This thesis presents the results from Monte Carlo calculations on classical vector spins in face-centered-cubic (FCC) lattices. The goal of the study was to understand the effect of interlayer coupling, dilution of magnetic atoms in the lattice, and symmetry-changing strain. Experimental work by T. M. Giebultowicz et al. and J. A. Borchers et al. greatly inspired my work [1, 2]. J. A. Borchers's group studied NiO/CoO superlattices and observed that the magnetic order of CoO persisted above its Neel temperature due to the effect of interlayer coupling with NiO, which has a higher Neel temperature than CoO [1]. Simulating on a model of NiO/CoO bilayer reproduced the experimental results from Borchers et al. [1]. I concluded that exchange pinning on the NiO/CoO interface preserves the magnetic order of CoO above its Neel temperature significantly. Building on this initial result, a ferromagnet/antiferromagnet/ferromagnet (FM/AFM/FM) trilayer model was studied, where the ferromagnetic (FM) layers were antiferromagnetically coupled. First, I calculated the strength of the AF coupling as a function of the number of antiferromagnetic (AFM) spacer monolayers and concluded that the strength of AFM coupling decreases as the number of AFM spacer monolayers increases. Secondly, I added a uniaxial anisotropy to the model and obtained magnetization curves which exhibited hysteresis-like features with an external field and a first order magnetic transition. Lastly, I diluted the AFM spacer layer in the FM/AFM/FM trilayer by replacing magnetic spins with zero spins in the model. The dilution of AFM spacer layer caused fluctuations in the magnetization curves with external field but the strength of AFM coupling decreases as the number of AFM monolayers increases as in the nondiluted cases. The experimental results from T.M. Giebultowicz's group on MnSe/ZnTe superlattices by neutron scattering showed incommensurate helical spin order in MnSe, where MnSe layers were under tensile strain due to a small mismatching in the lattice parameter [2]. In addition, they observed that the pitch of the spin helix increased as the temperature increased [2]. I modeled the MnSe/ ZnTe system with Monte Carlo method and found that the pitch of the spin helix increased with temperature. In fact, the dependence of helix pitch on temperature was present regardless of the thickness of the sample, so I concluded that this pitch increase is not from the weakening of coupling of surface spins / Graduation date: 2013 / Access restricted to the OSU Community at author's request from Jan. 18, 2013 - July 18, 2013

In this thesis we study the connection between continuum quantum field theory and corresponding lattice field theory, specifically for two cases: Landau gauge fixing and ’t Hooft-Polyakov monopoles. To study non-perturbative phenomena such as the confinement mechanism of quarks and gluons and dynamical chiral symmetry breaking in Quantum Chromodynamics (QCD), there are two major approaches: the Dyson-Schwinger equations (DSEs) approach, which is based on the covariant continuum formulation, and lattice gauge theory. The strength and beauty of lattice gauge theory is due to the fact that gauge invariance is manifest and fixing a gauge is not required. In the covariant continuum formulation of gauge theories, on the other hand, one has to deal with the redundant degrees of freedom due to gauge invariance and has to fix gauge (most popularly, Landau gauge). There, the gauge-fixing machinery is based on the so-called Faddeev-Popov procedure or more generally, the Becchi-Rouet-Stora-Tyutin (BRST) symmetry. Beyond perturbation theory this is aggravated by the existence of so-called Gribov copies, however, that satisfy the same gauge-fixing condition, but are related by gauge transformations, and are thus physically equivalent. When attempting to fix Landau gauge on the lattice to make a connection with its continuum counterpart, this ambiguity manifests itself in the Neuberger 0/0 problem that asserts that the expectation value of any physical observable will always be of the indefinite form 0/0. We explain the topological nature of this problem and how the complete cancellation of Gribov copies can