In this dissertation, I introduce a vortex method that is generally applicable to any two-dimensional, incompressible flow with or without boundaries. This method is deterministic, accurate, convergent, naturally adaptive, geometry independent and fully localized. For viscous flows, the vorticity distribution of each vortex element must evolve in addition to following a Lagrangian trajectory. My method relies upon an idea called core spreading. Core spreading is inconsistent by itself, but I have corrected it with a deterministic process known as "vortex fission" where one "fat" vortex is replaced by several "thinner" ones. Also, I examine rigorously a method for merging many blobs into one. This process maintains smaller problem sizes thus boosting the efficiency of the vortex method. To prove that this corrected core spreading method will converge uniformly, I adapted a continuous formalism to this grid-free scheme. This convergence theory does not rely on any form of grid. I only examine the linear problem where the flow field is specified, and treat the full nonlinear problem as a perturbation of the linear problem. The estimated rate of convergence is demonstrated to be sharp in several examples. Boundary conditions are approximated indirectly. The boundary is decomposed into a collection of small linear segments. I solve the no-slip and no-normal flow conditions simultaneously by superimposing a potential flow and injecting vorticity from the boundary consistent with the unsteady Rayleigh problem. Finally, the ultimate test for this new method is to simulate the wall jet. The simulations produce a dipole instability along the wall as observed in water tank and wind tunnel experiments and predicted by linear stability analysis. Moreover, the wavelength and height of these simulations agree quantitatively with experimental observations.

Orientadores: Ricardo Dahab, Michel Abdalla / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-27T04:48:10Z (GMT). No. of bitstreams: 1 Magalhaes_KarinaMochettide_D.pdf: 1527439 bytes, checksum: bde8a4343d856fa31a8cd9e9f0b1d2b7 (MD5) Previous issue date: 2014 / Resumo: Em um sistema de criptografia funcional, uma autoridade de posse de uma chave mestra pode gerar uma chave secreta que permite o cálculo de uma função sobre a mensagem nos dados criptografados. Assim, é possível calcular tal função no texto cifrado usando somente a chave secreta. Exemplos importantes de criptografia funcional são Criptografia Baseada em Identidades, Criptografia Baseada em Atributos, Criptografia com Produto Escalar, Criptografia Difusa Baseada em Identidades, Criptografia de Vector Oculto, Criptografia Baseada em Certificados, Criptografia com Pesquisa de Palavra-Chave e Criptografia Baseada em Identidades com Curinga. Esquemas de criptografia com predicados são uma especialização de esquemas de criptografia funcionais, em que a função utilizada não fornece informações sobre a mensagem, mas determina se a decriptação deve ou não funcionar corretamente. Criptografia baseada em reticulados é uma importante alternativa para os principais sistemas criptográficos utilizados atualmente, uma vez que elas são supostamente seguras contra algoritmos quânticos. O Algoritmo de Shor é capaz de resolver o Problema da Fatoração Inteira e o Problema do Logaritmo Discreto em tempo polinomial em um computador quântico, quebrando os sistemas criptográficos mais usados e importantes atualmente, como o RSA, o Diffie-Hellman e a Criptografia de Curvas Elípticas. Neste trabalho nos concentramos em esquemas de criptografia com predicados baseados em reticulados. Nós estudamos e descrevemos os principais sistemas baseados em reticulados encontrados na literatura, estendendo-os a versões hierárquicas e mostrando como o uso de um reticulado com estrutura ideal afeta a prova de segurança. Para cada esquema, uma prova formal de segurança é detalhada, as análises de complexidade e do tamanho das variáveis são mostradas e a escolha dos parâmetros garantindo o funcionamento correto da decriptação é dada / Abstract: In a functional encryption system, an authority holding a master secret key can generate a key that enables the computation of some function on the encrypted data. Then, using the secret key the decryptor can compute the function from the ciphertext. Important examples of functional encryption are Identity-Based Encryption, Attribute-Based Encryption, Inner Product Encryption, Fuzzy Identity-Based Encryption, Hidden Vector Encryption, Certificate-Based Encryption, Public Key Encryption with Keyword Search and Identity-Based Encryption with Wildcards. Predicate encryption schemes are a specialization of functional encryption schemes, in which the function does not give information of the plaintext, but it determines whether the decryption should or should not work properly. Lattice-Based Cryptography is an important alternative to the main cryptographic systems used today, since they are conjectured to be secure against quantum algorithms. Shor's algorithm is capable of solving the Integer Factorization Problem and the Discrete Logarithm Problem in polynomial time on a quantum computer, breaking the most used and important cryptosystems such as RSA, Diffie-Hellman and Elliptic Curve Cryptography. In this work we focus on Lattice-Based Predicate Encryption. We study and describe the main lattice-based schemes found in the literature, extending them to hierarchical versions and showing how the use of ideal lattice affects their security proof. For each scheme, a formal proof of security is detailed, analyses of complexity and variable's size are shown and the parameter's choice ensuring that the decryption works correctly is given / Doutorado / Ciência da Computação / Doutora em Ciência da Computação

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The procedure introduced by Cornish⁴ for estimating a missing value in a lattice design, has been extended here and modified to include not only intra-block information, but also inter-block information as well. The analysis of the lattice design has been presented with some simplification applicable to this type of lattice; thus, allowing a more uniform development than has appeared before. The implications in the limit were examined for the use of the modification of intra-block estimation formula, and it was shown that the form used was an appropriate practical tool. An actual experiment was analyzed, where certain plots were considered missing, and it was shown that the additional use of the inter-block information, as evidenced by the modified formula, would give a much better estimate of a missing value than had been possible previously in the presence of significant inter-block variation. The lattice design has thus been made stable in the event of loss of and plot value. This design has been proven useful in industrial analysis, and its utility may now be protected by a more complete recovery of missing information. / M.S.

