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FundaÃÃo de Amparo à Pesquisa do Estado do Cearà / Seja p um nÃmero primo Ãmpar. Uma famÃlia de reticulados (p-1)-dimensional produzindo novos empacotamentos pra vÃrios valores de p no intervalo [149... 3001] à apresentado. O resultado à obtido atravÃs da modificaÃÃo da construÃÃo de Craig e considerando conveniente escolhidos Z-submÃdulos de Q (ζ), onde ζ à raiz p-Ãsima primitiva da unidade. Para p ≥ 59, à mostrado que a densidade de centro do reticulado (p-1)-dimensional na nova famÃlia à pelo menos 2 vezes a densidade de centro do (p-1)-dimensional reticulado de Craig. / Let p an odd prime. A family of (p-1)-dimensional over-lattices yielding new record packings for several values of p in interval [149... 3001] is presented. The result is obtained by modifying Craig's construction and considering conveniently chosen Z-submodules of Q (ζ), where ζ is a primitive pth root of unity. For p ≥ 59, it is shown that the center density of the (p-1)-dimensional lattice in the new family is at least twice the center density of the (p-1)-dimensional Craig lattice.

Lattice-Boltzmann method(LBM), a promising new particle-based simulation technique for complex and multiscale fluid flows, has seen tremendous adoption in recent years in computational fluid dynamics. Even with a state-of-the-art LBM solver such as Palabos, a user still has to manually write his program using the library-supplied primitives. We propose an automated code generator for a class of LBM computations with the objective to achieve high performance on modern architectures. Tiling is a very important loop transformation used to improve the performance of stencil computations by exploiting locality and parallelism. In the first part of the work, we explore diamond tiling, a new tiling technique to exploit the inherent ability of most stencils to allow tile-wise concurrent start. This enables perfect load-balance during execution and reduces the frequency of synchronization required. Few studies have looked at time tiling for LBM codes. We exploit a key similarity between stencils and LBM to enable polyhedral optimizations and in turn time tiling for LBM. Besides polyhedral transformations, we also describe a number of other complementary transformations and post processing necessary to obtain good parallel and SIMD performance on modern architectures. We also characterize the performance of LBM with the Roofline performance model. Experimental results for standard LBM simulations like Lid Driven Cavity, Flow Past Cylinder, and Poiseuille Flow show that our scheme consistently outperforms Palabos–on average by3 x while running on 16 cores of a n Intel Xeon Sandy bridge system. We also obtain a very significant improvement of 2.47 x over the native production compiler on the SPECLBM benchmark.