be avoided in a modified lattice Landau gauge based on a new definition of gauge fields on the lattice as stereographically projected link variables. For compact U(1), where the Gribov copy problem is related to the classification the local minima of XY spin glass models, we explicitly show that there still remain Gribov copies but their number is exponentially reduced in lower dimensional models. We then formulate the corresponding Faddeev-Popov procedure on the lattice, for these models. Moreover, we explicitly demonstrate that the proposed modification circumvents the Neuberger 0/0 problem for lattices of arbitrary dimensions for compact U(1). Applied to the maximal Abelian subgroup this will avoid the perfect cancellation amongst the remaining Gribov copies for SU(N), and so the corresponding BRST formulation is also then possible for generic SU(N), in particular, for the Standard Model groups. For higher dimensional lattices, the gauge fixing conditions for both the standard and the modified lattice Landau gauges are systems of multivariate nonlinear equations, solving which in general is a highly non-trivial task. However, we show that these systems can be interpreted as systems of polynomial equations. They can then be solved exactly by computational Algebraic Geometry, the Groebner basis technique in particular, and numerically by the Polynomial Homotopy Continuation method. ’t Hooft-Polyakov monopoles play an important role in high energy physics due to their presence in grand unified theories and their usefulness in studying non-perturbative properties of quantum field theories through electric-magnetic dualities. In the second part of the thesis, we study adjoint Higgs models, which exhibit ’t Hooft-Polyakov monopoles, and have been extensively analyzed using semi-classical analysis in the continuum. However, to study them in a fully nonperturbative fashion, it is essential to put the theory on the lattice. Here, we investigate twisted C-periodic boundary conditions in SU(N) gauge field theory with an adjoint Higgs field and show that for even N with a suitable twist one can impose a non-zero magnetic charge relative to each of N − 1 residual U(1)’s in the broken phase, thereby creating ’t Hooft-Polyakov magnetic monopoles. This makes it possible then to use lattice Monte-Carlo simulations to study the properties of these monopoles in the full quantum theory and compare them with the existing results in the continuum. / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2010

La problématique des résonances acoustiques dans un tube corrugué sous écoulement a été étudiée conjointement sur le plan expérimental et numérique. Des analyses portant sur la structure de l’écoulement lors de l’apparition du sifflement sont réalisées. Elles visent à mieux comprendre la nature du phénomène et le couplage aéroacoustique en jeu.Des expériences en laboratoire sur trois géométries de veines corruguées de petites longueurs(1 à 2 m) ont été réalisées. Un écoulement d’air était appliqué pour des vitesses comprises entre10 et 25 m/s et une pression voisine de la pression atmosphérique faisant apparaître les résonancesacoustiques longitudinales. Des mesures par fil chaud, microphone et par technique laser (Particle ImageVelocimetry) ont permis de caractériser l’écoulement dans des conditions favorisant le sifflement. Sur ces différentes mesures, nous avons appliqué une technique de reconstitution spatio-temporelle, laLinear Staochastic Estimation (LSE). Des simulations numériques de type Lattice Boltzmann (2D, codePOWERFLOW, EXA) ont permis de prédire ce phénomène aéroacoustique avec une bonne détermination des modes préférentiels selon les conditions d’écoulement dans un tuyau corrugué court(1 à 2 m).Finalement, des essais à haute pression (P < 40 bars) conduits sur un riser industriel de 18 m ontcomplété cette étude. Dans ce cas, la résonance produite devenait transverse. Des traitements dessignaux tels que la transformation de Hilbert Huang ou par ondelettes de Gabor ont été appliqués mettant en évidence l’influence de la géométrie des corrugations sur le sifflement en temps, en fréquence et enamplitude.Dans les deux configurations, que ce soit en laboratoire