Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of North Texas, May, 2009. / Title from title page display. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xii, 286 p.; also includes graphics (some col.). Includes bibliographical references (p. 273-286). Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xv, 210 p.; also includes graphics (some col.). Includes bibliographical references (p. 205-210). Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--Ohio State University, 2005. / Title from second page of PDF file. Document formatted into pages; contains xxiii, 151 p.; also includes graphics (some col.). Includes bibliographical references (p. 140-151). Available online via OhioLINK's ETD Center

Thesis (Ph.D.)--York University, 2003. Graduate Programme in Chemistry. / Typescript. Includes bibliographical references. Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ99165

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 338-360).

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Este trabalho à constituÃdo de duas partes. Na primeira parte estudamos mÃnimos nÃo negativos de funcionais elÃpticos degenerados, ∫ F (X, u, ∇u)dX → min, para nÃcleos variacionais F que sÃo descontÃnuos em u com descontinuidade de ordem ~ X{u>0}. A equaÃÃo de Euler-Lagrange à governada por uma equaÃÃo elÃptica degenerada e nÃo-homogÃnea, com fronteira livre entre as fases positiva e zero do mÃnimo. Mostraremos estimativa gradiente Ãtima e nÃo-degenerescÃncia do mÃnimo. TambÃm trataremos de propriedades de regularidade fracas e fortes de fronteira livre. Provaremos que o conjunto {u>0} tem localmente perÃmetro finito e que a fronteira livre reduzida ∂ red {u>0} tem medida Hn-1-total. Para problemas mais especÃficos que aparecem em Jet flows, provaremos que a fronteira livre reduzida à localmente o grÃfico de uma funÃÃo C1,y. Na segunda parte do trabalho forneceremos uma descriÃÃo bastante completa da teoria de regularidade Ãtima para uma famÃlia de problemas de fronteira livre de duas fases, heterogÃneos, y→ min, governados por operadores elÃpticos degenerados e nÃo-lineares. IncluÃdos em tal famÃlia estÃo os problemas de Jet flows heterogÃneos e os problemas de cavidades do tipo Prandtl-Batchelor, y = 0; equaÃÃes elÃpticas degeneradas singulares e sistemas do tipo obstÃculo y =1.VersÃes lineares destes problemas tÃm sido objeto de intensa pesquisa nas Ãltimas quatro dÃcadas ou mais. As contrapartidas nÃo-lineares tratadas neste trabalho introduzem novas e considerÃveis dificuldades, pois a maioria das teorias desenvolvidas anteriormente, tais como fÃrmulas de monotonicidade e de quase monotonicidade nÃo estÃo disponÃveis. Contudo, as soluÃÃes inovadoras desenvolvidas neste trabalho fornecem novas respostas mesmo no contexto clÃssico de equaÃÃes lineares e nÃo-degeneradas. / This work consists of two parts. In the first part we study nonnegative minimizers of general degenerate elliptic functionals, ∫ F (X, u, ∇u)dX → min, for variational kernels F that are discontinuous in ụ with discontinuity of order ~ X{u>0}. The Euler-Lagrange equation is therefore governed by a non-homogeneous, degenerate elliptic equation with free boundary between the positive and the zero phases of the minimizer. We show optimal gradient estimate and nondegeneracy of minima. We also address weak and strong regularity properties of free boundary, ∂ red {u>0}, has H n-1- total measure. For more specific problems that arise in jet flows, we show the reduced free boundary is locally the graph of a C1,y function. In the second part of work we provide a rather complete description of the sharp regularity theory for a family of heterogeneous, two-phase variational free boundary problems, y→ min, ruled by nonlinear, degenerate elliptic operators. Included in such family are heterogeneous jets and cavities problems of Prandtl-Batchelor type, y = 0; singular degenerate elliptic equations and obstacle type systems, y = 1. Linear versions of these problems have been subjects of intense research for the past four decades or so. The nonlinear counterparts treated in this present work introduce substantial new difficulties since the most of the classical theories developed earlier, such that as monotonicity and almost monotonicity formulae, are no longer available. Nonetheless, the innovative solutions designed in this work provide new answers even in the classical context of linear, nondegenerate equations.

