Ye Mao. / "May 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 116-123). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Wang Hui Ying. / "June 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 67-72). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-07-17T12:51:37Z No. of bitstreams: 1 Pericles Carvalho.pdf: 1223900 bytes, checksum: f4ce61e56294f3bb3b3e192efa2993f2 (MD5) / Made available in DSpace on 2017-07-17T12:52:05Z (GMT). No. of bitstreams: 1 Pericles Carvalho.pdf: 1223900 bytes, checksum: f4ce61e56294f3bb3b3e192efa2993f2 (MD5) Previous issue date: 2017-05-02 / This paper begins with the definition of SRB measures, and the introduction of several concepts in ergodic theory necessary for the development of the presented results. We prove the existence and uniqueness of SRB measures for uniformly expanding transformations in compact connected manifolds whose Jacobian is H¨older continuous. Then, we present the definition of hyperbolic sets, hyperbolic attractors and their respective fundamental properties. As a main result, we prove the existence of SRB measures for hyperbolic attractors contained in compact manifolds, and its uniqueness if the hyperbolic attractor is transitive. First, it is shown the existence of invariant measures absolutely continuous along the unstable foliation. Then, we note that the restriction of this measure over certain subsets have the SRB property. Using the transitivity of the hyperbolic attractor, it is shown that there exists a unique subset such that this restriction is an SRB measure. We conclude that the system supports a unique SRB measure. / Este trabalho inicia-se com a definição de medida SRB, e a apresentação de diversos conceitos da teoria ergódica importantes para o desenvolvimento dos resultados apresentados. É demonstrada a existência e unicidade de medidas SRB para transformações expansoras em variedades compactas e conexas cujo jacobiano é Holder. Em seguida, apresenta-se a definição de conjuntos hiperbólicos, atratores hiperbólicos e suas respectivas propriedades fundamentais. Como resultado principal, é demonstrada a existência de medidas SRB para atratores hiperbólicos, bem como sua unicidade para o caso de atratores hiperbólicos transitivos, ambos dentro de variedades compactas. Primeiramente, é mostrado que existem medidas invariantes absolutamente contínuas ao longo da folheação instável. Em seguida, verifica-se que a restrição desta medida sob determinados conjuntos possuem a propriedade SRB. Utilizando a transitividade do atrator hiperbólico, mostra-se que existe um único conjunto tal que esta restrição seja uma medida SRB. Conclui-se que o sistema admite uma única medida SRB.

Analisam-se a variação de parâmetros obtidos da curva tensão-deformação dos solos, interpretada como uma hipérbole, em função dos parâmetros de compactação obtidos da curva de compactação Proctor Normal. Esta análise é feita em três solos típicos. / The variation of the parameters obtained by the stress-strain curve of the soils, understood as a hyperbola is analysed in function of the compactation parameters obtained from the Proctor Compactation Curve. This analysis is made with three typical soils.

On compact Riemann surfaces, the Laplacian $\Delta$ has a discrete, non-negative spectrum of eigenvalues $\{\lambda_{i}\}$ of finite multiplicity. The spectrum is intrinsically linked to the geometry of the surface. In this work, we consider surfaces of constant negative curvature with a large symmetry group. It is not possible to explicitly calculate the eigenvalues for surfaces in this class, so we combine group theoretic and analytical methods to derive results about the spectrum. In particular, we focus on the Bolza surface and the Klein quartic. These have the highest order symmetry groups among compact Riemann surfaces of genera 2 and 3 respectively. The full automorphism group of the Bolza surface is isomorphic to $\mathrm{GL}_{2}(\mathbb{Z}_{3})\rtimes\mathbb{Z}_{2}. We analyze the irreducible representations of this group and prove that the multiplicity of $\lambda_{1}$ is 3, building on the work of Jenni, and identify the irreducible representation that corresponds to this eigenspace. This proof relies on a certain conjecture, for which we give substantial numerical evidence and a hopeful method for proving. We go on to show that $\lambda_{2}$ has multiplicity 4.