ou en installation industrielle, les structures au sein de l’écoulement, dont la fréquence caractéristique était celle du sifflement, se déplaçaient à la vitesse de l’écoulement. Dans les deux cas, lorsque le tuyau corrugué se met à chanter, les mesures de vitesse et de pression dans l’écoulement montre une prédominance du pseudo-bruit sur le signal sonore. L’excitation observée sur les risers en condition de sifflement est celle d’un pseudo-bruit de niveau defluctuations très important sans distorsion non linéaire, et ce malgré un niveau de 170 dB. / The problem of acoustic resonances in a corrugated pipe under flow has been studied both experimentally and numerically. Analyzes concerning the flow structure during the whistling phenomenon are performed. They aim to better understand the nature of the phenomenon and the aeroacoustic coupling involved.Laboratory experiments were carried out on three geometries of corrugated veins of short lengths(1 to 2 m). An air flow was applied for speeds between 10 and 25 m/s and a pressure close toatmospheric pressure showing the longitudinal acoustic resonances. Measurements by hotwires,microphone and laser technique (Particle Image Velocimetry) allowed to characterize the flow under conditions favoring whistling. On these different measures, we applied a spatio-temporal reconstructiontechnique, the Linear Staochastic Estimation (LSE). Numerical simulations of Lattice Boltzmann method (2D, POWERFLOW code, EXA) have made possible the prediction of this aeroacousticphenomenon with a good determination of the preferential modes according to the flow conditions in ashort corrugated pipe (1 to 2 m).Finally, high pressure tests (P < 40 bars) conducted on an industrial riser of 18 m completed thisstudy. In this case, the resonance produced became transverse. Signal processing such as the HilbertHuang transformation or Gabor wavelet has been applied, highlighting the influence of the corrugation geometry on whistling in time, frequency and amplitude.In both configurations, whether in the laboratory or in an industrial facility, the structures within the flow, whose characteristic frequency was whistling, moved at the rate of flow. In both cases, when the corrugated pipe sings, velocity and pressure measurements in the flow show a predominance of the pseudo-noise on the sound signal. The excitation observed on the risers in the whistling condition is that of a pseudo-noise of very high level of fluctuations without non-linear distortion, and this despite a level of 170 dB.

[pt] Na construção de filtros digitais os coeficientes da sua função de transferência, calculados teoricamente, nem sempre podem ser implementados com exatidão. Isto gera o erro de quantização. A análise de sensibilidade permite conhecer tal alteração das especificações teóricas como também avaliar o desempenho do filtro. Este trabalho examina a estrutura Lattice-Ladder, tipo de filtro digital, descrita por equações de estado genéricas. O objetivo é estabelecer expressões de sensibilidade nos domínios do tempo e da freqüência, para resposta impulsional e resposta a uma excitação qualquer. / [en] In the construction of digital filters the coeficientes of its transfer function, calculated theorically, can´t often be implemented with accuracy. This leads to the quantization error. The sensitivy analysis allows to know this deviation from theoretical specifications and allows to estimate filter´s performance. This work examines Lattice- Ladder structure, a type of digital filter, described by generic state equations. The purpose is to establish sensivity expressions in time and frequency domains, for impulse and generic responses.

