Tesis: "Symmetry group"

1

George, Timothy Edward. "Symmetric representation of elements of finite groups". CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3105.

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The purpose of the thesis is to give an alternative and more efficient method for working with finite groups by constructing finite groups as homomorphic images of progenitors. The method introduced can be applied to all finite groups that possess symmetric generating sets of involutions. Such groups include all finite non-abelian simple groups, which can then be constructed by the technique of manual double coset enumeration.

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2

Carteret, Hilary Ann. "Symmetry and multiparticle entanglement". Thesis, University of York, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341118.

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3

Lee, Seungkyu Liu Yanxi. "Symmetry group extraction from multidimensional real data". [University Park, Pa.] : Pennsylvania State University, 2009. http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-4720/index.html.

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4

Bone, Richard George Andrew. "New applications of the molecular symmetry group". Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239761.

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5

Henninger, Helen Clare. "The symmetry group of a model of hyperbolic plane geometry and some associated invariant optimal control problems". Thesis, Rhodes University, 2012. http://hdl.handle.net/10962/d1018232.

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In this thesis we study left-invariant control offine systems on the symmetry group of a. model of hyperbolic plane geometry, the matrix Lie group SO(1, 2)₀. We determine that there are 10 distinct classes of such control systems and for typical elements of two of these classes we provide solutions of the left-invariant optimal wntrol problem with quauratic costs. Under the identification of the Lie allgebra .so(l, 2) with Minkowski spacetime R¹̕'², we construct a controllabilility criterion for all left-invariant control affine systems on 50(1. 2)₀ which in the inhomogeneous case depends only on the presence or absence of an element in the image of the system's trace in R¹̕ ²which is identifiable using the inner product. For the solutions of both the optimal control problems, we provide explicit expressions in terms of Jacobi elliptic functions for the solutions of the reduced extremal equations and determine the nonlinear stability of the equilibrium points.

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6

Huyal, Ulas. "Conformal Symmetry In Field Theory". Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613136/index.pdf.

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In this thesis, conformal transformations in d and two dimensions and the results of conformal symmetry in classical and quantum field theories are reviewed. After investigating the conformal group and its algebra, various aspects of conformal invariance in field theories, like conserved charges, correlation functions and the Ward identities are discussed. The central charge and the Virasoro algebra are briefly touched upon.

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7

Hills, Robert K. "The algebra of a class of permutation invariant irreducible operators". Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260729.

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8

Vaintrob, Dmitry. "Mirror symmetry and the K theory of a p-adic group". Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104578.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 59-61).
Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building whose stalks have finite-multiplicity isotypic components as representations of the stabilizer. Our construction is motivated by the "coherent-constructible correspondence" functor in toric mirror symmetry and a construction of [CCC]. We show that Loc has a number of useful properties, including the fact that the sections ... compactifying the finitely-generated representation V. We also construct a depth by Dmitry A. Vaintrob.
Ph. D.

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9

Gersch, Roland. "Symmetry breaking in interacting Fermi systems with the functional renormalization group". [S.l. : s.n.], 2007. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-32947.

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10

Cassart, Delphine. "Optimal tests for symmetry". Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210693.

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Dans ce travail, nous proposons des procédures de test paramétriques et nonparamétrique localement et asymptotiquement optimales au sens de Hajek et Le Cam, pour trois modèles d'asymétrie.

La construction de modèles d'asymétrie est un sujet de recherche qui a connu un grand développement ces dernières années, et l'obtention des tests optimaux (pour trois modèles différents) est une étape essentielle en vue de leur mise en application.

Notre approche est fondée sur la théorie de Le Cam d'une part, pour obtenir les propriétés de normalité asymptotique, bases de la construction des tests paramétriques optimaux, et la théorie de Hajek d'autre part, qui, via un principe d'invariance permet d'obtenir les procédures non-paramétriques.

