Includes bibliographical references (p. 81).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 93-94). Available also in a digital version from Dissertation Abstracts.

Real space renormalisation group scaling techniques are used to investigate the static critical behaviour of the pure and dilute, classical, anisotropic Heisenberg model. Transfer matrix methods are employed to obtain asymptotically exact expressions for the correlation lengths and susceptibilities of the one-dimensional system. The resulting scaling relationships are combined with an approximate bond moving scheme to treat pure and dilute models in higher dimensionalities. Detailed discussions are given for the dependence of correlation lengths and susceptibilities on temperature, anisotropy and concentration, and fcr the critical temperature on anisotropy and concentration. Particular emphasis is given to the weakly anisotropic system near percolation threshold and comparisons are made between the results of the present analysis and those of neutron-scattering experiments on dilute quasi-two- and three-dimensional systems.

Made available in DSpace on 2014-10-09T12:53:11Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:59:02Z (GMT). No. of bitstreams: 0 / Dissertação (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Made available in DSpace on 2014-10-09T12:53:11Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:59:02Z (GMT). No. of bitstreams: 0 / A avaliação metrológica da incerteza da medição, apesar de estar normalizada internacionalmente (ISO-GUM, 1995) desde a metade dos anos 90, só agora está se popularizando nas indústrias, nas escolas técnicas e de engenharia. Em algumas áreas, como na metrologia dimensional, está avançada e em outras, como na medição de variáveis de processos industriais tais como vazão, pressão e temperatura, ainda está numa fase intermediara. Um dos principais entraves para essa popularização é a falta de padronização da nomenclatura nas especificações técnicas dos instrumentos de medição, onde se declara a incerteza, por exemplo, de 1% de ?acurácia? sem definir se é percentual da leitura, da faixa calibrada ou da faixa máxima. Ou ainda, sem definir se a probabilidade de abrangência é 68, 95 ou 99,7%. Esse trabalho entra nesse cenário com a pretensão de clarificar e simplificar esses conceitos, começando pelo histórico da evolução do pensamento que transformou a incerteza numa variável quantitativa com sua avaliação efetuada de uma maneira padronizada e internacionalmente aceita. Em seguida é feita uma descrição conceitual sucinta do método ISO-GUM e também é desvendado o intrincado jogo de palavras e fórmulas das declarações de incertezas dos fabricantes de instrumentos de medição. Com o domínio desses conceitos, partimos para efetuar dois exemplos numéricos de avaliação metrológica de incertezas na medição de vazão, usando um conjuntos de fórmulas semelhantes Ás publicadas por renomados fabricantes de instrumentos de medição. No primeiro exemplo usando a medição de vazão por pressão diferencial com placa de orifício e no segundo usando um medidor volumétrico, nos quais são identificadas e quantificadas todas as potenciais fontes de incerteza. A visualização e a analise é feita através de gráficos e planilhas em Excel. / Dissertação (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

