Ilmenau, Techn. University, Diss., 2005.

Η εν λόγω διπλωματική εργασία έχει ως αντικείμενο μελέτης το ρόλο των διαφόρων συντελεστών μεταφοράς σε συνθήκες ψυχρού πλάσματος, για τη δημιουργία και διάδοση των κυμάτων ιονισμού (streamers), και τον υπολογισμό αυτών των συντελεστών μέσω του λογισμικού επίλυσης της εξισώσεως Boltzmann, καθώς και τη σύγκλιση που παρουσιάζει πειραματικά και θεωρητικά ο υπολογισμός αυτών με τη χρήση του συγκεκριμένου προγράμματος. Εν αρχή παρουσιάζονται κάποιες βασικές έννοιες και στοιχεία σχετικά με τις ηλεκτρικές εκκενώσεις, το πλάσμα και τις αρχές που το διέπουν. Το πλάσμα παράγεται μέσω ηλεκτρικών εκκενώσεων σε αέρια, τα οποία μετατρέπονται σε αγώγιμα μέσα. Με κριτήρια την ηλεκτρονική του θερμοκρασία, πυκνότητα και το βαθμό ιονισμού του το κατατάσσουμε σε ψυχρό, θερμικό και θερμό. Η δημιουργία πλάσματος εξαρτάται από μια πληθώρα παραγόντων, όπως η γεωμετρία του αντιδραστήρα και του διακένου, τα χαρακτηριστικά του αερίου και φυσικά το σύστημα τροφοδοσίας. Οι εφαρμογές του ποικίλλουν, και κυμαίνονται από την παραγωγή Laser, ηλεκτρικής ισχύος μέσω της θερμοπυρηνικής σύντηξης, όζοντος αλλά και την επεξεργασία υλικών και επιφανειών. Ακολουθεί έπειτα μια σύντομη ανάλυση των εξισώσεων Μεταφοράς Boltmann και κατανομής Maxwell-Boltzmann. Παρακάτω ακολουθεί η ανάπτυξη στοιχείων της θεωρίας των ηλεκτρικών εκκενώσεων, όπως αυτών της διάσπασης δια του μηχανισμού Streamer. Εν συνεχεία, αναλύεται ο ρόλος των προγραμμάτων επιλύσεως της εξισώσεως Boltzmann στον υπολογισμό των συντελεστών μεταφοράς και στην αξιόπιστη εξομοίωση των φαινομένων των ηλεκτρικών εκκενώσεων, παρουσιάζεται το λογισμικό επιλύσεως της εξίσωσης Boltzmann, Bolsig+, οι παράμετροι λειτουργίας καθώς και οι δυνατότητες αυτού. Κατόπιν, ακολουθούν σε αντιπαραβολή πειραματικές μετρήσεις με τις αντίστοιχες προβλέψεις του Bolsig+ για ταυτόσημες συνθήκες. Εν κατακλείδι, συνοψίζεται η χρησιμότητα αξιόπιστων προγραμμάτων επίλυσης, όπως το προαναφερθέν καθώς και η βαρύτητα των συντελεστών μεταφοράς στα υπό μελέτη φαινόμενα ηλεκτρικών εκκενώσεων. / The main subject of this thesis is the investigation of the importance and role of the macroscopic coefficients, in cold plasma conditions, in the creation and propagation of streamers and also the calculation of these coefficients through the sollution of the Boltzmann equation, via a Boltzmann equation solver, and their convergence with experimental data. First some fundamental principles ,concerning electric discharges, are presented. Plasma is produced through gas discharges, which become conductive as a result. Depending on their electronic temperature, density and ionization degree the plasmas are categorized as cold, thermal and thermonuclear. The creation of plasma depends on a number of factors, such as the reactor's and the gap's geometry, the nature of the gas and the power system. Its applications vary, ranging from Lasers, production of electric power through nuclear fusion, ozone production to the processing of materials and surfaces. A brief analysis of Boltzmann's Distribution Law and Boltzmann's Transport equation follows, while the fundamental principles of gas discharges, such as the streamer mechanism, are also presented. In addition to the above, the specific method for the numerical solution of the Boltzmann equation used by the Boltzmann solvers, such as BOLSIG+, is thoroughly analyzed. The importance of the equation's solution is further explained, as are the natural processes and mechanisms that lead to the creation and propagation of the streamer phenomenon. Moreover, several calculations of the macroscopic coefficients, through experimental data and their respective models are presented in comparison to calculations of the same coefficients through the solution of Boltzmann's Transport equation. Finally, the necessity for reliable and fast Boltzmann equation solvers is summarized, as well as the gravity of the transport coefficients in the investigation and analysis of gas discharges, such as streamers.

No description available.

