Orientador: Rogério Custodio / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-18T08:56:05Z (GMT). No. of bitstreams: 1 Abreu_Leandrode_M.pdf: 3333566 bytes, checksum: 9df2fe3268e83e70fae31b792fc76513 (MD5) Previous issue date: 2011 / Resumo: Este trabalho avaliou o cálculo de energias de ionização verticais e as possibilidades de construção e interpretação de diagramas de correlação através do uso dos métodos Monte Carlo Quântico (MCQ) e Outer Valence Green¿s Function (OVGF). O trabalho foi dividido em quatro partes: Energias de ionização simples: Avaliou-se a capacidade dos métodos MCQ e OVGF em descrever os valores de energia de ionização de valência e de caroço e testou-se o uso de funções de onda relaxadas. A faixa dos desvios observados obtidas com o método Monte Carlo Quântico de Difusão (MCQD), em relação aos valores experimentais, é comparável a de outros métodos, como DFT (Teoria do Funcional de Densidade - Density Functional Theory) e CCGF (Funções de Green com Pares Acoplados - Coupled-Cluster Green¿s Function), 0,01 a 2 eV, e verificou-se que uso das funções de onda relaxadas é importante na descrição das ionizações de caroço. Energias de ionização sucessivas: Estimou-se as energias de ionização sucessivas dos elementos do 2º período a partir das energias orbitais do sistema neutro e comparou-se com resultados obtidos através dos métodos MCQ utilizando-se a função de onda do sistema não-ionizado. Pode-se demonstrar a falha das energias orbitais em descrever as energias de ionização sucessivas e obter correções com o uso dos métodos MCQ. Diagramas de correlação: Construíram-se diagramas de energia eletrônica total e de correlação quantitativos utilizando energia de ionização como binding energy para moléculas do tipo BAB (H2O e Li2O) através do uso dos métodos MCQ. Foram construídos diagramas de cargas parciais de Bader através das distribuições discretas de carga obtidas com os métodos MCQ para tentar interpretar os diagramas de correlação, porém a interpretação por comparação direta não foi possível, contudo foram obtidas informações importantes através dos diagramas de cargas parciais. Energias de dupla ionização: Foram calculadas energias de dupla ionização de sistemas atômicos e moleculares através do método OVGF e compararam-se os resultados obtidos com a Teoria do Funcional de Densidade (DFT). O método OVGF mostrou-se tão preciso quanto a teoria DFT na descrição das energias de dupla ionização / Abstract: The study was divided into 4 parts: Simple Ionization Energies: We evaluated the ability of MQC and OVGF methods in describing the values of the ionization energy of valence and core and tested the use of relaxed wave functions. The range of deviations obtained with the method of diffusion quantum Monte Carlo (MCQD), in relation to the experimental values, is comparable to other methods such as DFT (Density Functional Theory) and CCGF (Coupled-Cluster Green's Function), from 0.01 to 2 eV, and it was found that the use of the relaxed wave functions is important in the description of core ionizations. Successive Ionization Energies: We estimated the successive ionization energies of successive elements of the 2nd period from the orbital energies of the neutral system and compared with results obtained using the methods MCQ with the wave function of nonionized system. It can be shown the failure of the orbital energies to describe the successive ionization energies and to obtain corrections with the use of MCQ methods. Correlation Diagrams: Diagrams of total electronic energy and quantitative correlation diagrams were constructed using the ionization energy as binding energy for molecules of the type BAB (Li2O and H2O) through the use of MCQ methods. We constructed Bader¿s partial charges diagrams with the discrete charge distributions obtained with MCQ methods to try to interpret the correlation diagrams, but the interpretation by direct comparison was not possible, however, important information was obtained through diagrams of partial charges. Double Ionization Energies: We calculated double ionization energies of atomic and molecular systems by the OVGF method and compared the results obtained with the Density Functional Theory (DFT). The OVGF method proved to be as accurate as the DFT theory in describing the double ionization energies / Mestrado / Físico-Química / Mestre em Química