Discutimos um modelo de calibre com simetria Z (N) na rede, sendo as variáveis dinâmicas definidas em faces de cubos. Mostramos a dualidade com um sistema de spins Z (N) em quatro dimensões e a autodualidade em seis dimensões para este modelo, utilizando o formalismo da matriz de transferência. Analisamos as funções de correlação invariantes por transformações de calibre, constatando os decaimentos exponenciais com o volume (para altas temperaturas e d &#8805 3) e com a área (para baixas temperaturas e d > 3). Para três dimensões, o modelo não apresenta transição de fase sendo exatamente solúvel. Estudamos também a versão U (1) do modelo e mostramos sua equivalência com uma teoria de campos clássica livre na região de baixas temperaturas / We discussus a model with a Z (N) gauge symmetry on a lattice, the dynamical variables being defined on faces of cubes. The duality with a Z (N) spin system in four dimensions and the selfduality in six dimensions is shown for this model, using the transfer matrix formalism. The gauge invariant correlation functions have been analysed and we verify their exponential decay with volume (at high temperatures and d &#8805 3) and with the área (at low temperatures and d > 3). For three dimensions, the model exhibits no phase transition, being exactly soluble. We also study a U (I) version o four model and show its equivalence with a free classical field theory in the low temperature region

Un large spectre d’applications en ingénierie est concerné par les écoulements de fluides en interaction avec des structures poreuses, allant de problèmes à petite échelle jusqu’à des problématiques de plus grande échelle. Ces structures poreuses, souvent à géométries complexes, peuvent se déplacer ou se déformer en réponse au forçage exercé par l’écoulement environnant.Le but de ce travail est de proposer un modèle numérique pour la simulation macroscopique d’écoulements de fluide interagissant avec des milieux poreux mobiles à géométries complexes, qui soit facile d’implémentation et pouvant être utilisé dans une large gamme d’applications. Pour atteindre cet objectif, la méthode de Lattice Boltzmann est utilisée pour résoudre l’écoulement dans des milieux poreux à l’échelle d’un volume représentatif élémentaire. Pour l’implémentation du mouvement désiré, le concept de frontières immergées est adopté. Dans ce contexte, un nouveau modèle est proposé pour traiter des milieux poreux en volume, dont la résistance à l’écoulement environnant est modélisé par la loi de Brinkman-Forchheimer-Darcy étendue.L’algorithme est d’abord testé sur l’écoulement à travers un cylindre fixe. La simplicité de ce cas test académique permet de caractériser finement la précision de la méthode. Le modèle est ensuite utilisé pour simuler des écoulements de fluide autour et à travers des corps poreux mobiles, à la fois pour des géométries confinées et pour des écoulements ouverts. L’invariance Galiléenne des équations moyennées macroscopiques gouvernant la dynamique du fluide est démontrée. D’excellents accords avec les résultats de référence sont obtenus pour les différents cas testés. / A wide spectrum of engineering problems is concerned with fluid flows in interaction with porous structures, ranging from small length-scale problems to large ones. These structures, often of complex geometry, may move/deform in response to the forces exerted by the surrounding flow. Despite the advancements in computational fluid dynamics, the numerical simulation of such configurations - a valuable tool for the study of the flow physics involved - remains a challenging task.The aim of the present work is to propose a numerical model for the macroscopic simulation of fluid flows interacting with moving porous media of complex geometry, that is easy to implement and can be used in a range of applications. To achieve this, the Lattice Boltzmann method is employed for solving the flow in porous media at the representative elementary volume scale. For the implementation of the desired body motion, the concept of the Immersed Boundary method is adopted. In this context, a novel model is proposed for dealing with moving volumetric porous media, whose resistance to the surrounding flow obeys the Brinkman-Forchheimer-extended Darcy law. The algorithm is initially tested for flow past a static cylinder. The simplicity of this academic test case allows us to assess in detail the accuracy of the proposed method. The model is later used to simulate fluid flows around and through moving porous bodies, both in a confined geometry and in open space. We are able to demonstrate the Galilean invariance of the macroscopic volume-averaged flow governing equations. Excellent agreement with reference results is obtained in all cases.