Three different definitions for the determinant of a matrix over arbitrary lattices have been developed to determine which properties and relations were reminiscent of the determinant or permanent of elementary algebra. In each determinant there are properties concerning: the elements of the matrix in the expansion of its determinant; the determinant of a matrix and its transpose; a principle of duality for rows and columns; the interchange of rows and columns; the determinant of a matrix formed from another by a row or column meet of certain elements; and evaluations of certain special matrices. An expansion by row or column is given for one determinant and a lemma on inverses is proven in light of another. A preliminary section on Lattice Theory is also included. / Master of Science

We study various quotient maps between frames which are defined by stipulating that they satisfy certain conditions on the cozero parts of their domains and codomains. By way of example, we mention that C-quotient and C -quotient maps (as defined by Ball and Walters- Wayland [7]) are typical of the types of homomorphisms we consider in the initial parts of the thesis. To be little more precise, we study uplifting quotient maps, C1- and C2-quotient maps and show that these quotient maps possess some properties akin to those of a C-quotient maps. The study also focuses on R - and G - quotient maps and show, amongst other things, that these quotient maps coincide with the well known C - quotient maps in mildly normal frames. We also study quasi-F frames and give a ring-theoretic characterization that L is quasi-F precisely when the ring RL is quasi-B´ezout. We also show that quasi-F frames are preserved and reflected by dense coz-onto R -quotient maps. We characterize normality and some of its weaker forms in terms of some of these quotient maps. Normality is characterized in terms of uplifting quotient maps, -normally separated frames in terms of C1-quotient maps and mild normality in terms of R - and G -quotient maps. Finally we define cozero complemented frames and show that they are preserved and reflected by dense z#- quotient maps. We end by giving ring-theoretic characterizations of these frames. / Mathematical Science / D. Phil. (Mathematics)

Thesis (PhD (Mathematical Sciences))--Stellenbosch University, 2008 / Please refer to full text for abstract.

The problem undertaken in this paper is to determine what the algebraic structure of the class of C-sets is, when the notion of sum is to be the "set sum. " While the preliminary work done by Appling took place in the space of additive and bounded real valued functions, the results here are found in the more general setting of a complete lattice ordered group. As a conseque n c e , G . Birkhof f' s book, Lattice Theory, is used as the standard reference for most of the terminology used in the paper. The direction taken is prompted by a paper by W. D. L. Appling, "A Generalization of Absolute Continuity and of an Analogue of the Lebesgue Decomposition Theorem. " Since some of the results obtained provide another approach to a problem originally studied by Nakano, and improved upon by Bernau, reference is made to their work to provide other terminology and examples of alternative approaches to the problem of lateral completion. Thus Chapter I contains a brief history of the notion of C-sets and their relationship to lattice ordered groups, along with a summary of the properties of lattice ordered groups needed for later developments. In addition, several results in the general theory of lattice ordered groups are cited to provide insight into the comparability of the assumptions that will ultimately be made about the groups. Chapter II begins with the axiomatization of the collection of nearest point functions" for the closed A-ideals of the cone of a complete lattice ordered group. The basic results in the chapter establish that the functions defined do indeed characterize the complete A-ideals, and that the maps have a 'nearest point property." The maps are then extended to the entire group and shown to correspond to the "nearest point maps" for a C-set in PAB' Chapter III is devoted to exploring the algebraic structures found in the collection of all closed A-ideal maps, denoted J. J is shown to be a lattice ordered monoid, abelian and complete, containing a maximal group cone P*. It is further shown that the original group cone P is isomorphic to a subset of P*. Chapter IV looks into a rather interesting characterization of P*, one that, in the terminology of Bernau, implies that P* is the cone of the group that is the lateral completion of the original group. A final result is a demonstration that the members of j each have a representation as the sum of an element of P* and an additive element of j.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 74-75. / Ph.D.

In this thesis we make four contributions to the state of the art in numerical lattice simulations of quantum chromodynamics (QCD). First, we present the most detailed investigation yet of the autocorrelations of topological observations in hybrid Monte Carlo simulations of QCD and of the effects of the boundary conditions on these autocorrelations. This results in a numerical criterion for deciding when open boundary conditions are useful for reducing these autocorrelations, which are a major barrier to reliable calculations at fine lattice spacings. Second, we develop a dislocation-enhancing determinant, and demonstrate that it reduces the autocorrelation time of the topological charge. This alleviates problems with slow topological tunneling at fine lattice spacings, enabling simulations on fine lattices to be completed with much less computational effort. Third, we show how to apply the recently developed zMöbius technique to hybrid Monte Carlo evolutions with domain wall fermions, achieving nearly a factor of two speedup in the the light quark determinant, the single most expensive part of the calculation. The dislocation-enhancing determinant and the zMöbius technique have enabled us to begin simulations of fine ensembles with four flavors of dynamical domain wall quarks. Finally, we show how to include the previously-neglected G1 operator in nonperturbative renormalization of the ∆S = 1 effective weak Hamiltonian on the lattice. This removes an important systematic error in lattice calculations of weak matrix elements, in particular the important K → ππ decay.