Centrosomin (Cnn) is an integral centrosomal protein in Drosophila with orthologues in several species, including humans. The human orthologue of Cnn is required for brain development with Cnn hypothesised to play a similar role in Drosophila. Control of Cnn incorporation into centrosomes is crucial for controlling asymmetric division in certain types of Drosophila stem cells. FRAP experiments on Cnn show that Cnn recovers in a pe- culiar fashion, which suggest that Cnn may be incorporated closest to the centrioles and then spread radially outward, either diffusively or ad- vectively. The aim of this thesis is to understand the mechanism of Cnn incorporation into the Drosophila centrosomes, to determine the mode of transport of the incorporated Cnn, and to obtain parameter estimates for transport and biochemical reactions. A crucial unknown in the modelling process is the distribution of Cnn receptors. We begin by constructing coupled partial differential equation models with either diffusion or advection as the mechanism for incorpo- rated Cnn transport. The simplest receptor distribution we begin with involves a spherical, infinitesimally thick, impermeable shell. We refine the diffusion models using the insights gained from comparing the model out- put with data (gathered during mitosis) and through careful assessment of the behaviour of the data. We show that a Gaussian receptor distribution is necessary to explain the Cnn FRAP data and that the data cannot be explained by other simpler receptor distributions. We predict the exact form of the receptor distribution through data fitting and present pre- liminary experimental results from our collaborators that suggest that a protein called DSpd2 may show a matching distribution. Not only does this provide strong experimental support for a key prediction from our model, but it also suggests that DSpd2 acts as a Cnn receptor. We also show using the mitosis FRAP data that Cnn does not exhibit appreciable radial movement during mitosis, which precludes the use of these data to distinguish between diffusive and advective transport of Cnn. We use long time Cnn FRAP data gathered during S-phase for this purpose. We fit the S-phase FRAP data using the DSpd2 profiles gath- ered for time points corresponding to the Cnn FRAP experiments. We also use data from FRAP experiments where colchicine is injected into the embryos to destroy microtubules (since microtubules are suspected to play a role in advective transport of Cnn). From the analysis of all these data we show that Cnn is transported in part by advection and in part by diffusion. Thus, we are able to provide the first mechanistic description of the Cnn incorporation process. Further, we estimate parameters from the model fitting and predict how some of the parameters may be altered as nuclei progress from S-phase to mitosis. We also generate testable predic- tions regarding the control of the Cnn incorporation process. We believe that this work will be useful to understand the role of Cnn incorporation in centrosome function, particularly in asymmetrically dividing stem cells.

Phonons are primary heat carriers in carbon nanotubes (CNTs) and graphene; a fundamental understanding of phonon transport in these nano-structures is required for the energy efficient design of their devices such as integrated circuit, flexible displays, and transparent electrodes. In this work, atomistic simulations have been performed to investigate thermal transport at interfaces of CNT and graphene that are typically encountered in their applications, e.g., CNT-CNT junctions on silicon oxide substrate, interfaces between shells of double-wall CNTs (DWNTs), and graphene-metal interfaces. Firstly, heat dissipation at CNT junctions supported on the silicon dioxide substrate is investigated using molecular dynamics (MD) simulations and methods for phonon spectrum analysis. The results show the inefficient heat removal from CNTs not making direct contact with the oxide substrate is responsible for the breakdown of CNT network. At interfaces between shells of DWNTs, the radial vibration modes are identified as phonons that are strongly coupled and can efficiently exchange energy between shells of DWNTs. Secondly, the thermal conductivity of suspended single layer graphene (SLG) and SLG supported on Cu is determined using equilibrium MD simulations following Green-Kubo method and relaxation time approximation approach at room temperature. It is demonstrated that the interaction with Cu substrate can significantly reduce the thermal conductivity of SLG, and that the reduction of thermal conductivity from three acoustic phonons is the major reason. Lastly, using atomistic Green’s function method and density function theory calculations, the thermal boundary conductance at interfaces across graphene layers sandwiched by different metals including Cu, Au, and Ti is predicted. The work shows how the bonding strength changes the graphene/metal and graphene/graphene phonon coupling, and demonstrated the transition of thermal transport mechanism from metal/graphene dominated resistance to graphene/graphene dominated resistance as the metal/graphene bonding strength increases in metal/MLG/metal structure.

