Made available in DSpace on 2014-12-17T15:04:57Z (GMT). No. of bitstreams: 1 AndreiaCSC_DISSERT.pdf: 2649141 bytes, checksum: dae08204df4fb46613c38f0ae1be765c (MD5) Previous issue date: 2011-10-26 / The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem / O presente trabalho de pesquisa compreende em um estudo de Leonhard Euler sobre os n?meros pentagonais e o artigo Mirabilibus Proprietatibus Numerorum Pentagonalium -E524. Depois de uma breve revis?o da vida e obra de Euler, analisamos os conceitos matem?ticos abordados no referido artigo como tamb?m a sua contextualiza??o hist?rica. Para tanto, explicamos o conceito de n?meros figurados, mostrando seu modo de gera??o, bem como suas representa??es geom?tricas e alg?bricas. Em seguida, faz-se um pequeno hist?rico da busca euleriana para o Teorema dos N?meros Pentagonais, perpassando sua correspond?ncia sobre o assunto com Daniel Bernoulli, Nikolaus Bernoulli e Christian Goldbach. No in?cio, Euler afirma o teorema, por?m admite que n?o sabe demonstr?-lo. Finalmente, em uma carta ? Goldbach, de 1750, faz a procurada demonstra??o, a qual ? publicada em E541, junto ? demonstra??o alternativa. A expans?o do conceito de n?mero pentagonal ? ent?o explicada e justificada, tendo em vista a compara??o das representa??es geom?trica e alg?brica dos novos n?meros pentagonais com as dos n?meros pentagonais tradicionais. Em seguida, explana-se o Teorema dos N?meros Pentagonais, isto ?, o fato de que o produto infinito (1 x)(1 xx)(1 x 3)(1 x 4)(1 x 5)(1 x 6)(1 x 7) ... ser igual ? s?rie infinita 1 x 1 x 2+x 5+x 7 x 12 x 15+x 22+x 26 ..., onde os expoentes s?o dados pelos n?meros pentagonais (expandidos) e o sinal ? dado como mais ou menos conforme o expoente ? um n?mero pentagonal (seja tradicional, seja expandido) de ordem par ou ?mpar. Tamb?m mencionamos que Euler, utiliza os n?meros pentagonais e o referido teorema sobre outras partes da matem?tica, como: o conceito de parti??o, fun??es geradoras, a teoria do produto infinito e a soma de divisores. Finalizamos com uma explica??o da demonstra??o do Teorema dos N?meros Pentagonais.

abstract: Single-layer pentagonal materials have received limited attention compared with their counterparts with hexagonal structures. They are two-dimensional (2D) materials with pentagonal structures, that exhibit novel electronic, optical, or magnetic properties. There are 15 types of pentagonal tessellations which allow plenty of options for constructing 2D pentagonal lattices. Few of them have been explored theoretically or experimentally. Studying this new type of 2D materials with density functional theory (DFT) will inspire the discovery of new 2D materials and open up applications of these materials in electronic and magnetic devices.In this dissertation, DFT is applied to discover novel 2D materials with pentagonal structures. Firstly, I examine the possibility of forming a 2D nanosheet with the vertices of type 15 pentagons occupied by boron, silicon, phosphorous, sulfur, gallium, germanium or tin atoms. I obtain different rearranged structures such as a single-layer gallium sheet with triangular patterns. Then the exploration expands to other 14 types of pentagons, leading to the discoveries of carbon nanosheets with Cairo tessellation (type 2/4 pentagons) and other patterns. The resulting 2D structures exhibit diverse electrical properties. Then I reveal the hidden Cairo tessellations in the pyrite structures and discover a family of planar 2D materials (such as PtP2), with a chemical formula of AB2 and space group pa ̄3. The combination of DFT and geometries opens up a novel route for the discovery of new 2D materials. Following this path, a series of 2D pentagonal materials such as 2D CoS2 are revealed with promising electronic and magnetic applications. Specifically, the DFT calculations show that CoS2 is an antiferromagnetic semiconductor with a band gap of 2.24 eV, and a N ́eel temperature of about 20 K. In order to enhance the superexchange interactions between the ions in this binary compound, I explore the ternary 2D pentagonal material CoAsS, that lacks the inversion symmetry. I find out CoAsS exhibits a higher Curie temperature of 95 K and a sizable piezoelectricity (d11=-3.52 pm/V). In addition to CoAsS, 34 ternary 2D pentagonal materials are discovered, among which I focus on FeAsS, that is a semiconductor showing strong magnetocrystalline anisotropy and sizable Berry curvature. Its magnetocrystalline anisotropy energy is 440 μeV/Fe ion, higher than many other 2D magnets that have been found. Overall, this work not only provides insights into the structure-property relationship of 2D pentagonal materials and opens up a new route of studying 2D materials by combining geometry and computational materials science, but also shows the potential applications of 2D pentagonal materials in electronic and magnetic devices. / Dissertation/Thesis / Doctoral Dissertation Materials Science and Engineering 2020