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Nous présentons les outils fondamentaux du formalisme de la mécanique quantique non relativiste basée sur un principe dincertitude généralisé, impliquant lexistence dune longueur élémentaire. En considérant deux systèmes simples, à savoir le potentiel delta de Dirac à 1 dimension et le potentiel de Coulomb à 3 dimensions, nous illustrons comment on peut résoudre léquation de Schrödinger et extraire le spectre dénergie, analytiquement ou perturbativement, dans ce formalisme. Nous appliquons ce formalisme au potentiel singulier -α/r²(α > 0) à 3 dimensions, qui nécessite une régularisation aux petites distances en mécanique quantique ordinaire. Nous étudions la solution de léquation de Schrödinger dans lespace des impulsions. Nous montrons que la longueur élémentaire régularise le potentiel naturellement. Le spectre dénergie est calculé comme dans le cas des potentiels réguliers, sans introduction dun paramètre arbitraire, et le système possède un état fondamental avec une énergie finie. Nous généralisons notre étude en étudiant léquation de Schrödinger déformée pour le potentiel −α/r² à N dimensions, pour toutes les valeurs du nombre quantique du moment orbital l. La solution analytique est une fonction de Heun qui se réduit à une fonction hypergéométrique dans certains cas particuliers. Nous appliquons nos résultats à 2 dimensions spatiales au problème dun dipôle dans le champ dune corde cosmique. Nous étudions en détail lexistence des états liés du système pour différentes valeurs de la constante de couplage, qui d´epend de langle (θ) entre la corde cosmique et le dipôle. Nous montrons en particulier que la corde cosmique ne peut pas lier le dipôle si θ ≤ π/4. Nous éxaminons également le nombre des états liés du potentiel −α/x² à 1 dimension dans ce nouveau formalisme de la mécanique quantique. Les résultats sont en accord qualitatif avec ceux de la mécanique quantique ordinaire. Nous concluons que dans une théorie quantique non relativiste incluant une longueur élémentaire, celle-ci représenterait une dimension intrinsèque du système étudié. Le formalisme de cette nouvelle version de la mécanique quantique serait utile pour résoudre des problèmes caractérisés par des anomalies dues à des singularités aux petites distances./We discuss the fundamental tools of the formalism of nonrelativistic quantum mechanics based on a generalized uncertainty principle, implying the existence of a minimal length. We consider two simple systems, namely the one-dimensional Dirac delta potential and the three-dimensional Coulomb potential to illustrate how the Schrödinger equation and the eigenvalue problem in the presence of the minimal length can be solved exactly or perturbatively. We apply this formalism to the singular potential −α/r² (α > 0), whose short distance behavior must be regularized in ordinary quantum mechanics. We solve analytically the three-dimensional Schrödinger equation in momentum space. We show that the presence of a minimal length in the formalism regularizes the potential in a natural way. The energy spectrum is calculated as in the case of regular potentials, without introducing any arbitrary parameters, and the system possesses a finite energy in the ground state. We generalize our study by solving analytically the deformed Schrödinger equation for the potential −α/r² in N-dimensions, and for all values of orbital momentum quantum number l. The solution is a Heun function which reduces to a hypergeometric function in some special cases. We apply our results in two spatial dimensions to the problem of a dipole in a cosmic string background. We study in detail the existence of bound states of the system for all values of the coupling constant, depending on the angle (θ between the cosmic string and the dipole. We show in particular that the cosmic string cannot bind the dipole if θ ≤ π/4. We investigate also the number of bound states for the one-dimensional −α/x² potential in this new formalism of quantum mechanics. The results are in qualitative agreement with those of ordinary quantum mechanics. We conclude that the minimal length in a non relativistic quantum theory may represent an intrinsic dimension of the system under study. The formalism of this deformed version of quantum mechanics would be useful to solve problems characterized by anomalies dues to singularities at small distances.

The dawn of quantum technology unveils a plethora of new possibilities and challenges in the world of information technology, one of which is the quest for secure information transmission. A breakthrough in classical algorithm or the development of a quantum computer could threaten the security of messages encoded using public key cryptosystems based on one-way function such as RSA. Quantum key distribution (QKD) offers an unconditionally secure alternative to such schemes, even in the advent of a quantum computer, as it does not rely on mathematical or technological assumptions, but rather on the universality of the laws of quantum mechanics. Physical concepts associated with quantum mechanics, like the uncertainty principle or entanglement, paved the way to the first successful security proof for QKD. Ever since, further development in security proofs for QKD has been remarkable. But the connection between entanglement distillation and the uncertainty principle has remained hidden under a pile of mathematical burden. Our main goal is to dig the physics out of the new advances in security proofs for QKD. By introducing an alternative definition of private state, which elaborates the ideas of Mayers and Koashi, we explain how the security of all QKD protocols follows from an entropic uncertainty principle. We show explicitly how privacy amplification protocol can be reduced to a private state distillation protocol constructed from our observations about the uncertainty principle. We also derive a generic security proof for one-way permutation-invariant QKD protocols. Considering collective attack, we achieve the same secret key generation rate as the Devetak-Winter's bound. Generalizing an observation from Kraus, Branciard and Renner, we have provided an improved version of the secret key generation rates by considering a different symmetrization. In certain situations, we argue that Azuma's inequality can simplify the security proof considerably, and we explain the implication, on the security level, of reducing a QKD protocol to an entanglement or a more general private state distillation protocol. In a different direction, we introduce a QKD protocol with multiple-photon encoding that can be implemented without a shared reference frame. We prove the unconditional security of this protocol, and discuss some features of the efficiency of multiple-photon QKD schemes in general.