Cette thèse comprend trois sujets différents, tous en rapport à des problèmes de structures électroniques. Ces trois sujets sont présentés dans trois parties indépendantes.Cette thèse commence par une introduction générale présentant les problématiques et les principaux résultats.La première partie traite de la théorie de la fonctionnelle de la densité lorsqu'elle est appliquée aux modèles d'électrons avec spins polarisés. Cette partie est divisée en deux chapitres. Dans le premier de ces chapitres, nous introduisons la notion de N-représentabilité, et nous caractérisons les ensembles de matrices de densité de spin représentables. Dans le second chapitre, nous montrons comment traiter mathématiquement le terme de Zeeman qui apparaît dans les modèles comprenant une polarisation de spin. Le résultat d'existence qui est démontré dans (Anantharaman, Cancès 2009) pour des systèmes de Kohn-Sham sans polarisation de spin est étendu au cas des systèmes avec polarisation de spin.Dans la seconde partie, nous étudions l'approximation GW. Dans un premier temps, nous donnons une définition mathématique de la fonction de Green à un corps, et nous expliquons comment les énergies d'excitation des molécules peuvent être obtenues à partir de cette fonction de Green. La fonction de Green peut être numériquement approchée par la résolution des équations GW. Nous discutons du caractère bien posé de ces équations, et nous démontrons que les équations GW0 sont bien posées dans un régime perturbatif. Ce travail a été effectué en collaboration avec Eric Cancès et Gabriel Stoltz.Dans le troisième et dernière partie, nous analysons des méthodes numériques pour calculer les diagrammes de bandes de structures cristallines. Cette partie est divisée en deux chapitres. Dans le premier, nous nous intéressons à l'approximation de Hartree-Fock réduite (voir (Cances, Deleurence, Lewin 2008)). Nous prouvons que si le cristal est un insolant ou un semi-conducteur, alors les calculs réalisés dans des supercellules convergent exponentiellement vite vers la solution exacte lorsque la taille de la supercellule tend vers l'infini. Ce travail a été réalisé en collaboration avec Salma Lahbabi. Dans le dernier chapitre, nous présentons une nouvelle méthode numérique pour le calcul des diagrammes de bandes de cristaux (qui peuvent être aussi bien isolants que conducteurs). Cette méthode utilise la technique des bases réduites, et accélère les méthodes traditionnelles. Ce travail a été fait en collaboration avec Eric Cancès, Virginie Ehrlacher et Damiano Lombardi / This thesis contains three different topics, all related to electronic structure problems. These three topics are presented in three independent parts.This thesis begins with a general introduction presenting the problematics and main results.The first part is concerned with Density Functional Theory (DFT), for spin-polarized models. This part is divided in two chapters. In the first of these chapters, the notion of N-representability is introduced and the characterizations of the N-representable sets of spin-density 2X2 matrices are given. In the second chapter, we show how to mathematically treat the Zeeman term in spin-polarized DFT models. The existence of minimizers that was proved in (Anantharaman, Cancès 2009) for spin-unpolarized Kohn-Sham models within the local density approximation is extended to spin-polarized models.The second part of this thesis focuses on the GW approximation. We first give a mathematical definition of the one-body Green's function, and explain why methods based on Green's functions can be used to calculate electronic-excited energies of molecules. One way to compute an approximation of the Green's function is through the self-consistent GW equations. The well-posedness of these equations is discussed, and proved in the GW0 case in a perturbative regime. This is joint work with Eric Cancès and Gabriel Stoltz.In the third and final part, numerical methods to compute band-diagrams of crystalline structure are analyzed. This part is divided in two chapters.In the first one, we consider a perfect crystal in the reduced Hartree-Fock approximation (see (Cances, Deleurence, Lewin 2008)). We prove that, if the crystal is an insulator or a semi-conductor, then supercell calculations converge to the exact solution with an exponential rate of convergence with respect to the size of the supercell. This is joint work with Salma Lahbabi. In the last chapter, we provide a new numerical method to calculate the band diagram of a crystal (which can be either an insulator or a conductor). This method, based on reduced basis techniques, speeds up traditional calculations. This is joint work with Eric Cancès, Virginie Ehrlacher, and Damiano Lombardi

An efficient integral equation method based on a method of moment (MoM) discretization of the Mixed-Potential Integral Equation (MPIE) for the analysis of 2.5D or 3D planar microwave circuits is presented. The robust Discrete Complex Image Method (DCIM) is employed to approximate the Greens functions in layered media for horizontal and vertical sources of fields, where closed-form formulations of the z-integrations are derived in the spectral domain. Meanwhile, an efficient and accurate numerical integration technique based on the Khayat-Wilton transform is used to integrate functions with 1/R singularities and near singularities. The fast iterative solver - Quadrature Sampled Pre-Corrected Fast Fourier Transform (QSPCFFT) - is associated with the MoM formulation to analyze electrically large, dense and complex microwave circuits.

