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.

No presente trabalho propomos e estudamos um modelo teórico que denominamos Cristal de Wigner Blindado. Assumindo para este sistema uma estrutura ordenada, nos foi possível verificar a ocorrência de uma transição de fase entre as estruturas bcc e fcc, para este modelo em função da densidade e/ou do parâmetro de blindagem. Após esta análise estática nos estendemos aos aspectos dinâmicos. Determinamos os modos normais para estas estruturas obtendo espectros de frequência para diversas blindagem e/ou densidade. Levando o parâmetro de blindagem para o limite zero, recuperamos diversos resultados conhecidos para o Cristal de Wigner. Isto era esperado urna vez que este modelo apenas difere do nosso pela natureza das interações, que neste caso são puramente coulombianas, sem blindagem. Além disto, nos foi possível efetuar comparação com sistemas reais formados por esferas de poliestireno em suspensão aquosa, permitindo-nos concluir que o modelo por nós proposto é aplicável aos mesmos / We present and develop a theoretical model which we designate Screened Wigner Lattice (SWL). In the ordered phase of this system we were able to predict a bcc-fcc transition, by varying the screening parameter and/or the density. After this static analysis we calculated the normal modes of such crystals and got the frequency spectra in function of the screening and/or density. Taking for the screening parameter the limit zero we reproduced several results already known for the Wigner Lattice (WL). This was expected since the only difference between the SWL and WL models consists on the nature of the interaction, some of our theoretical results with experimental data obtained for crystals formed by polystyrene spheres in aqueous suspension. The agreement allows us to conclude that the SWL model applies for such systems

En raison de la tendance positives pour le développement durable, les systèmes solaires(capteurs solaires, concentrateur solaire, etc.) Intègrent (et demandent d'intégrer encore plus)intensivement les résidences et les industries. Dans ce contexte, les systèmes diphasiques comme le caloduc semblent être très efficaces en raison de leurs capacités élevées de transport de chaleur et de leur fonctionnement passif appliqués aux capteurs. Compte-tenu de la complexité des caloducs à structure poreuse dans ce type d'application, la plupart des systèmes existants sur le marché utilisent des thermosiphons. Ainsi, le besoin croissant de solutions de contrôle thermique fiables et plus efficaces croit rapidement pour de tels systèmes.Ce travail de thèse porte sur la caractérisation des performances des caloducs à structure poreuse utilisés dans les applications solaires. Une étude numérique a été réalisée pour modéliser et simuler le comportement d'un caloduc typique à l'aide de la méthode Lattice Boltzmann. Une étude expérimentale a également été réalisée pour caractériser les performances de trois prototypes testes dans différentes conditions (température du condenseur, puissance introduite et angle d'inclinaison). Les effets induits par plusieurs paramètres incluant le taux de remplissage, le fluide de travail et la symétrie de la puissance appliquée sur les performances de ces dispositifs ont également été étudiés. En particulier, l'asymétrie du chauffage induit un assèchement plus précoce, toutes choses étant égales par ailleurs. L'inclinaison optimale est également déterminée là où est équilibrée la chaleur solaire maximale disponible et reçue par le caloduc et l'écoulement de liquide assisté par gravité à l'intérieur de ce dispositif. / Owing to the trend to development sustainability, solar systems (solar collector, solar concentrator, etc.) Are integrating (and asked to integrate even more) intensively residences and industries. In this context, two-phase systems like heat pipe seem highly effective because of their high heat transport capabilities and their passive operation in collectors’ technology. In view of the complexity of the heat pipes with a porous structure in this kind of application,most of the existing systems on the market use thermosyphons. Thus, the growing need of reliable and more efficient thermal control solutions is increasing for such systems. This thesis work focuses on the performance characterization of heat pipes with porous structure used in solar applications. A numerical study has been performed to model and simulate the behavior of a typical heat pipe using the Lattice Boltzmann method. An experimental study has also been done to characterize the performance of three prototypes tested under different conditions (condenser temperature, heat input and inclination angle). The effects induced by several parameters including the filling rate, working fluid and symmetry of the applied heat on the performance of these devices has also been investigated. In particular, heating asymmetry is found to induce dry-out earlier, all other things being equal. Optimal inclination is also determined where is balanced the maximum solar heat available and received by the heat pipe and the gravity-assisted liquid flow inside that device.

This thesis describes the duality methods used in the tensor renormalization group method and their application to quantum simulation with cold atoms in optical lattices. Here we consider specifically the O(2) and O(3) nonlinear sigma models in two dimensions, as well as the Abelian Higgs model in two dimensions. We give numerical results from the tensor renormalization group and comparisons with other numerical methods for all three models. We give proposals for possible experimental methods with which these models could be simulated using cold atoms trapped in optical lattices as is done in ongoing experiments.

The thesis analyzes some aspects of the theory of distributive lattices, particularly two representation theorems: Birkhoff's representation theorem for finite distributive lattices and Stone's representation theorem for infinite distributive lattices.

