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Call number: LD2668 .T4 1960 M55

We prove the existence of a one-parameter family of solutions of the porous medium equation, a nonlinear heat equation. In our work, with space dimension 3, the interface is a half line whose end point advances at constant speed. We prove, by using maximum principle, that the solutions are stable under a suitable class of perturbations. We discuss the relevance of our solutions, when restricted to two dimensions, to gravity driven flows of thin films. Here we extend the results of J. Iaia and S. Betelu in the paper "Solutions of the porous medium equation with degenerate interfaces" to a higher dimension.

Graduation date: 1997

In this thesis, we study nonlinear partial differential equations arising from image processing and cheomotaxis. We analyze mathematical models in conservative form from the perspective of traveling wave solutions. We show the existence and the stability of traveling wave solutions in the models, which helps to understand the behaviors of solutions in the models. The thesis largely consists of two parts: (1) We develop stability analysis for a traveling wave solution of a nonlinear conservation law arising from image processing. To be specific, we prove that if the initial perturbation between a solution and a traveling wave solution to the problem is small, the solution converges to the traveling wave solution.To show this, we construct a weight function in establishing energy estimates to overcome difficulties caused by the absence of the convexity of a flux of the conservation law. (2) We develop dynamical systems theory to study traveling wave solutions in a chemotaxis model. A traveling wave solution to the model in a partial differential equation is a heteroclinic/homoclinic orbit to the model in an ordinary differential equation. Thus, we investigate the existence and non-existence of a heteroclinic/homoclinic orbit in certain ranges of parameters in the model by applying dynamical systems theory.

Thesis (M.S.)--University of Wisconsin--Madison, 1965. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 101-104.

This thesis describes the design of two particular types of conventional distributed amplifiers and treats a proposed split-band amplifier. The method used for the conventional designs is an iterative synthesis process developed at Stanford University in 1952. The objective was to investigate the possibility of producing distributed amplifiers of superior performance. Only amplifiers with a flat amplitude response were considered since the calculating equipment available was inadequate for the computations involved in producing amplifiers with other types of response characteristics. Three designs of one form of conventional distributed amplifier were carried out. These were amplifiers with ladder networks for delay lines and with both delay lines identical except for a possible difference in impedance level. None of the three amplifiers had theoretical characteristics which justified an attempt to construct them. The other conventional amplifier was one employing ladder-like networks for the delay lines with each of the lines symmetrical about the mid-point of its length and with both lines identical except for a possible difference in impedance level. An attempt to design one of these amplifiers produced new information beyond that reported in the original work at Stanford University. Furthermore, when using the iterative technique to design this amplifier, there seemed to be reasonable doubt as to whether or not the process was always convergent. No definite opinion on the matter was formulated since it would have required that the calculations be continued through more cycles of iteration than could reasonably be carried out with the computing equipment at hand. Finally, a proposed split-band amplifier was investigated and its theoretical gain-bandwidth characteristics were compared with those of a conventional distributed amplifier. It showed a slight advantage, but this was far outweighed by certain serious inherent disadvantages and the project was discontinued. The investigation has shown that it is impractical to carry out the calculations involved in the iterative prodecure when using a hand calculator. Also, some doubt as to the general convergence of the iterative synthesis process has been raised. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