Understanding physical configurations and how these can emerge from the underlying gauge theory is a fundamental problem in modern particle physics. This thesis investigates the study of these configurations primarily focussing on the need for gauge invariance in constructing the gauge invariant fields for any physical theory. We consider Wu’s approach to gauge invariance by identifying the gauge symmetry preserving conditions in quantum electrodynamics and demonstrate how Wu’s conditions for one-loop order calculations (under various regularisation schemes) leads to the maintenance of gauge invariance. The need for gauge invariance is stressed and the consequences discussed in terms of the Ward identities for which various examples and proofs are presented in this thesis. We next consider Zwanziger’s description of a mass term in Yang-Mills theory, where an expansion is introduced in terms of the quadratic and cubic powers of the field strength. Although Zwanziger introduced this expansion there is, however, no derivation or discussion about how it arises and how it may be extended to higher orders. We show how Zwanziger’s expansion in terms of the inverse covariant Laplacian can be derived and extended to higher orders. An explicit derivation is presented, for the first time, for the next to next to leading order term. The role of dressings and their factorisation lies at the heart of this analysis.

Sound propagation in a waveguide is greatly dependent on the acoustic properties of the boundaries. The effect of these properties can be described by a bottom reflection coefficient RB, and surface reflection coefficient RS. Two methods for estimating reflection coefficients are used in this research. The first, the ratio method, is based on the variations of the Green's function with depth utilizing the ratio of the wavenumber spectra at two depths. The second, the pole method, is based on the wavenumbers of the modal peaks in the spectrum at a particular depth. A method to invert for sound speed and density is also examined. Estimates of RB and RS based on synthetic data by the ratio method were very close to their predicted values, especially for higher frequencies and longer apertures. The pole method returned less precise estimates though with longer apertures, the estimates were better. Using experimental data, results of the pole method as well a geoacoustic inversion technique based on them were mixed. The ratio method was used to estimate RS based on the actual data and returned results close to the predicted phase of p. / by Alexander Conrad. / Vita. / Thesis (M.S.C.S.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

Neste trabalho é desenvolvido um método, que utiliza funções de Green, para a solução analítica da equação de difusão de nêutrons em multigrupo, para um reator refletido, cujo fluxo tem dependência apenas radial e com distribuição de combustível não uniforme no cerne. As propriedades de moderação, difusão e absorção são consideradas diferentes no cerne e refletor. Uma distribuição de densidade de potência, que estabelece a condição de criticalidade do reator, é assumida a priori e determina a distribuição de combustível no cerne. Com auxílio das funções de Green e das condições de continuidade do fluxo e da densidade de corrente de nêutrons na interface cerne-refletor, a equação de difusão em multigrupo é transformada em um sistema de equações lineares, contendo como incógnitas os valores dos fluxos na interface entre as regiões. Resolvido esse sistema, obtém-se os valores dos fluxos na interface e, com eles, a distribuição de fluxo em cada região e para cada grupo. Como verificação do método proposto, é feita uma aplicação numérica, utilizando dois grupos de energia, para um reator TRIGA de 1MW. Nessa aplicação são calculadas, além das distribuições de fluxos para os dois grupos de energia, a distribuição de combustível no cerne, a massa crítica e a potência específica linear, para diferentes distribuições de densidade de potência. / In the present work a method is developed for applying Green\'s functions to obtain an analytical solution o£ the neutron diffusion equation to the case o£ a reflected reactor. The problem of a non-uniform fuel distribution in the core is treated. Multigroup theory is used and the neutron flux is assumed to have only radial dependence. Different values are employed to characterize the moderation, diffusion and absorption properties o£ the core and the reflector. A power density distribution which establishes the reactor critica1 condition \"a priori\" is assumed and is then used to calculate the fuel distribution. By using the Green\'s functions and the continuity relations (for neutron fluxes and neutron current densities) at the core-reflector interface, the multigroup diffusion equation is transformed into a system of linear equations. In this system o£ equations the unknowns are the neutron fluxes at the core- reflector interface. Once this system is solved and the interface fluxes are determined, it follows immediately that the neutron flux distribution in the core and in the reflector is determined. The method employed and proposed in the present study has been applied to the problem of calculating the neutron distribution in a 1MW TRIGA reactor, using two energy group. This numerical application, in addition to calculating the two-group flux distribution, the fuel distribution in the core, the critical mass and the linear specific power for different assumed power density distribution have been evaluated.