Les nanofils semiconducteurs suscitent un vif intérêt tant pour leurs propriétés fondamentales originales que pour leurs applications potentielles en opto- et nano-Électronique. La physique des nanofils et en particulier des matériaux à la base est difficile à caractériser. Dans ce contexte, la simulation numérique peut apporter des réponses quantitatives aux problèmes posés par ces objets et aider à explorer leur potentiel. En particulier, leur cristallisation se fait dans une phase hexagonale wurtzite mais avec des fautes d’empilement qui donnent lieu à des insertions de séquence cubique. La structure cubique blende de zinc a été largement étudiée, les différents aspects physiques des semiconducteurs l’adoptant sont bien illustrés dans la littérature. Par contre, ils sont mal compris en phase wurtzite. C’est pourquoi, l’étude des propriétés structurales et électroniques des cristaux III-V et hétérostructures wurtzite a fait l’objet du présent travail. En particulier, je me suis intéressée à déterminer les paramètres structuraux et électroniques d’ InAs et InP. Pour aborder ces problématiques il convient de trouver une méthode théorique adaptée. Dans ce contexte, les modélisations ab initio permettent d’explorer les propriétés globales sans une connaissance expérimentale à priori des systèmes étudiés. Elles reposent sur la résolution variationnelle de l’équation de Schrödinger qui est lourde d’un point de vue computationnel. Il existe donc toute une hiérarchie de modèles plus ou moins sophistiqués qui approchent plus ou moins la solution exacte du problème. Dans le cadre de ce travail, j’ai utilisé la théorie de la fonctionnelle de la densité qui reproduit les résultats expérimentaux de structures mais peine à évaluer les niveaux énergétiques vides. Cette difficulté est due à la définition des effets à N corps et notamment aux effets de corrélation entre les électrons. L’erreur dans l’évaluation des énergies est corrigée grâce à la correction apportée par l’approximation GW ou les fonctionnelles hybrides. Ainsi, j’ai pu obtenir des structures électroniques correctes et exploitables afin de déterminer les potentiels de déformation. Il est notamment possible de faire varier la composition des nanofils de long de leur axe de croissance afin d’y introduire des jonctions p-N, des boîtes quantiques ou des barrières tunnel. Ces hétérostructures offrent de multiples opportunités : la faisabilité de transistors, de diodes à effet tunnel résonant ou de dispositifs à un électron basés sur les nanofils de silicium ou de III-V a ainsi déjà été démontrée. Ces matériaux permettent de réaliser des hétérostructures inédites car ils peuvent s’accommoder de forts désaccords de maille en déformant leur surface. La relaxation des contraintes structurales a toutefois un impact important sur leurs propriétés électroniques et optiques. Un des paramètres importants pour bien comprendre le comportement de ces structures quantiques est l’offset électronique ou la discontinuité énergétique. Il a été calculé pour le système InAs/InP et confronté à des études expérimentales suivant les directions de croissance. / Semiconductor nanowires are attracting much attention both for their original properties and their potential applications in opto- and nanoelectronics. The physics of nanowires and in particular materials at the base is poorly understood and difficult to characterize. In this context, the numerical simulation can provide quantitative answers to the problems posed by these objects and help to explore their potential. In particular, their crystallization is in a wurtzite (WZ) hexagonal phase but with stacking faults that result in insertions of cubic sequences. The zinc blende structure has been widely studied; the various structural, electronic and optical properties of semiconductor materials adopting this structure are well illustrated and discussed in the literature. On the other side, these properties are poorly understood for WZ. Study of WZ III-V materials and related heterostructures is the subject of this work. In particular, I have simulated the structural and electronic properties of relaxed InAs and InP and under strain condition. ab initio modeling or first principle may explore structural, electronic and dynamics of matter without any experimental prior knowledge. Here, DFT calculations are performed to model the structural and electronic properties of WZ InAs and InP. The error in the evaluation of conduction energy states has been circumvented with the use of GW approximation and hybrid functionals. Finally, I have studied band offset alignment and polarizations effects in InAs/InP WZ system.