Nous considérons dans ce travail deux classes de distributions univariées asymétriques, l'une fondée sur un développement d'Edgeworth (décrit dans le Chapitre 1), et l'autre construite en utilisant un paramètre d'échelle différent pour les valeurs positives et négatives (le modèle de Fechner, décrit dans le Chapitre 2).

Le modèle d'asymétrie elliptique étudié dans le dernier chapitre est une généralisation multivariée du modèle du Chapitre 2.

Pour chacun de ces modèles, nous proposons de tester l'hypothèse de symétrie par rapport à un centre fixé, puis par rapport à un centre non spécifié.

Après avoir décrit le modèle pour lequel nous construisons les procédures optimales, nous obtenons la propriété de normalité locale asymptotique. A partir de ce résultat, nous sommes capable de construire les tests paramétriques localement et asymptotiquement optimaux. Ces tests ne sont toutefois valides que si la densité sous-jacente f est correctement spécifiée. Ils ont donc le mérite de déterminer les bornes d'efficacité paramétrique, mais sont difficilement applicables.

Nous adaptons donc ces tests afin de pouvoir tester les hypothèses de symétrie par rapport à un centre fixé ou non, lorsque la densité sous-jacente est considérée comme un paramètre de nuisance.

Les tests que nous obtenons restent localement et asymptotiquement optimaux sous f, mais restent valides sous une large classe de densités.

A partir des propriétés d'invariance du sous-modèle identifié par l'hypothèse nulle, nous obtenons les tests de rangs signés localement et asymptotiquement optimaux sous f, et valide sous une vaste classe de densité. Nous présentons en particulier, les tests fondés sur les scores normaux (ou tests de van der Waerden), qui sont optimaux sous des hypothèses Gaussiennes, tout en étant valides si cette hypothèse n'est pas vérifiée.

Afin de comparer les performances des tests paramétriques et non paramétriques présentés, nous calculons les efficacités asymptotiques relatives des tests non paramétriques par rapport aux tests pseudo-Gaussiens, sous une vaste classe de densités non-Gaussiennes, et nous proposons quelques simulations.
Doctorat en sciences, Orientation statistique
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11

Basalaev, Alexey [Verfasser]. "Mirror symmetry for simple elliptic singularities with a group action / Alexey Basalaev". Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2015. http://d-nb.info/1073604454/34.

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12

Bauer, Johannes. "Renormalisation group study of broken symmetry states in strongly correlated electron systems". Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.502607.

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13

Knight, Jason. "Various methods for calculating reducible and irreducible representations of the symmetric group a thesis presented to the faculty of the Graduate School, Tennessee Technological University /". Click to access online, 2009. http://proquest.umi.com/pqdweb?index=30&sid=1&srchmode=1&vinst=PROD&fmt=6&startpage=-1&clientid=28564&vname=PQD&RQT=309&did=1760001861&scaling=FULL&ts=1251310430&vtype=PQD&rqt=309&TS=1251310467&clientId=28564.

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14

Wiseman, Robin D. "The Jahn-Teller effect in icosahedral symmetry : unexpected lie group symmetries and their exploitation". Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299385.

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15

Sonnenschein, Jonas [Verfasser]. "Mean-field theory and projective symmetry group classifications of quantum spin liquids / Jonas Sonnenschein". Berlin : Freie Universität Berlin, 2020. http://d-nb.info/1220288179/34.

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16

Mukai, Daichi. "Mirror symmetry of nonabelian Landau-Ginzburg orbifolds with loop type potentials". Kyoto University, 2020. http://hdl.handle.net/2433/253068.

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17

Wagner, Andrew. "On the Existence of a Second Hamilton Cycle in Hamiltonian Graphs With Symmetry". Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/30290.

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In 1975, Sheehan conjectured that every simple 4-regular hamiltonian graph has a second Hamilton cycle. If Sheehan's Conjecture holds, then the result can be extended to all simple d-regular hamiltonian graphs with d at least 3. First, we survey some previous results which verify the existence of a second Hamilton cycle if d is large enough. We will then demonstrate some techniques for finding a second Hamilton cycle that will be used throughout this paper. Finally, we use these techniques and show that for certain 4-regular Hamiltonian graphs whose automorphism group is large enough, a second Hamilton cycle exists.