Les écoulements autour de structures en mouvement font l'objet de plusieurs travaux numériques et expérimentaux. L'objectif de ce travail de thèse consiste à montrer la pertinence de la combinaison de la pénalisation volumique avec la méthode de lattice Boltzmann (LBM), dans l'étude du mouvement d'obstacles mobiles dans un écoulement, et de leur interaction avec celui-ci. La LBM,qui est simple et précise à mettre en œuvre, a prouvé ces dernières années son efficacité dans le domaine de la mécanique des fluides. Par ailleurs, la méthode de pénalisation volumique consiste à introduire un terme de pénalisation dans l'équation que l'on souhaite résoudre, afin de prendre en compte l'influence de l'obstacle sur le domaine fluide. Comme cette équation est résolue sur l'ensemble du domaine composé du fluide et du solide, les conditions aux limites à l'interface fluide-solide sont appliquées de façon naturelle. Il semble donc aisé de combiner cette technique avec la méthode de lattice Boltzmann. Nous avons dans un premier temps rappelé les notions de base et les principales caractéristiques de la méthode de lattice Boltzmann. On a présenté quelques exemples d'applications sur des cas tests, que nous avons programmés. Ensuite, une étude bibliographique faisant état des différentes approches qui utilisent la LBM dans l'étude des problèmes d'interaction fluide structure (IFS) a été réalisée. Puis, la combinaison de la pénalisation volumique avec la LBM a été testée avec succès sur l'équation de Burgers monodimensionnelle. La validation s'est portée en premier lieu, sur un écoulement autour d'un solide fixe, puis sur un écoulement autour d'une structure dont le mouvement est imposé, et finalement sur un problème d'IFS de type masse-ressort. La méthode développée a été ensuite testée sur les équations de Navier-Stokes, en considérant un fluide incompressible et une structure rigide. La validation s'est portée tout d'abord sur un écoulement autour d'obstacles immobiles (carré et cylindre), puis autour d'un cylindre mobile en oscillations forcées et libres. Enfin, une dernière application a été portée sur un écoulement entre deux plaques mobiles dans un canal. Nous avons montré que pour tous les cas étudiés, l'approche développée donne de bons résultats, elle reproduit avec précision les résultats de référence. / Flows around moving bodies are the subject of several numerical and experimental studies. The work presented in this document deals with the implementation of a volume penalization technique in a lattice Boltzmann model (LBM), in order to compute flows around moving obstacles. The LBM, which is accurate and easy to implement, has been successfully applied in fluid mechanics during the last decades. It was thus chosen in the present work, for flow computation. Furthermore, the volume penalization technique consists in introducing a volume penalization term into the equation that needs to be solved, in order to take into account the influence of the obstacle on the fluid domain. Since this equation is solved on both fluid and solid domains, the boundary conditions at the fluid-solid interface are naturally applied. Hence this technique seems easy to implement in a lattice Boltzmann framework. In the first chapter, the foundations and the main features of the lattice Boltzmann method are recalled, and several test cases that we simulated are presented. The second chapter deals with a literature review of the techniques developed for the simulation of fluid structure interaction problems in combination with the LBM. In the third chapter, the volume penalization method combined with the LBM was first applied to the one dimensional Burgers equation, considering motionless and moving obstacles (forced motion, and coupling between the fluid force calculated with the penalized Burgers equation and the motion of the obstacle). The combination of the volume penalization approach and the LBM was then employed to solve the incompressible NavierStokes equations, for cases of flows past motionless obstacles (flows over a square obstacle, and past a circular cylinder), and past an oscillating cylinder (where forced and free oscillations of the cylinder were simulated). Finally, this method was also applied to a symmetric Couette flow. For all these simulated cases, a good agreement with numerical results obtained with other techniques, and with results found in literature, was obtained.

Quantum Chromo Dynamics (QCD) is a relativistic field theory of a non-abelian gauge field coupled to several flavors of fermions. Two dimensional (one space and one time) QCD serves as an interesting toy model that shares several features with the four dimensional physically relevant theory. The main aim of the research is to study two dimensional QCD using the lattice regularization. Two dimensional QCD without any fermion content is solved analytically using lattice regularization. Explicit expressions for the expectation values of Wilson loops and the correlation of two Polyakov loops oriented in two different directions are obtained. Physics of the QCD vacuum is explained using these results. The Hamiltonian formalism of lattice QCD with fermion content serves as an approach to study quark excitations out of the vacuum. The formalism is first developed and techniques to numerically evaluate the spectrum of physical particles, namely, meson and baryons are described. The Hybrid Monte Carlo technique was used to numerically extract the lowest meson and baryon masses as a function of the quark masses. It is shown that neither the lowest meson mass nor the lowest baryon mass goes to zero as the quark mass is taken to zero. This numerically establishes the presence of a mass gap in two dimensional QCD.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21568号 / 理博第4475号 / 新制||理||1642(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 青木 慎也, 教授 田中 貴浩, 准教授 髙山 史宏 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23005号 / 理博第4682号 / 新制||理||1672(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 大西 明, 准教授 菅沼 秀夫, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM