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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
31

Família de aplicações bilhares geradas pelo fluxo de curvatura / Family of billiards maps generated by curvature flow

Damasceno, Josué Geraldo, 1975- 12 July 2011 (has links)
Orientadores: Mário Jorge Dias Carneiro, Marco Antonio Teixeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T10:54:43Z (GMT). No. of bitstreams: 1 Damasceno_JosueGeraldo_D.pdf: 1045427 bytes, checksum: 2cb1e5f51924e8667d69ad7267aeaa4e (MD5) Previous issue date: 2011 / Resumo: Descrevemos algumas propriedades dinâmicas de uma família de aplicações bilhares sobre curvas convexas (ovais) as quais são deformadas pelo fluxo de curvatura. Quando a mesa se deforma, a razão entre as curvaturas mínima e máxima converge a 1 e por um resultado clássico de Gage e Hamilton, depois de uma normalização, as curvas tendem a um círculo. Como conseqüência, a região de Lazutkin, isto é, a região que contém cáusticas convexas, cresce gradualmente. Descreveremos algumas bifurcações dinâmicas nesse processo, em particular, descreveremos o que acontece com a família de órbitas de período dois e as órbitas "zig-zag" / Abstract: We describe some dynamical properties of one parameter families of billiards on convex curves (ovals) which are deformed by the curvature flow. As the billiard table deforms, the ratio between minimal and maximal curvature converges to 1 and by a classical result of Gage and Hamilton [GH], after a normalization, the curves tend to a circle. As a consequence, the Lazutkin region, i.e. the region that contains convex caustics, gradually increases. We describe some dynamical bifurcations in this process, in particular, we describe what happens with the family of period two orbits and the "zig-zag"orbits / Doutorado / Matematica / Doutor em Matemática
32

Comptage d'orbites périodiques dans le modèle de windtree / Counting problem on wind-tree models

Pardo, Angel 22 June 2017 (has links)
Le problème du cercle de Gauss consiste à compter le nombre de points entiers de longueur bornée dans le plan. Autrement dit, compter le nombre de géodésiques fermées de longueur bornée sur un tore plat bidimensionnel. De très nombreux problèmes de comptage en systèmes dynamiques se sont inspirés de ce problème. Depuis 30 ans, on cherche à comprendre l’asymptotique de géodésiques fermées dans les surfaces de translation. H. Masur a montré que ce nombre a une croissance quadratique. Calculer l’asymptotique quadratique (constante de Siegel–Veech) est un sujet de recherches très actif aujourd’hui. L’objet d’étude de cette thèse est le modèle de windtree, un modèle de billard non compact. Dans le cas classique, on place des obstacles rectangulaires identiques dans le plan en chaque point entier. On joue au billard sur le complémentaire. Nous montrons que le nombre de trajectoires périodiques a une croissance asymptotique quadratique et calculons la constante de Siegel–Veech pour le windtree classique ainsi que pour la généralisation de Delecroix– Zorich. Nous prouvons que, pour le windtree classique, cette constante ne dépend pas des tailles des obstacles (phénomène “non varying” analogue aux résultats de Chen–Möller). Enfin, lorsque la surface de translation compacte sous-jacente est une surface de Veech, nous donnons une version quantitative du comptage. / The Gauss circle problem consists in counting the number of integer points of bounded length in the plane. In other words, counting the number of closed geodesics of bounded length on a flat two dimensional torus. Many counting problems in dynamical systems have been inspired by this problem. For 30 years, the experts try to understand the asymptotic behavior of closed geodesics in translation surfaces. H. Masur proved that this number has quadratic growth rate. Compute the quadratic asymptotic (Siegel–Veech constant) is a very active research domain these days. The object of study in this thesis is the wind-tree model, a non-compact billiard model. In the classical setting, we place identical rectangular obstacles in the plane at each integer point. We play billiard on the complement. We show that the number of periodic trajectories has quadratic asymptotic growth rate and we compute the Siegel–Veech constant for the classical wind-tree model as well as for the Delecroix–Zorich variant. We prove that, for the classical wind-tree model, this constant does not depend on the dimensions of the obstacles (non-varying phenomenon, analogous to results of Chen–Möller). Finally, when the underlying compact translation surface is a Veech surface, we give a quantitative version of the counting.
33

Chaotic electron transport in semiconductor devices

Scannell, William Christian, 1970- 06 1900 (has links)
xix, 171 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / The field of quantum chaos investigates the quantum mechanical behavior of classically chaotic systems. This dissertation begins by describing an experiment conducted on an apparatus constructed to represent a three dimensional analog of a classically chaotic system. Patterns of reflected light are shown to produce fractals, and the behavior of the fractal dimension D F is shown to depend on the light's ability to escape the apparatus. The classically chaotic system is then used to investigate the conductance properties of semiconductor heterostructures engineered to produce a conducting plane relatively free of impurities and defects. Introducing walls that inhibit conduction to partition off sections considerably smaller than the mean distance between impurities defines devices called 'billiards'. Cooling to low temperatures enables the electrons traveling through the billiard to maintain quantum mechanical phase. Exposure to a changing electric or magnetic field alters the electron's phase, leading to fluctuations in the conductance through the billiard. Magnetoconductance fluctuations in billiards have previously been shown to be fractal. This behavior has been charted using an empirical parameter, Q , that is a measure of the resolution of the energy levels within the billiard. The relationship with Q is shown to extend beyond the ballistic regime into the 'quasi-ballistic' and 'diffusive' regimes, characterized by having defects within the conduction plane. A model analogous to the classically chaotic system is proposed as the origin of the fractal conductance fluctuations. This model is shown to be consistent with experiment and to account for changes of fine scale features in MCF known to occur when a billiard is brought to room temperature between low temperature measurements. An experiment is conducted in which fractal conductance fluctuations (FCF) are produced by exposing a billiard to a changing electric field. Comparison of D F values of FCF produced by electric fields is made to FCF produced by magnetic fields. FCF with high D F values are shown to de-correlate at smaller increments of field than the FCF with lower D F values. This indicates that FCF may be used as a novel sensor of external fields, so the response of FCF to high bias voltages is investigated. / Adviser: Stephen Kevan, Chairperson, Physics; Richard Taylor, Advisor, Physics; Robert Zimmerman, Member, Physics; Stephen Gregory, Member, Physics; David Johnson, Outside Member, Chemistry
34

Estudo da dinâmica de caos no gás tridimensional de elétrons de alta mobilidade / Study of the dynamics of chaos in three-dimensional gas in electron of high mobility

Nilo Mauricio Sotomayor Choque 12 September 2002 (has links)
A dinêmica caótica, em arranjos de bilhares eletrônicos bidimensionais e tridimensionais , em heteroestruturas semicondutoras de AlxGa1-xAs/GaAs foi estudada tanto de forma experimental como através de simulações numéricas. Como primeira parte, a dinâmica eletrônica caótica em super-redes de antipontos bidimensionais foi tratada sob a influência de campo magnético uniforme aplicado de forma pararela ao plano do gás de elétrons. Nestas circunstâncias, a anisotropia do contorno de Fermi do gás bidimensional de elétrons produzida pelo campo magnético pararelo, distorce fortemente a forma das trajetórias eletrônicas induzindo mudanças drásticas nas oscilações de comensurabilidade da magnetoresistência na região de campo fraco, em temperaturas criogênicas. Como segunda parte, arranjos de bilhares eletrônicos tridimensionais foram realizadas, pela primeira vez, através da gravação de super-redes retangulares de buracos mecânicos cilíndricos em poços quânticos parabólicos, os quais contêm o gás tridimensional de elétrons de alta mobilidade. Medidas de resistividade nestes sistemas revelam a presença de picos anomalos na região de campo fraco, em forma similar às medições em sistemas de antipontos bidimensionais. Foi calculada a dinâmica eletrônica do bilhar tridimensional analisando -se a evolução das trajetórias no espaço de fases através das seções espaciais de Poincaré. Calculou-se também a magnetoresistência pxx do gás tridimensional através da teoria de resposta linear, encontrando-se que a presença de ressonância não lineares é refletida nos picos anômalos observados. A realização destes sistemas permitiu o estudo de fenômenos físicos novos como as oscilações de comensurabilidade em sistemas tridimensionais e os efeitos de tamanho galvano-magnéticos devido às ressonâncias geométricas. / The chaotic electron dynamics in two-dimensional and three-dimensional arrays of elec­ tron billiards in ALx Ga1-xAs/GaAs semiconductor heterostructures has been studied in experimental way and also through numerical simulations. As a first part, the chaotic electron dynamics in two-dimensional antidot super-lattices has been studied under the influence of a uniform magnetic field applied in parallel configuration related to the plane of the electron gas. In this case, the Fermi contour anisotropy of the two-dimensional elec­ tron gas induced by the parallel field highly distorts the shape of the electron trajectories inducing pronounced changes in the commensurability peaks of the low field magnetoresis­ tance, in cryogenic temperatures. In the second part, arrays of three dimensional electron billiards were obtained, by first time, through the patterning of rectangular super-lattices of cylindrical voids in ALx Ga1-xAs/GaAs parabolic quantum wells containing a high mo­ bility three-dimensional electron gas. Resistivity measurements in these systems reveal anomalous peaks in the low magnetic field region in similar way as measurements in two-dimensional antidots systems. The electron dynamics of the three-dimensional bil­ liard was calculated, analyzing the evolution of trajectories in phase space by means of Poincaré space of sections. The magnetoresistance xx of the three-dimensional electron gas was calculated through linear responde theory, being found that nonlinear resonances are reflected in the observed anomalous peaks. The accomplishment os these systems allowed the study of new physical phenomena such as the commensurability oscillations in three-dimensional systems and size-effects due to geometrical resonances.
35

Estudo da dinâmica de caos no gás tridimensional de elétrons de alta mobilidade / Study of the dynamics of chaos in three-dimensional gas in electron of high mobility