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18

Kangwai, Riki Dale. "The analysis of symmetric structures using group representation theory". Thesis, University of Cambridge, 1998. https://www.repository.cam.ac.uk/handle/1810/265422.

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Group Representation Theory is the mathematical language best suited to describing the symmetry properties of a structure, and a structural analysis can utilises Group Representation Theory to provide the most efficient and systematic method of exploiting the full symmetry properties of any symmetric structure. Group Representation Theory methods currently exist for the Stiffness Niethod of structural analysis, where the stiffness matrix of a structure is block-diagonalised into a number of independent submatrices, each of which relates applied loads and displacements with a particular type of symmetry. This dissertation extends the application of Group Representation Theory to the equilibrium and compatibility matrices which are commonly used in the Force Method of structural analysis. Group Representation Theory is used to find symmetry-adapted coordinate systems for both the external vector space which is suitable for representing the loads applied to a structure, and the internal vector space wh",t-k is-suitable for representing the internal forces. Using these symmetry-adapted coordinate systems the equilibrium matrix is block-diagonalised into a number of independent submatrix blocks, thus decomposing the analysis into a number of subproblems which require less computational effort. Each independent equilibrium submatrix block relates applied loads and internal forces with particular symmetry properties, and hence any states of self-stress or inextensional mechanisms in one of these equilibrium submatrix blocks will necessarily have ~rresponding symmetry properties. Thus, a symmetry analysis provides valuable insight into the behaviour of symmetric structures by helping to identify and classif:)'. any states of self-stress .or inextensional mechanisms present in a structure. In certain cases it is also possible for a symmetry analysis to identify when a structure contains a :ijnite rather than infinitesimal mechanism. To do this a symmetry analysis must b~ carried out using the symmetry properties of the inextensional mechanism of interest. If the analysis shows that any states of self-stress which exist in the structure have "lesser" symmetry properties, then the states of self-stress exist independently from the mechanism and cannot prevent its finite motion.

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19

Ariyabuddhiphongs, Kris. "Symmetry of Interpersonal Rhythmic Coordination: The Case of a Three-Person Drumming Task". University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1490352126579119.

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20

Nikolaishvili, George. "Investigation of the Equations Modelling Chemical Waves Using Lie Group Analysis". Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-3996.

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A system of nonlinear di fferential equations, namely, the Belousov-Zhabotinskii reaction model has been investigated for nonlinear self-adjointness using the recent work of Professor N.H.Ibragimov. It is shown that the model is not nonlinearly self-adjoint. The symmetries of the system and nonlinear conservation laws are calculated. The modi fied system, which is nonlinearly self-adjoint, is also analysed. Its symmetries and conservation laws are presented.

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21

Jain, Akash. "Estimation of Melting Points of Organic Compounds". Diss., Tucson, Arizona : University of Arizona, 2005. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu%5Fetd%5F1303%5F1%5Fm.pdf&type=application/pdf.

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22

Fedosov, Boris, Bert-Wolfgang Schulze y Nikolai Tarkhanov. "On index theorem for symplectic orbifolds". Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2655/.

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23

Dong, Bin. "Modal Analysis of General Cyclically Symmetric Systems with Applications to Multi-Stage Structures". Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/102605.

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This work investigates the modal properties of general cyclically symmetric systems and the multi-stage systems with cyclically symmetric stages. The work generalizes the modal properties of engineering applications, such as planetary gears, centrifugal pendulum vibration absorber (CPVA) systems, multi-stage planetary gears, etc., and provides methods to improve the computational efficiency to numerically solve the system modes when cyclically symmetric structures exist. Modal properties of cyclically symmetric systems with vibrating central components as three-dimensional rigid bodies are studied without any assumptions on the system matrix symmetries: asymmetric inertia matrix, damping, gyroscopic, and circulatory terms can be present. In the equation of motion of such a cyclically symmetric system, the matrix operators are proved to have properties related to the cyclic symmetry. These symmetry-related properties are used to prove the modal properties of general cyclically symmetric systems. Only three types of modes can exist: substructure modes, translational-tilting modes, and rotational-axial modes. Each mode type is characterized by specific central component modal deflections and substructure phase relations. Instead of solving the full eigenvalue problem,all vibration modes and natural frequencies can be obtained by solving smaller eigenvalue problems associated with each mode type. This computational advantage is dramatic for systems with many substructures or many degrees of freedom per substructure. Group theory is applied to further generalize the modal properties of cyclically symmetric systems when both rigid-body and compliant central components exist, such as planetary gears with an elastic continuum ring gear. The group theory for symmetry groups is introduced, and the group-theory-based modal analysis does not rely on any knowledge of the properties of system matrices in system equations of motion. The three types of modes (substructure modes, translational-tilting modes, and rotational-axial modes) are characterized by specific rigid-body central component modal defections, substructure phase relations, and nodal diameter components of compliant central components. The general formulation of reduced eigenvalue problems for each mode type is obtained through group-theory-based method, and it applies to discrete, continuous, or hybrid discrete-continuous cyclically symmetric systems. The group-theory-based modal analysis also applies to systems with other symmetry types. The group-theory-based modal analysis is generalized to analyze the multi-stage systems that are composed of symmetric stages coupled through the motions of rigid-body central components. The proposed group-theory-based modal analysis applies to multi-stage systems with cyclically symmetric stages, such as multi-stage planetary gears and CPVA systems with multiple groups of absorbers. The method also applies to multi-stage systems with component stages that have different types of symmetry. For a multi-stage system with symmetric stages, a unitary transformation matrix can be built through an algorithmic and computationally inexpensive procedure. The obtained unitary transformation matrix provides the foundation to analyze the modal properties based on the principles of group-theory-based modal analysis. For general multi-stage systems with symmetric component stages, the vibration modes are classified into two general types, single-stage substructure modes and overall modes, according to the non-zero modal deflections in each component stage. Reduced eigenvalue problems for each mode type are formulated to reduce the computational cost for eigensolutions. Finite element models of multi-stage bladed disk assemblies consist of multiple cyclically symmetric bladed disks that are coupled through the boundary nodes at the inter-stage interface. To improve the computational efficiency of calculating the full system modes, a numerical method is proposed by combination of the multi-stage cyclic symmetry reduction method and the subspace iteration method. Compared to the multi-stage cyclic symmetry reduction method, the proposed method improves the accuracy of obtained eigensolutions through an iterative process that is derived from the subspace iteration method. Based on the cyclic symmetry in each component stage of bladed disk, the proposed iterative method that can be performed using single stage sector models only, instead of using matrix operators for the full multi-stage bladed disks. Parallel computations can be performed in the proposed iterative method, and the computational speed for eigensolutions can be increased significantly.
Doctor of Philosophy

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24

Robinson, Matthew Brandon Cleaver Gerald B. "Towards a systematic investigation of weakly coupled free fermionic heterotic string gauge group statistics". Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5358.

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25

Tighe, John Francis. "Derivative expansions of the exact renormalisation group and SU(NN) gauge theory". Thesis, University of Southampton, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368120.

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26

Nosrati, Mona. "Touching the intangible : high-school students' encounters with, explorations of, and discoveries about the symmetry group of the square". Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708235.

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27

Magini, Marcio. "Análise de simetrias nos grupos do tipo Dm usando conceitos de sistemas dinâmicos". Universidade de São Paulo, 1999. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-10092008-105333/.

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O entendimento de quebra espontânea de simetria é um problema importante para o estudo de fenômenos na evolução de sistemas abertos, tanto em física quanto em química, como também na biologia. Aqui estudamos um método a mais para este tipo de análise, usando conceitos de sistemas dinâmicos com simetria. O sistema dinâmico escolhido é discreto, isto é, realizado por iteração de um difeomorfismo equivariante sob a ação de um grupo compacto, neste caso um grupo finito do tipo Dm. Especificamente, investigamos o comportamento de atratores caóticos sob a variação dos parâmetros.
The understanding of spontaneous symmetry breaking is an important problem in the study of phenomena in the evolution of open systems, in physics and chemistry as well as in biology. Here we study another method for this kind of analysis, using concepts from dynamical systems with symmetry. The chosen dynamical system is discrete, that is, realized by iteration of an equivariant diffeomorphism under the action of a compact group, in this case one of the finite groups of type Dm. Specifically, we investigate the behavior of chaotic attractors under variation of the parameters.

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28

Alrashdi, Huda Daefallh A. "q-discrete Painleve equations, their hierarchies and properties". Thesis, The University of Sydney, 2019. https://hdl.handle.net/2123/21311.

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The main objective of this thesis is to derive hierarchies of q-discrete Painelevé equations. Some of the important properties of these hierarchies will also be given, namely Lax pairs, Bäcklund transformations, solutions of their associated linear problems for special values of parameters and their symmetry groups. To construct these hierarchies, we apply a geometric reduction and a staircase method on a multi-parameteric generalized lattice modified Korteweg-de Vries equation. In addition, the property of consistency around the cube is used in order to find Bäcklund transformations. Starting with the base case of q-discrete second, third and fourth Painlevé equations on A_5 initial-values surface, new hierarchies of q-discrete third and fourth Painlevé equations are discovered, and we also rediscover the hierarchy of q-discrete second Painlevé equation. In this thesis, we provide the Lax pairs for each member in these hierarchies. Using the consistency around the cube, we also provide Bäcklund transformation for the entire hierarchy of q-discrete second and third Painlevé hierarchies. We generate a hierarchy of special solutions starting with seed solutions for q-discrete second and third Painlevé hierarchies. An assumption made is that particular parameter values would enable the ability to diagonalize the Lax pair. As a consequence, we found that the associated linear problem for the three hierarchies can be solved in terms of q-Gamma function. Furthermore, the hierarchy of q-discrete fourth Painlevé hierarchy can be reduced to one equation that can be linearlized to become Riccati equation which has hypergeometric special solutions. Finally, we investigated the affine Weyl group structure of the symmetry group for each hierarchy. In this thesis, we construct the explicit representation of the symmetry group for the first and second member of these hierarchies.

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29

Wasserman, Benjamin. "Variétés magnifiques de rang deux". Grenoble 1, 1997. http://www.theses.fr/1997GRE10037.

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Soit g un groupe reductif complexe (connexe). Les g-varietes magnifiques les plus connues sont celles de rang zero, a savoir les varietes de drapeaux generalisees g/p, celles de rang un, classifiees par akhiezer, et certaines varietes symetriques completes decrites par de concini et procesi comme par exemple le celebre espace des coniques completes. Il y a recemment un interet renouvele pour les varietes magnifiques de rang deux car des travaux de luna, brion, pauer et knop montrent que celles-ci jouent un role clef dans la theorie des varietes spheriques. L'objectif de ce travail est la classification des varietes magnifiques de rang deux. Ces dernieres peuvent se caracteriser de la maniere suivante. Ce sont des g-varietes lisses completes contenant quatre orbites, a savoir une orbite dense et deux orbites de codimension un dont les adherences d#1 et d#2 se coupent transversalement en la quatrieme orbite qui est de codimension deux. Nous avons recueilli nos resultats dans des tables, contenant groupes d'isotropie et donnees combinatoires en rapport avec la theorie des varietes spheriques.

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30

Marchese, Luca. "Quantum simulation of abelian and non-abelian gauge theories". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/24857/.

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Le teorie di gauge sono onnipresenti nella fisica moderna, trovando applicazioni in diversi ambiti, dal modello standard alla fisica della materia condensata. Il recente sviluppo della tecnologia quantistica apre ora le porte a nuove tecniche utili al loro approfondimento, ampliando la nostra conoscenza di questi modelli ed oltrepassando i limiti degli approcci basati sul metodo di Montecarlo, quali il problema del segno e l'impossibilità di studiare la dinamica dei sistemi in tempo reale. Questa tesi si concentra sull'implementazione di una simulazione per una teoria di Yang-Mills su reticolo con un gruppo di simmetria finito. Abbiamo testato diversi gruppi, sia abeliani (Z2 e Z4) che non abeliani (D4), per i quali abbiamo emulato i risultati di un computer quantistico in un modello a 2+1 dimensioni. Una caratteristica fondamentale di questi modelli è la presenza di vincoli sullo spazio di Hilbert che determinano quali stati possono entrare nella dinamica. Nel caso abeliano siamo in grado di sfruttare la minore dimensione dello spazio degli stati fisici per introdurre una codifica più efficiente nella base computazionale. Nel caso invece di una simmetria data da gruppi non abeliani, questo metodo non può essere direttamente implementato a causa della comparsa di stati più complessi. Usando la misura del valore di aspettazione di vari Wilson loop, abbiamo trovato che tutti i sistemi analizzati presentano due fasi, una confinata e una non confinata. Sfruttando la semplicità dei sistemi abeliani siamo anche riusciti in quei casi a verificare direttamente la legge del perimetro e la legge dell'area, che descrivono il comportamento dei Wilson loop nelle due differenti fasi.

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31

Franzini, Tommaso. "Thermodynamic Bethe Ansatz for a family of scattering theories with U_q(sl(2)) symmetry". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20546/.

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In this thesis work we analyze a wide class of 1+1 dimensional integrable scattering theories with Uq(sl(2)) quantum group symmetry, whose asymptotic states are multiplets of particles with iso-spin k/2. Their two-body S-matrices have been recently found in terms of the R matrix of the quantum group. Since they satisfy Yang-Baxter equation, unitarity and crossing symmetry, they represent a consistent integrable factorized scattering theory. The question of finding the corresponding underlying QFT can be addressed once the Thermodynamic Bethe Ansatz (TBA) is obtained. In this work we get the TBA equations and we compare them to previous known results of S. R. Aladim e M. J. Martins for the particular case when q→1.

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32

Lindman, Hornlund Josef. "Sigma-models and Lie group symmetries in theories of gravity". Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209911.

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En utilisant des modèles sigma non-linéaires de fonctions d'un espace-temps D-dimensionnel à un espace symétrique G/H, nous discutons de solutions de type trou noir et membrane noire dans diverses théories de gravité supersymétriques. Un espace symétrique est une variété, riemannienne ou pseudo-riemannienne, pour laquelle le tenseur de Riemann est covariantement constant. L'utilisation du dictionnaire Kac-Moody/supergravité et les techniques de réduction dimensionnelles nous permettent de décrire des trous noirs de cohomogénéité un comme des géodésiques sur G/H. Un espace-temps M, potentiellement agrémenté d'un trou noir, est de cohomogénéité un s'il existe un groupe d'isométries Iso qui agit sur M et dont le quotient M/Iso est uni-dimensionnel. L'utilisation d'algèbres de Kac-Moody dans les théories de gravité a été développé dans l'espoir de décourvrir la symétrie sous-jacente de la théorie des cordes, aussi appelée théorie M. Les techniques de réduction dimensionnelle ont depuis longtemps été utilisées pour dévoiler les symétries cachées des théories de gravité. Dans la description du modèle sigma, les trous noirs extrémaux ou branes noires sont des géodésiques nulles et correspondent à un élément nilpotent de l'algèbre de Lie g de G. Un élément X nilpotent est caractérisé par la propriété X^n = 0. En utilisant le formalisme mathématique decrivant les orbites nilpotentes, nous classifions tous les trous noirs extrémaux dans la supergravité N=2 minimale à quatre dimensions, N=2 S^3 supergravité en quatre dimensions et la supergravité minimale en cinq dimensions. De la même manière, quand G est un sous-groupe d'un groupe Kac-Moody, très-étendu ou sur-étendu, on envoie l'orbite nilpotente minimale, en utilisant le plus haut poids de g, sur des solutions supersymétriques et non-supersymétriques de type brane dans les théories de supergravité à dix et onze dimensions. Nos résultats montrent que les symétries du groupe de Lie sont très utiles de ces solutions pour classer et trouver de nouvelles solutions de type trou noir. Afin de prouver l'unicité et plusieurs autres résultats formels, nous avons développé des méthodes préliminaires dans l'espoir qu'elles puissent être utilisées à l'avenir pour l'étude des trous noirs.
Doctorat en Sciences
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33