Mak Ka Wai Charles. / Thesis submitted in: October 2001. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 89-91). / Text in English; abstracts in English and Chinese. / Mak Ka Wai Charles. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview of the Mathematical Framework --- p.2 / Chapter 1.2 --- System of Interest --- p.7 / Chapter 1.2.1 --- Klein-Gordon equation --- p.7 / Chapter 1.2.2 --- QNM boundary conditions --- p.12 / Chapter 1.3 --- Outline of This Thesis --- p.14 / Chapter 2 --- Green's Function --- p.15 / Chapter 2.1 --- "Formal Expression for G(x,y，w)" --- p.16 / Chapter 2.2 --- "Leaver's Series Solution: An Analytic Expression for g(r, w)" --- p.17 / Chapter 2.3 --- Location of the Cut --- p.22 / Chapter 2.4 --- "Jaffe's Series Solution: An Analytic Expression for f(r,w)" --- p.23 / Chapter 2.5 --- QNMs and Their Locations --- p.26 / Chapter 2.5.1 --- Alternative definitions of QNM --- p.26 / Chapter 2.5.2 --- Methods of searching for QNMs --- p.28 / Chapter 2.5.3 --- Locations of QNMs --- p.29 / Chapter 2.6 --- Green's Function and Eigenspectra --- p.30 / Chapter 3 --- Normalization Function: Analytical Treatment --- p.34 / Chapter 3.1 --- Definition and Properties --- p.34 / Chapter 3.2 --- Analytic Approximations for --- p.36 / Chapter 3.3 --- Polar Perturbations --- p.39 / Chapter 4 --- Normalization Function: Numerical Treatment --- p.42 / Chapter 4.1 --- "Numerical Algorithm for g(x,w)" --- p.42 / Chapter 4.1.1 --- Method --- p.42 / Chapter 4.1.2 --- Equation governing R(z) --- p.45 / Chapter 4.1.3 --- "Equations governing A(x, z) and B(x, z)" --- p.45 / Chapter 4.2 --- "Numerical Algorithm for g(x, ´ؤw)" --- p.49 / Chapter 4.3 --- Numerical Result of q(γ) --- p.50 / Chapter 4.4 --- Comparison of Numerical Result with Analytic Approximations --- p.56 / Chapter 5 --- "Branch Cut Strength of G(x, y, w)" --- p.58 / Chapter 5.1 --- "Relation between q(γ) and ΔG(x,y, ´ؤiγ)" --- p.58 / Chapter 5.2 --- Proof of the Power Law --- p.60 / Chapter 5.3 --- "Numerical Results for ΔG(x, y, ´ؤiγ)" --- p.63 / Chapter 5.4 --- Study of a Physically Important Limit --- p.65 / Chapter 5.4.1 --- Limiting x and y --- p.65 / Chapter 5.4.2 --- Poles on the unphysical sheet --- p.69 / Chapter 5.4.3 --- Zerilli potential --- p.77 / Chapter 6 --- Conclusion --- p.81 / Chapter A --- Tortoise Coordinate --- p.84 / Chapter B --- Solution of the Generalized Coulomb Wave Equation --- p.86 / Chapter C --- Derivation of (5.1) --- p.88 / Bibliography --- p.89

<p>U disertacije je sprovedeno teorijsko istraživanje mikroskopskih i makroskopskih (termodinamičkih) osobina tankoslojnih i niskodimenzionih kristalnih struktura u okviru modela fonona akustičkog tipa. Upoređivanjem fononskih spektara i termodinamičkih svojstava u neograničenim i posmatranim nanostrukturama ustanovljeno je da se oni znatno razlikuju usled postojanja granica kod niskodimenzionih sistema. Takođe je primećeno da u fononskim spektrima niskodimenzionih struktura postoji energijski procep, &scaron;to znači da je energija pobuđivanja fonona u niskodimenzionim kristalnim strukturama veća od one u balku. Ovo uzrokuje da toplotna kapacitivnost u niskotemperaturskoj oblasti ima i znatno niže vrednosti u ograničenim strukturama nego u masovnim uzorcima.</p> / <p>In ths work, a theoretical study of microscopic and thermodynamic properties of thin-layered and low-dimensional crystalline structures &nbsp;of the model type of acoustic phonons was carried out. Comparison of the phonon spectra and &nbsp;thermodynamic properties of the infinite with the observed &nbsp;nanostructures revealed that they differ greatly because of the existence of borders in the low-dimensional systems. It is also noted that in the phonon spectra of nanostructures an energy gap exists, which means that the energy od excitation of phonons in the nanostructured crystal systems is higher than those of the bulk. This indicates that the heat capacitance in the low-temperature range ha a significantly lower values in bounded structures than in massive samples.</p>