O presente trabalho descreve os processos de preparação do aluminato de bário e cálcio, material emissor de elétrons, empregados nos catodos do tipo impregnado para utilização em uma válvula de microondas do tipo TWT. Os catodos investigados constituem-se de uma pastilha de tungstênio porosa impregnada com aluminato de bário e cálcio com proporção molar 5:3:2. Para a síntese do aluminato, utilizaram-se três diferentes métodos: reação em estado sólido, precipitação e cristalização. A termogravimetria auxiliou na consolidação dos procedimentos de preparação dos aluminatos de modo a definir os parâmetros de pirólise/calcinação. Verificou-se que a técnica que apresentou melhores características de síntese foi o método da cristalização, pois esta apresentou uma menor temperatura de formação do aluminato (800ºC) em atmosfera oxidante (O2), quando comparada às técnicas de reação em estado sólido e de precipitação (temperatura de 1000ºC em atmosfera redutora – H2). Utilizou-se o conceito da distribuição da função trabalho prática (PWFD) de Miram para a caracterização termiônica dos catodos impregnados. Empregando-se este método, foi possível traçar o perfil termiônico do catodo com aluminato de bário e cálcio. As curvas PWFD apresentaram a função trabalho média do catodo aluminato de, aproximadamente, 2,00 eV. / In the present work it is described the barium calcium aluminate manufacture processes employed to produce impregnated cathodes to be used in a traveling-wave tube (TWT). The cathodes were developed using a tungsten body impregnated with barium and calcium aluminate with a 5:3:2 proportion (molar). Three different processes were investigated to obtain this material: solid-state reaction, precipitation and crystallization. Thermal analysis, thermogravimetry specifically, supported to determine an adequate preparation procedure (taking into account temperature, time and pirolisys atmosphere). It was verified that the crystallization showed a better result when compared to those investigated (solid-state reaction and precipitation techniques – formation temperature is about 1000ºC in hydrogen atmosphere), whereas it presented the lower formation temperature (800ºC) in oxidizing atmosphere (O2). It was used the practical work function distribution theory (PWFD) of Miram to characterize thermionic impregnated cathode. The PWFD curves were used to characterize the barium-calcium aluminate cathode. PWFD curves shown that the aluminate cathode work function is about 2,00 eV.

O presente trabalho descreve os processos de preparação do aluminato de bário e cálcio, material emissor de elétrons, empregados nos catodos do tipo impregnado para utilização em uma válvula de microondas do tipo TWT. Os catodos investigados constituem-se de uma pastilha de tungstênio porosa impregnada com aluminato de bário e cálcio com proporção molar 5:3:2. Para a síntese do aluminato, utilizaram-se três diferentes métodos: reação em estado sólido, precipitação e cristalização. A termogravimetria auxiliou na consolidação dos procedimentos de preparação dos aluminatos de modo a definir os parâmetros de pirólise/calcinação. Verificou-se que a técnica que apresentou melhores características de síntese foi o método da cristalização, pois esta apresentou uma menor temperatura de formação do aluminato (800ºC) em atmosfera oxidante (O2), quando comparada às técnicas de reação em estado sólido e de precipitação (temperatura de 1000ºC em atmosfera redutora – H2). Utilizou-se o conceito da distribuição da função trabalho prática (PWFD) de Miram para a caracterização termiônica dos catodos impregnados. Empregando-se este método, foi possível traçar o perfil termiônico do catodo com aluminato de bário e cálcio. As curvas PWFD apresentaram a função trabalho média do catodo aluminato de, aproximadamente, 2,00 eV. / In the present work it is described the barium calcium aluminate manufacture processes employed to produce impregnated cathodes to be used in a traveling-wave tube (TWT). The cathodes were developed using a tungsten body impregnated with barium and calcium aluminate with a 5:3:2 proportion (molar). Three different processes were investigated to obtain this material: solid-state reaction, precipitation and crystallization. Thermal analysis, thermogravimetry specifically, supported to determine an adequate preparation procedure (taking into account temperature, time and pirolisys atmosphere). It was verified that the crystallization showed a better result when compared to those investigated (solid-state reaction and precipitation techniques – formation temperature is about 1000ºC in hydrogen atmosphere), whereas it presented the lower formation temperature (800ºC) in oxidizing atmosphere (O2). It was used the practical work function distribution theory (PWFD) of Miram to characterize thermionic impregnated cathode. The PWFD curves were used to characterize the barium-calcium aluminate cathode. PWFD curves shown that the aluminate cathode work function is about 2,00 eV.

Charles Edward Muehe, Jr. / "October 16, 1952." "This report is based on a thesis submitted to the Department of Electrical Engineering, M.I.T. ... August 1952." / Bibliography: p. 38. / Army Signal Corps Contract DA36-039 sc-100 Project 8-102B-0 Dept. of the Army Project 3-99-10-022