Thesis (M. A.)--Marshall University, 2009. / Title from document title page. Includes abstract. Document formatted into pages: contains 43 p. Includes bibliographical references (p.42-43)

This Licentiate presents the main results of theoretical study of light propagation in photonic structures, namely lasing disk microcavities and photonic crystals. In the first two papers (Paper I and Paper II) we present the developed novel scattering matrix technique dedicated to calculation of resonant states in 2D disk microcavities with the imperfect surface or/and inhomogeneous refractive index. The results demonstrate that the imperfect surface of a cavity has the strongest impact on the quality factor of lasing modes. The generalization of the scattering-matrix technique to the quantum-mecha- nical case has been made in Paper III. That generalization has allowed us to treat a realistic potential of quantum-corrals (which can be considered as nanoscale analogues of optical cavities) and to obtain a good agreement with experimental observations. Papers IV and V address the novel effective Green's function technique for studying propagation of light in photonic crystals. Using this technique we have analyzed characteristics of surface modes and proposed several novel surface-state-based devices for lasing/sensing, waveguiding and light feeding applications. / <p>Report code: LIU-TEK-LIC 2006:5</p>

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No / Graded porous materials are of growing interest because of their ability to improve the impedance matching between air and material itself. Theoretical models have been developed to predict the acoustical properties of these media. Traditionally, graded materials have been manufactured by stacking a discrete number of homogeneous porous layers with different pore microstructure. More recently a novel foaming process for the manufacturing of porous materials with continuous pore stratification has been developed. This paper reports on the application of the numerical procedure proposed by De Ryck to invert the parameters of the pore size distribution from the impedance tube measurements for materials with continuously stratified pore microstructure. Specifically, this reconstruction procedure has been successfully applied to retrieve the flow resistivity and tortuosity profiles of graded porous materials manufactured with the method proposed by Mahasaranon et al. In this work the porosity and standard deviation in pore size are assumed constant and measured using methods which are applied routinely for homogenous materials characterisation. The numerical method is based on the wave splitting together with the transmission Green's functions approach, yielding an analytical expression of the objective function in the Least-square sense.

Single-particle Green's function method is a direct way of calculating electron binding energy, which relies on expanding the Fock subspace in a finite single-particle basis. However, these methods suffer from slow asymptotic decay of basis set incompleteness error. An energy-dependent explicitly correlated (F12) formalism for Green's function is presented that achieves faster convergence to the basis set limit. The renormalized second-order Green's function method (NR2-F12) scales as iterative N^5 where N is the system size. These methods are tested on a set of small (O21) and medium-sized (OAM24) organic molecules. The basis set incompleteness error in ionization potential (IP) obtained from the NR2-F12 method and aug-cc-pVDZ basis for OAM24 is 0.033 eV compared to 0.067 eV for NR2 method and aug-cc-pVQZ basis. Hence, accurate electron binding energies can be calculated at a lower cost using NR2-F12 method. For aug-cc-pVDZ basis, the electron binding energies obtained from NR2-F12 are comparable to EOM-IP-CCSD method that uses a CCSD reference and scales as iterative N^6. / Master of Science / Solving the non-relativistic time-independent Schrödinger equation is a central problem in quantum chemistry with the primary goal of finding the exact electronic wave function. Like all many-body problems, the applications of highly accurate electronic structure methods are limited to small molecules since they are computationally expensive. With scalable algorithms and parallel implementation of computer programs, the chemistry of large molecular systems can be investigated. Electron binding energies give an insight into the orbital picture of a molecule, which is manifested in chemical structure and properties of a molecule. Green’s function provides an alternative to wave function based methods to calculate ionization potential and electron affinity directly rather than solving for the wave function itself. For accurate electron binding energies, the wave function needs to be represented by large number of basis functions, which make these methods computationally expensive. Explicitly correlated electronic structure methods are designed to produce accurate results at a smaller basis set. This work investigates the use of explicitly correlated Green’s function methods to calculate electron binding energies of small and medium sized organic molecules. These results are compared to coupled cluster methods, which are known to provide accurate benchmarks in quantum chemistry.

This Thesis is concerned with the quasiclassical theory of meso-scopic superconductivity. The aim of the Thesis is to introduce the boundary conditions for a quasiclassical Green’s function on partially transparent interfaces in mesoscopic superconducting structures and to analyze the range of applicability of the quasiclassical theory. The linear boundary conditions for Andreev amplitudes, factoring the quasiclassical Green’s function, are presented.  The quasiclassical theory on classical trajectories is reviewed and then generalized to include knots with paths intersections.  The main focus of the Thesis is on the range of validity of the quasiclassical theory. This goal is achieved by comparison of quasiclassical and exact Green’s functions.  The exact Gor’kov Greens function cannot be directly used for the comparison because of its strong microscopic variations on the length-scale of λF. It is the coarse-grain averaged exact Green’s function which is appropriate for the comparison. In most of the typical cases the calculations show very good agreement between both theories. Only for certain special situations, where the classical trajectory contains loops, one encounters discrepancies. The numerical and analytical analysis of the role of the loop-like structures and their influence on discrepancies between both exact and quasiclassical approaches is one of the main results of the Thesis. It is shown that the terms missing in the quasiclassical theory can be attributed to the loops formed by the interfering paths.  In typical real samples any imperfection on the scale larger than the Fermi wavelength disconnects the loops and the path is transformed into the tree-like graph. It is concluded that the quasiclassical theory is fully applicable in most of real mesoscopic samples. In the situations where the conventional quasiclassical theory is inapplicable due to contribution of the interfering path, one can use the modification of the quasiclassical technique suggested in the Thesis.

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.