PEO/aPMMA = 50/50 at the temperature range of 393-433 K and PEO-PVAc blends with different compositions and temperatures were calculated from the determined equation-of-state parameters based on Flory solution theory modified by Hamada ed al. Results show that interaction parameters of the PEO-aPMMA blend are negative and can be comparable with values obtained from neutron-scattering measurements by Ito et al. (Macromolecules, 1987, 20, 2213). Also, interaction parameters and excess volumes of PEO-PVAc blends are negative and increase with enhancing the content of PEO and the temperature. (C) 1998 Elsevier Science Ltd. All rights reserved.

The application of the MPB4 theory to the interface between between two immiscible electrolyte solutions .4. The differential capacitance of the water/nitrobenzene interface in the presence of 2:2 electrolyte

We have developed a new theoretical model based on the MPB4 theory to calculate the differential capacitance of the interface of 0.05mol/L MgSO4 in water and 0.1mol/L TBATPB in nitrobenzene. Our results coincide with the experimental values very well. It indicates that our model may describe well the structure of ITIES not only in the presence of 1:1 electrolyte but also in the presence of 2:2 electrolyte.