We studied the pressure effect of polycrystal BiMnO3 (type-I multiferroic) and single crystal Co3TeO6 (type-II multiferroic) with different magnetic fields and pressures. With the primary objective of understanding the pressure effect on BiMnO3, complex multiple magnetic transitions (kink I, II and III) are observed under the maximum applied pressure of 15.94 kbar (~1.6 GPa). Kink I, a long-range soft ferromagnetic transition at TcI ~ 100 K under ambient pressure, is suppressed completely at 11.74 kbar. Kink II emerges at 8.66 kbar along with TcII ~ 93 K. Kink II is a long-range soft ferromagnetic the same as kink I but canted in nature. Kink III, a canted antiferromagnetic transition at TcIII ~ 72.5 K appears along with kink II also at 8.66 kbar. These results indicate the complicated correlation between the lattice distortion and the spin configuration under pressures and magnetic fields in multiferroic system. Whereas, two distinct anomalies (T1 ~ 26 K and T2 ~ 18 K) are observed on single crystal Co3TeO6 in magnetic susceptibility, specific heat, and neutron diffraction measurements. Interestingly, the strong anisotropic magnetic variations are also noticed in high-magnetic-field hysteresis measurements with applied magnetic field parallel to a- and c- axes. Dielectric studies were also carried out in different magnetic fields at the temperature range 5 ¡V 300 K. Concomitantly, frequency-independent step-like dielectric anomaly is observed around 18 K, coinciding with the transition of magnetic susceptibility, specific heat, and neutron diffraction. The dielectric constant is also modified by external magnetic fields. These experimental results strongly suggest the multiferroicity of Co3TeO6. From temperature-dependent X-ray diffraction studies, it is evident that a structural distortion appears around 18 K, responsible of dielectric and/or magnetic ordering. The transition at 18 K is disappeared under pressure above 9.82 kbar, indicative of suppressing structural distortion. Similarly, the lattice distortion and the spin configuration under pressures are important factors for multiferroic property. Through the specific heat and pressure-dependent susceptibility, the structural distortion probably results from the magnetic ordering, indication the dielectric anomaly at 18 K.

Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

abstract: The Tamari lattice T(n) was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Since then it has been studied in various areas of mathematics including cluster algebras, discrete geometry, algebraic combinatorics, and Catalan theory. Although in several related lattices the number of maximal chains is known, the enumeration of these chains in Tamari lattices is still an open problem. This dissertation defines a partially-ordered set on equivalence classes of certain saturated chains of T(n) called the Tamari Block poset, TB(lambda). It further proves TB(lambda) is a graded lattice. It then shows for lambda = (n-1,...,2,1) TB(lambda) is anti-isomorphic to the Higher Stasheff-Tamari orders in dimension 3 on n+2 elements. It also investigates enumeration questions involving TB(lambda), and proves other structural results along the way. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2016

No presente trabalho propomos e estudamos um modelo teórico que denominamos Cristal de Wigner Blindado. Assumindo para este sistema uma estrutura ordenada, nos foi possível verificar a ocorrência de uma transição de fase entre as estruturas bcc e fcc, para este modelo em função da densidade e/ou do parâmetro de blindagem. Após esta análise estática nos estendemos aos aspectos dinâmicos. Determinamos os modos normais para estas estruturas obtendo espectros de frequência para diversas blindagem e/ou densidade. Levando o parâmetro de blindagem para o limite zero, recuperamos diversos resultados conhecidos para o Cristal de Wigner. Isto era esperado urna vez que este modelo apenas difere do nosso pela natureza das interações, que neste caso são puramente coulombianas, sem blindagem. Além disto, nos foi possível efetuar comparação com sistemas reais formados por esferas de poliestireno em suspensão aquosa, permitindo-nos concluir que o modelo por nós proposto é aplicável aos mesmos / We present and develop a theoretical model which we designate Screened Wigner Lattice (SWL). In the ordered phase of this system we were able to predict a bcc-fcc transition, by varying the screening parameter and/or the density. After this static analysis we calculated the normal modes of such crystals and got the frequency spectra in function of the screening and/or density. Taking for the screening parameter the limit zero we reproduced several results already known for the Wigner Lattice (WL). This was expected since the only difference between the SWL and WL models consists on the nature of the interaction, some of our theoretical results with experimental data obtained for crystals formed by polystyrene spheres in aqueous suspension. The agreement allows us to conclude that the SWL model applies for such systems

<p>The lattice of varieties of distributive pseudo-complemented lattices is completely described, viz. a chain of type W + 1. Moreover, each variety is determined by a single equation in addition to those equations which define distributive pseudo-complemented lattices. Characterizations of distributive pseudo-complemented lattices satisfying a certain equation are given which turn out to be generalizations of L. Nachbin's result for Boolean algebras and the results for Stone algebras obtained by G. Gratzer-E. '11. Schmidt and J. C. Varlet. </p> / Thesis / Doctor of Philosophy (PhD)