Dans cette thèse, nous étudions le couplage électron-phonon dans le graphène, et en particulier l’influence du substrat. Il s’agit de quantifier par des mesures opto-électroniques le couplage des électrons avec les modes de phonons du substrat, que ce soit les modes de phonons polaritons de surface (SPP) pour les substrats isotropes comme le SiO2 ou les modes de phonons polaritons hyperboliques pour les substrats fortement anisotropes comme le h-BN. Pour ce faire, nous commençons par une revue générale du couplage électron-phonon dans le graphène avant de détailler les différentes méthodes expérimentales utilisées durant la thèse. Puis, nous détaillons les différents régimes de couplage pour un échantillon de graphène sur SiO2 et nous mettons en évidence la nécessité d’étudier des substrats ultra-propres. Nous présentons enfin les résultats obtenus pour un échantillon de graphène sur h-BN dans lequel nous mettons en évidence, en plus du couplage aux HPP,un régime de couplage nouveau qui consiste en l’émission de phonons-polaritons hyperboliques dans un régime d’effet tunnel Zener-Klein / In this thesis we study the electron-phonon coupling in graphene and in particular theinfluence of the substrate in the aforementioned coupling. We want to quantify by optoelectronicalmeasurements the coupling between the phonon modes of the substrate. It might be the couplingwith Surface Phonon Polaritons (SPPs) in case of isotropic substrates as SiO2 or Hyperbolic PhononPolaritons (HPPs) in case of highly anisotropic substrates. We start by a review about the state of theart on electron phonon coupling in graphene. Then we introduce the different experimental methodsused during this thesis. We present experimental results on an graphene on SiO2 sample. We identifythe different coupling regimes and point out the necessity of working on ultra clean samples toinvestigate the high energy regimes. Finally we prensent experimental results on a graphene on BNsample where we identify a new coupling regime consisting in HPP emission in a Zener-Klein transportregime

Under adequate conditions on $g$, we show the density in $L^2((0,\pi),(0,2\pi))$ of the set of functions $p$ for which \begin{equation*} u_{tt}(x,t)-u_{xx}(x,t)= g(u(x,t)) + p(x,t) \end{equation*} has a weak solution subject to \begin{equation*} \begin{aligned} u(x,t)&=u(x,t+2\pi)\\ u(0,t)&=u(\pi,t)=0. \end{aligned} \end{equation*} To achieve this, we prove a Saddle Point Principle by means of a refined variant of the deformation lemma of Rabinowitz. Generally, inf-sup techniques allow the characterization of critical values by taking the minimum of the maximae on some particular class of sets. In this version of the Saddle Point Principle, we introduce sufficient conditions for the existence of a saddle-structure which is not restricted to finite-dimensional subspaces.

This thesis examines the Euler equations of gas dynamics and develops a new adaption indicator, which is based on the weak local residual measured for the non- conservative pressure variable. We demonstrate that the proposed indicator is capable of automatically detecting discontinuities and distinguishing between the shock and contact waves when they are isolated from each other. We use the developed indi- cator to design a scheme adaption algorithm, according to which nonlinear limiters are used only in the vicinity of shocks. The new adaption algorithm is realized using a second-order limited scheme and a high-order nonlimited central-upwind scheme. Robustness and high resolution of the designed method is shown on a number of one- and two-dimensional numerical examples. / acase@tulane.edu

Numerical schemes for the partial differential equations used to characterize stiffly forced conservation laws are constructed and analyzed. Partial differential equations of this form are found in many physical applications including modeling gas dynamics, fluid flow, and combustion. Many difficulties arise when trying to approximate solutions to stiffly forced conservation laws numerically. Some of these numerical difficulties are investigated. A new class of numerical schemes is developed to overcome some of these problems. The numerical schemes are constructed using an infinite sequence of conservation laws. Restrictions are given on the schemes that guarantee they maintain a uniform bound and satisfy an entropy condition. For schemes meeting these criteria, a proof is given of convergence to the correct physical solution of the conservation law. Numerical examples are presented to illustrate the theoretical results.

In this thesis a method for direct evaluation of Generalized B-splines (GB-splines) via the representation of these curves as piecewise functions is presented. A local structure is introduced that makes the GB-spline curves more amenable to the integration used in constructing bases of higher degree. This basis is used to perform direct computation of piecewise representation of GB-spline bases and curves. Algorithms for refinement using these local structures are also developed.