Cabonate-hosted hydrocarbon reservoirs will play an increasingly important role in the energy supply, as 60% of the world's remaining hydrocarbon resources are trapped within carbonate rocks. The properties of carbonates are controlled by deposition and diagenesis, which includes calcite cementation that begins immediately after deposition and may have a strong impact on subsequent diagenetic pathways. This thesis aims to understand the impact of early calcite cementation on reservoir properties through object-based modelling and Lattice Boltzmann ow simulation to obtain permeability. A Bayesian inference framework is also developed to quantify the ability of Lattice Boltzmann method to predict the permeability of porous media. Modelling focuses on the impact of carbonate grain type on properties of early cemented grainstones and on the examination of the theoretical changes to the morphology of the pore space. For that purpose process-based models of early cementation are developed in both 2D (Calcite2D) and 3D (Calcite3D, which also includes modelling of deposition). Both models assume the existence of two grain types: polycrystalline and monocrystalline, and two early calcite cement types specific to these grain types: isopachous and syntaxial, respectively. Of the many possible crystal forms that syntaxial cement can take, this thesis focuses on two common rhombohedral forms: a blocky form 01¯12 and an elongated form 40¯41. The results of the 2D and 3D modelling demonstrate the effect of competition of growing grains for the available pore space: the more monocrystalline grains present in the sample, the stronger this competition becomes and the lesser the impact of each individual grain on the resulting early calcite cement volume and porosity. The synthetic samples with syntaxial cements grown of the more elongated crystal form 40¯41 have lower porosity for the same monocrystalline grains content than synthetic samples grown following more blocky crystal form 01¯12. Moreover, permeability at a constant porosity is reduced for synthetic samples with the form 40¯41. Additionally, synthetic samples with form 40¯41 exhibit greater variability in the results as this rhombohedral form is more elongated and has the potential for producing a greater volume of cement. The results of the 2D study suggest that for samples at constant porosity the higher the proportion of monocrystalline grains are in the sample, the higher the permeability. The 3D study suggests that for samples with crystal form 01¯12 at constant porosity the permeability becomes lower as the proportion of monocrystalline grains increase, but this impact is relatively minor. In the case of samples with crystal form 40¯41 the results are inconclusive. This dependence of permeability on monocrystalline grains is weaker than in the 2D study, which is most probably a result of the bias of flow simulation in the 2D as well as of the treatment of the porous medium before the cement growth model is applied. The range of the permeability results in the 2D modelling may be artificially overly wide, which could lead to the dependence of permeability on sediment type being exaggerated. Poroperm results of the 2D modelling (10-8000mD) are in reasonable agreement with the data reported for grainstones in literature (0.1-5000mD) as well as for the plug data of the samples used in modelling (porosity 22 - 27%, permeability 200 - 3000mD), however permeability results at any given porosity have a wide range due to the bias inherent to the 2D flow modelling. Poroperm results in the 3D modelling (10 - 30, 000mD) exhibit permeabilities above the range of that reported in the literature or the plug data, but the reason for that is that the initial synthetic sediment deposit has very high permeability (58, 900mD). However, the trend in poroperm closely resembles those reported in carbonate rocks. As the modelling depends heavily on the use of Lattice Boltzmann method (flow simulation to obtain permeability results), a Bayesian inference framework is presented to quantify the predictive power of Lattice Boltzmann models. This calibration methodology is presented on the example of Fontainebleau sandstone. The framework enables a systematic parameter estimation of Lattice Boltzmann model parameters (in the scope of this work, the relaxation parameter τ ), for the currently used calibrations of Lattice Boltzmann based on Hagen-Poiseuille law. Our prediction of permeability using the Hagen-Poiseuille calibration suggests that this method for calibration is not optimal and in fact leads to substantial discrepancies with experimental measurements, especially for highly porous complex media such as carbonates. We proceed to recalibrate the Lattice Boltzmann model using permeability data from porous media, which results in a substantially different value of the optimal τ parameter than those used previously (0.654 here compared to 0.9). We augment our model introducing porosity-dependence, where we find that the optimal value for τ decreases for samples of higher porosity. In this new semi-empirical model one first identifies the porosity of the given medium, and on that basis chooses an appropriate Lattice Boltzmann relaxation parameter. These two approaches result in permeability predictions much closer to the experimental permeability data, with the porosity-dependent case being the better of the two. Validation of this calibration method with independent samples of the same rock type yields permeability predictions that fall close to the experimental data, and again the porosity-dependent model provides better results. We thus conclude that our calibration model is a powerful tool for accurate prediction of complex porous media permeability.

In a recent paper we studied the effect of new-physics operators with different Lorentz structures on the semileptonic Λb → Λcτν¯τ decay. This decay is of interest in light of the R(D(∗)) puzzle in the semileptonic B¯ → D(∗)τν¯τ decays. In this work we add tensor operators to extend our previous results and consider both model-independent new physics (NP) and specific classes of models proposed to address the R(D(∗)) puzzle. We show that a measurement of R(Λc) = B[Λb → Λcτν¯τ ]/B[Λb → Λcℓν¯ℓ] can strongly constrain the NP parameters of models discussed for the R(D(∗)) puzzle. We use form factors from lattice QCD to calculate all Λb → Λcτν¯τ observables. The Λb → Λc tensor form factors had not previously been determined in lattice QCD, and we present new lattice results for these form factors here.