The dawn of quantum technology unveils a plethora of new possibilities and challenges in the world of information technology, one of which is the quest for secure information transmission. A breakthrough in classical algorithm or the development of a quantum computer could threaten the security of messages encoded using public key cryptosystems based on one-way function such as RSA. Quantum key distribution (QKD) offers an unconditionally secure alternative to such schemes, even in the advent of a quantum computer, as it does not rely on mathematical or technological assumptions, but rather on the universality of the laws of quantum mechanics. Physical concepts associated with quantum mechanics, like the uncertainty principle or entanglement, paved the way to the first successful security proof for QKD. Ever since, further development in security proofs for QKD has been remarkable. But the connection between entanglement distillation and the uncertainty principle has remained hidden under a pile of mathematical burden. Our main goal is to dig the physics out of the new advances in security proofs for QKD. By introducing an alternative definition of private state, which elaborates the ideas of Mayers and Koashi, we explain how the security of all QKD protocols follows from an entropic uncertainty principle. We show explicitly how privacy amplification protocol can be reduced to a private state distillation protocol constructed from our observations about the uncertainty principle. We also derive a generic security proof for one-way permutation-invariant QKD protocols. Considering collective attack, we achieve the same secret key generation rate as the Devetak-Winter's bound. Generalizing an observation from Kraus, Branciard and Renner, we have provided an improved version of the secret key generation rates by considering a different symmetrization. In certain situations, we argue that Azuma's inequality can simplify the security proof considerably, and we explain the implication, on the security level, of reducing a QKD protocol to an entanglement or a more general private state distillation protocol. In a different direction, we introduce a QKD protocol with multiple-photon encoding that can be implemented without a shared reference frame. We prove the unconditional security of this protocol, and discuss some features of the efficiency of multiple-photon QKD schemes in general.

Typically, design is approached as a sequence of decisions in which designers select what they believe to be the best alternative in each decision. While this approach can be used to arrive at a final solution quickly, it is unlikely to result in the most-preferred solution. The reason for this is that all the decisions in the design process are coupled. To determine the most preferred alternative in the current decision, the designer would need to know the outcomes of all future decisions, information that is currently unavailable or indeterminate. Since the designer cannot select a single alternative because of this indeterminate (interval-based) uncertainty, a set-based design approach is introduced. The approach is motivated by the engineering practices at Toyota and is based on the structure of the Branch and Bound Algorithm. Instead of selecting a single design alternative that is perceived as being the most preferred at the time of the decision, the proposed set-based design approach eliminates dominated design alternatives: rather than selecting the best, eliminate the worst. Starting from a large initial design space, the approach sequentially reduces the set of non-dominated design alternatives until no further reduction is possible ??e remaining set cannot be rationally differentiated based on the available information. A single alternative is then selected from the remaining set of non-dominated designs. In this thesis, the focus is on the elimination step of the set-based design method: A criterion for rational elimination under interval-based uncertainty is derived. To be efficient, the criterion takes into account shared uncertainty ??certainty shared between design alternatives. In taking this uncertainty into account, one is able to eliminate significantly more design alternatives, improving the efficiency of the set-based design approach. Additionally, the criterion uses a detailed reference design to allow more elimination of inferior design sets without evaluating each alternative in that set. The effectiveness of this elimination is demonstrated in two examples: a beam design and a gearbox design.