Plasmonic circuitry is considered as a promising solution-effectivetechnology for miniaturizing and integrating the next generation ofoptical nano-devices. The realization of a practical plasmonic circuitry strongly depends on the complete understanding of the propagation properties of two key elements: surface plasmons and electrons. The critical part constituting the plasmonic circuitry is a waveguide which can sustain the two information-carriers simultaneously. Therefore, we present in this thesis the investigations on the propagation of surface plasmons and the co-propagation of surface plasmons and electrons in single crystalline metal nanowires. This thesis is therefore divided into two parts. In the first part, we investigate surface plasmons propagating in individual thick penta-twinned crystalline silver nanowires using dual-plane leakage radiation microscopy. The effective index and the losses of the mode are determined by measuring the wave vector content of the light emitted in the substrate. Surface plasmon mode is determined by numerical simulations and an analogy is drawn with molecular orbitals compound with similar symmetry. Leaky and bound modes selected by polarization inhomogeneity are demonstrated. We further investigate the effect of wire geometry (length, diameter) on the effective index and propagation losses. On the basis of the results obtained during the first part, we further investigate the effect of an electron flow on surface plasmon properties. We investigate to what extend surface plasmons and current-carrying electrons interfere in such a shared circuitry. By synchronously recording surface plasmons and electrical output characteristics of single crystalline silver and gold nanowires, we determine the limiting factors hindering the co-propagation of electrical current and surface plasmons in these nanoscale circuits. Analysis of wave vector distributions in Fourier images indicates that the effect of current flow on surface plasmons propagation is reflected by the morphological change during the electromigration process. We further investigate the possible crosstalk between co-propagating electrons and surface plasmons by applying alternating current bias

Pas de résumé en français / Plasmonic circuitry is considered as a promising solution-effectivetechnology for miniaturizing and integrating the next generation ofoptical nano-devices. The realization of a practical plasmonic circuitry strongly depends on the complete understanding of the propagation properties of two key elements: surface plasmons and electrons. The critical part constituting the plasmonic circuitry is a waveguide which can sustain the two information-carriers simultaneously. Therefore, we present in this thesis the investigations on the propagation of surface plasmons and the co-propagation of surface plasmons and electrons in single crystalline metal nanowires. This thesis is therefore divided into two parts. In the first part, we investigate surface plasmons propagating in individual thick penta-twinned crystalline silver nanowires using dual-plane leakage radiation microscopy. The effective index and the losses of the mode are determined by measuring the wave vector content of the light emitted in the substrate. Surface plasmon mode is determined by numerical simulations and an analogy is drawn with molecular orbitals compound with similar symmetry. Leaky and bound modes selected by polarization inhomogeneity are demonstrated. We further investigate the effect of wire geometry (length, diameter) on the effective index and propagation losses. On the basis of the results obtained during the first part, we further investigate the effect of an electron flow on surface plasmon properties. We investigate to what extend surface plasmons and current-carrying electrons interfere in such a shared circuitry. By synchronously recording surface plasmons and electrical output characteristics of single crystalline silver and gold nanowires, we determine the limiting factors hindering the co-propagation of electrical current and surface plasmons in these nanoscale circuits. Analysis of wave vector distributions in Fourier images indicates that the effect of current flow on surface plasmons propagation is reflected by the morphological change during the electromigration process. We further investigate the possible crosstalk between co-propagating electrons and surface plasmons by applying alternating current bias

Ce travail porte sur la dynamique intramoléculaire des Hydrocarbures Aromatiques Polycycliques soumis aux conditions du milieu interstellaire (PAH isolé rotationnellement froid mais vibrationnellement excité). Des études théoriques et expérimentales ont été menées sur leur deux voies de relaxation: émission IR ou fragmentation. Le spectre d'absorption IR a été obtenu par dynamique moléculaire couplée à une méthode semi-classique Adiabatic Switching. La dynamique a été réalisée sur une surface de potentiel semi-empirique Tight-Binding dans le but de simuler tous types de PAHs pouvant dépasser une centaine de carbones (systèmes encore inaccessibles aux expériences et aux calculs ab-inito). Une paramétrisation du potentiel adaptée aux PAHs a été développée ainsi qu'un modèle donnant la densité d'états anharmonique quantique. La simulation spectrale reproduit les grandes tendances en fonction des variables pertinentes en astrophysique: rôle de l'ionisation fort changement de l'allure du spectre et de l'intensité totale absolue), et de la température (décalage vers le rouge, élargissement et modification des intensités des bandes), effet d'anharmonicité (énergie de point zéro, fréquences), et de structure (compacité, cycle pentagonal et taille). La cinétique de fragmentation (induite par absorption séquentielle de photons) d'un hydrogène du cation fluorène (ionisation REMPI) a été étudiée à l'aide d'un jet supersonique et d'un spectromètre de masse. Cette méthode expérimentale originale a permis de déterminer la section efficace absolue d'absorption, d'analyser son atténuation avec le nombre de photons absorbés et l'évolution de la constante de dissociation dans un domaine d'énergie relativement large. Une attention particulière a été portée sur les techniques d'analyse des données. (la loi de Poisson, matrice de branchement, la loi cinétique, matrice d'évolution, simulation de la forme de signaux du spectromètre). Un ajustement libre de la variation de cette constante est proche de celui du modèle statistique PTD mais très différent à basse énergie du modèle RRK. L'énergie d'activation obtenue par ces deux modèles est compatible avec celle déduite du potentiel Tight-Binding.