Choque, Nilo Mauricio Sotomayor 12 September 2002 (has links)
A dinêmica caótica, em arranjos de bilhares eletrônicos bidimensionais e tridimensionais , em heteroestruturas semicondutoras de AlxGa1-xAs/GaAs foi estudada tanto de forma experimental como através de simulações numéricas. Como primeira parte, a dinâmica eletrônica caótica em super-redes de antipontos bidimensionais foi tratada sob a influência de campo magnético uniforme aplicado de forma pararela ao plano do gás de elétrons. Nestas circunstâncias, a anisotropia do contorno de Fermi do gás bidimensional de elétrons produzida pelo campo magnético pararelo, distorce fortemente a forma das trajetórias eletrônicas induzindo mudanças drásticas nas oscilações de comensurabilidade da magnetoresistência na região de campo fraco, em temperaturas criogênicas. Como segunda parte, arranjos de bilhares eletrônicos tridimensionais foram realizadas, pela primeira vez, através da gravação de super-redes retangulares de buracos mecânicos cilíndricos em poços quânticos parabólicos, os quais contêm o gás tridimensional de elétrons de alta mobilidade. Medidas de resistividade nestes sistemas revelam a presença de picos anomalos na região de campo fraco, em forma similar às medições em sistemas de antipontos bidimensionais. Foi calculada a dinâmica eletrônica do bilhar tridimensional analisando -se a evolução das trajetórias no espaço de fases através das seções espaciais de Poincaré. Calculou-se também a magnetoresistência pxx do gás tridimensional através da teoria de resposta linear, encontrando-se que a presença de ressonância não lineares é refletida nos picos anômalos observados. A realização destes sistemas permitiu o estudo de fenômenos físicos novos como as oscilações de comensurabilidade em sistemas tridimensionais e os efeitos de tamanho galvano-magnéticos devido às ressonâncias geométricas. / The chaotic electron dynamics in two-dimensional and three-dimensional arrays of elec­ tron billiards in ALx Ga1-xAs/GaAs semiconductor heterostructures has been studied in experimental way and also through numerical simulations. As a first part, the chaotic electron dynamics in two-dimensional antidot super-lattices has been studied under the influence of a uniform magnetic field applied in parallel configuration related to the plane of the electron gas. In this case, the Fermi contour anisotropy of the two-dimensional elec­ tron gas induced by the parallel field highly distorts the shape of the electron trajectories inducing pronounced changes in the commensurability peaks of the low field magnetoresis­ tance, in cryogenic temperatures. In the second part, arrays of three dimensional electron billiards were obtained, by first time, through the patterning of rectangular super-lattices of cylindrical voids in ALx Ga1-xAs/GaAs parabolic quantum wells containing a high mo­ bility three-dimensional electron gas. Resistivity measurements in these systems reveal anomalous peaks in the low magnetic field region in similar way as measurements in two-dimensional antidots systems. The electron dynamics of the three-dimensional bil­ liard was calculated, analyzing the evolution of trajectories in phase space by means of Poincaré space of sections. The magnetoresistance xx of the three-dimensional electron gas was calculated through linear responde theory, being found that nonlinear resonances are reflected in the observed anomalous peaks. The accomplishment os these systems allowed the study of new physical phenomena such as the commensurability oscillations in three-dimensional systems and size-effects due to geometrical resonances.
36

Combinatoire et dynamique du flot de Teichmüller

Delecroix, Vincent 16 November 2011 (has links)
Ce travail de thèse porte sur la dynamique du flot linéaire des surfaces de translation et de sa renormalisation par le flot de Teichmüller introduite par H. Masur et W. Veech en 1982. Une version combinatoire de cette renormalisation, l'induction de Rauzy sur les échanges d'intervalles, fût introduite auparavant par G. Rauzy en 1979. D'une part, nous faisons une étude combinatoire des classes de Rauzy qui forment une partition de l'ensemble des permutations irréductibles et interviennent dans l'algorithme d'induction de Rauzy. Nous donnons une formule pour la cardinalité de chaque classe. D'autre part, nous étudions un modèle de billard infini périodique dans le plan appelé le "vent dans les arbres" introduit dans une version stochastique par P. et T. Ehrenfest en 1912 et par J. Hardy et J. Weber en 1980 dans la version périodique. Nous construisons une famille de directions pour lesquelles le flot du billard est divergent donnant ainsi des exemples de Z^2-cocycles divergents au-dessus d'échanges d'intervalles. De plus, nous démontrons que le taux polynomial de diffusion générique est 2/3 autrement dit que la distance maximale atteinte par une particule au temps t est de l'ordre de t^2/3. / In this thesis, we study the dynamics of the linear flow of translation surfaces and its renormalization by the Teichmüller flow introduced by H. Masur and W. Veech in 1982. A combinatorial version of the renormalization, the Rauzy induction on interval exchange transformations, was introduced by G. Rauzy in 1979. First of all, we consider the combinatorics of Rauzy classes which form a partition of the set of irreducible permutations and are part of the Rauzy induction. In a second time, we consider an infinite Z^2-periodic billiard in the plane called the wind-tree model. It was introduced in a stochastic version by P. and T. Ehrenfest in 1912 and in the periodic version by J. Hardy and J. Weber in 1980. We construct a family of directions for which the flow of the billiard is divergent and hence give examples of divergent Z^2-cocycles over interval exchange transformations. Moreover, we prove that the polynomial rate of diffusion is generically 2/3. In other words, the maximal distance reached by a particule below time t has the order of t^2/3.

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