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / This investigation is concerned with the evaluation and interpretation of the propagator, or conditional probability distribution function P(y,t| y0), of the Linear Boltzmann or Master equation from the "central limit viewpoint". We have obtained what is to our knowledge the first evaluation in series of the propagator for the typical kinetic-theoretical processes studied here, which are those underlying the problems usually studied in the approximation of the Fokker-Planck equation. We have been able to put the successive terms of this series in closed form; and have shown that the series can be interpreted as a generalized solution of the central limit problem of mathematical probability theory, the generalization consisting in the extension to a process in continuous time with non-independent increments. [TRUNCATED] / 2031-01-01

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The differential-operator approximation to the linear Boltzmann operator (the Master equation operator) has been studied by several authors. In 1960 Siegel proposed a systematic approach called the CD expansion. He represents the approximating series in terms of creation and destruction operators for Hermite functions. In this thesis we study the physical meaning of a small parameter which usually exists in the CD expansion and which ensures the convergence of the series. We also establish the CD-expansion formalism for N-dimensional processes and initiate the study of the CD-expansion of the linear Boltzmann collision operator in the kinetic theory of gases. In the case of one-dimensional processes; the models we study are the density fluctuations with a particle reservoir of finite volume, Alkemade's diode model, and Rayleigh disk. We find that the expansion parameter is the ratio of the average microscopic agitation interval to the macroscopic relaxation time. We further prove that this ratio is equal to the ratio of the average variance of the discontinuity of the random process determined by the linear. Boltzmann operator to the variance of the macroscopic observable at equilibrium. Since the CD expansion is an expansion with respect to the parameter of discontinuity, the expansion series reduces to the Fokker-Planck operator in the limiting case where the parameter becomes zero. In the N-dimensional formalism, we use tensor Hermite polynomials and find a formalism valid for processes of any finite dimensionality. In extending the study to the kinetic theory of gases, we establish a method of obtaining derivate moments directly from the collision operator, and obtain a formula for the Hermite coefficients of derivate moments for an arbitrary force field. We propose the CD hypothesis: The terms of the CD expansion are homogeneous and of successively increasing order in the parameter of discontinuity of the process. This hypothesis I holds for all the models we study in the one-dimension case. In three-dimensional collision processes it holds for an intermolecular force field obeying an inverse power law and for rigid spheres. Beyond these cases, the necessary and sufficient conditions for the hypothesis are rather complicated. A sufficient condition is, however, that the scattering cylinder (scattering cross section multiplied by the magnitude of the relative velocity) be a homogeneous function of the magnitude of the relative velocity. In addition to the general results mentioned in the above, we obtain a number of particular results. Special cases of our density fluctuation model are the density fluctuations studied by van Kampen (1961), and Ehrenfest's urn model. We also introduce an isotropic Maxwellian particle which corresponds to s-wave scattering in wave mechanics, and which yields the CD expansion in a diagonal form. / 2031-01-01

Thesis (M.S.)--University of Wyoming, 2008. / Title from PDF title page (viewed on August 3, 2009). Includes bibliographical references (p. 65-68).

In this study, the applicability of the Lattice Boltzmann Method to neutron transport is investigated. The transport model used, is derived from the Boltzmann equation for neutral particles by inverting the streaming operator and casting the integral transport equation into an operator form. From the operator equation, an iterative solution to the transport problem is presented, with the first collision source as the starting point for the iteration scheme. One of the main features of the method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. A full description of the discretization scheme is given along with the iterative procedure and quadrature set used for the angular discretization. To mitigate lattice ray effects, an angular refinement scheme is introduced to increase the angular coverage of the problem phase space. The method is then applied to a model problem to investigate its applicability to neutron transport. Three cases are considered where constant, linear and exponential interpolants are used to account for the accumulation of flux due to the streaming of particles between nodes. The results obtained are compared to a reference solution, that was calculated by using the MCNP code and to the values calculated using a nodal SN method. Finally, areas of improvement are identified and possible extensions to the algorithm are provided. / Thesis (MIng (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013

In this study, the applicability of the Lattice Boltzmann Method to neutron transport is investigated. The transport model used, is derived from the Boltzmann equation for neutral particles by inverting the streaming operator and casting the integral transport equation into an operator form. From the operator equation, an iterative solution to the transport problem is presented, with the first collision source as the starting point for the iteration scheme. One of the main features of the method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. A full description of the discretization scheme is given along with the iterative procedure and quadrature set used for the angular discretization. To mitigate lattice ray effects, an angular refinement scheme is introduced to increase the angular coverage of the problem phase space. The method is then applied to a model problem to investigate its applicability to neutron transport. Three cases are considered where constant, linear and exponential interpolants are used to account for the accumulation of flux due to the streaming of particles between nodes. The results obtained are compared to a reference solution, that was calculated by using the MCNP code and to the values calculated using a nodal SN method. Finally, areas of improvement are identified and possible extensions to the algorithm are provided. / Thesis (MIng (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013

Thesis (M. S.)--Paper Science Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Aidun, Cyrus; Committee Member: Graham, Samuel; Committee Member: Joshi, Yogendra. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Bielefeld, University, Diss., 2003.