Ph.D. (Mathematics) / Our objective in this thesis is to investigate two fundamental questions concerning Riesz operators de ned on a Banach space. Recall that Riesz operators are generalizations of compact operators in the sense that Riesz operators have the same spectral properties as compact operators. However, they do not possess the same algebraic properties as compact operators. Our rst question that we investigate is: When is a Riesz operator a nite rank operator? This question is motivated from the fact that if a compact operator de ned on a Banach space has closed range, then it is a nite rank operator. Also, Ghahramani proved that a compact homomorphism de ned on a C -algebra is a nite rank operator, see . Martin Mathieu, in his paper, generalized the result of Ghahramani by proving that a weakly compact homomorphism de ned on a C -algebra is a nite rank operator...

The idea of keychains, an (n+1)-tuple of non-increasing real numbers in the unit interval always including 1, naturally arises in study of finite fuzzy set theory. They are a useful concept in modeling ideas of uncertainty especially those that arise in Economics, Social Sciences, Statistics and other subjects. In this thesis we define and study some basic properties of keychains with reference to Partially Ordered Sets, Lattices, Chains and Finite Fuzzy Sets. We then examine the role of keychains and their lattice diagrams in representing uncertainties that arise in such problems as in preferential voting patterns, outcomes of competitions and in Economics - Preference Relations.

La méthode Lattice Boltzmann (LBM) est une alternative viable à la simulation directe (DNS) des équations de Navier et Stokes, particulièrement en Mécanique des Fluides. La clé de son succès se situe dans l’exactitude, la simplicité et la propriété conforme de parallélisation de l’algorithme stream-collision. L’inconvénient majeur de cette méthode provient de la limitation aux mailles cubiques spatialement uniformes. Pour y remédier, plusieurs extensions de la LBM aux mailles non-homogènes ont été proposées. Ces techniques ont été revisitées dans la thèse. La revue de maillage montre que la meilleure technique de raffinement remplit certains critères: elle doit satisfaire aux lois de conservation et doit être stable. Elle suggère l’adoption des approches de type Volumes Finis (FV LBM). Une revue de ces techniques a permis de conclure que bien qu’intéressantes, elles présentent de nombreux inconvénients. Cette étude présente une méthode de discrétisation de type FV pour Lattice Boltzmann de haute précision et avec un faible coût de calcul. Afin d’évaluer la performance de la méthode FV nous effectuons une comparaison systématique axée sur la précision et les performances de calcul avec la méthode de Lattice Boltzmann standard (ST). En particulier, nous cherchons à clarifier si et dans quelles conditions l’algorithme proposé et plus généralement tout algorithme FV peut être considéré comme la méthode de choix pour les simulations en Mécanique des Fluides. Nous présentons la première simulation des écoulements convectifs à haut nombre de Rayleigh réalisée avec une méthode Lattice Boltzmann de type FV avec des mailles réduites près de la paroi. / Lattice Boltzmann Method (LBM) has become a viable alternative to Navier-Stokes Direct Numerical Simulations (DNS) in fluid dynamics research. The key of this success is the accuracy/simplicity and parallelization compliant property of the stream-collision algorithm. One shortcoming however, comes from the limitation to spatially uniform cubic grids. To overcome this, several LBM extension to non-homogeneous grids have been proposed. These techniques have been reviewed in this thesis. Such review suggests that a better refinement technique should fulfill some properties: obey conservation laws and be stable. This suggests a pathway to adopt Finite Volume approaches (FV LBM). A review on such volumetric approach to LBM concludes that although interesting, at present such methods suffer from several drawbacks. In this study, a new FV discretization method for the Lattice Boltzmann equation that combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming (ST) Lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. We report the first successful simulation of high-Rayleigh number convective flow performed by a Lattice Boltzmann FV based algorithm with wall grid refinement.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.