Maroncelli, Andrea. "QED and Abelian lattice gauge theories in 2+1 dimensions". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18042/.

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La simulazione di sistemi quantistici con molti gradi di libertà è oggi una sfida impegnativa per la comunità scientifica a causa degli elevati tempi computazionali che crescono esponenzialmente all'aumentare del numero di particelle. Al seguito degli orizzonti aperti dall'articolo "Simulating physics with computers" di Feynman, oggi sono stati fatti numerosi progressi. Egli teorizzò un simulatore quantistico che fosse un vero e proprio apparato fisico che evolvesse nello stesso modo del sistema da studiare e la cui dinamica potesse essere controllata. Sulla base di quest'idea, oggi è possibile abbattere l'elevato costo computazionale che, in tal modo, cresce linearmente con la taglia dello spazio di Hilbert. Negli ultimi anni, infatti, sono stati svolti diversi esperimenti in numerosi laboratori. Ad esempio, sono stati utilizzati atomi ultrafreddi intrappolati in reticoli ottici per simulare fenomeni quantistici come la superconduttività. Seguendo tale principio, in questo lavoro di tesi abbiamo implementato teorie abeliane, in special modo la QED, su reticolo bidimensionale che serviranno per una futura simulazione quantistica. Da qui, abbiamo analizzato alcuni fenomeni di attivo interesse di ricerca, come lo studio di transizioni di fase in modelli con simmetria $\mathbb{Z}_2$ e $\mathbb{Z}_3$, che presentano una fase confinata e una deconfinata, classificato gli stati gauge invarianti ed esaminato il meccanismo dello string-breaking su reticolo.

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34

Ruzziconi, Romain. "On the Various Extensions of the BMS Group". Doctoral thesis, Universite Libre de Bruxelles, 2020. https://dipot.ulb.ac.be/dspace/bitstream/2013/307600/4/Contents.pdf.

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The Bondi-Metzner-Sachs-van der Burg (BMS) group is the asymptotic symmetry group of radiating asymptotically flat spacetimes. It has recently received renewed interest in the context of the flat holography and the infrared structure of gravity. In this thesis, we investigate the consequences of considering extensions of the BMS group in four dimensions with superrotations. In particular, we apply the covariant phase space methods on a class of first order gauge theories that includes the Cartan formulation of general relativity and specify this analysis to gravity in asymptotically flat spacetime. Furthermore, we renormalize the symplectic structure at null infinity to obtain the generalized BMS charge algebra associated with smooth superrotations. We then study the vacuum structure of the gravitational field, which allows us to relate the so-called superboost transformations to the velocity kick/refraction memory effect. Afterward, we propose a new set of boundary conditions in asymptotically locally (A)dS spacetime that leads to a version of the BMS group in the presence of a non-vanishing cosmological constant, called the Λ-BMS asymptotic symmetry group. Using the holographic renormalization procedure and a diffeomorphism between Bondi and Fefferman-Graham gauges, we construct the phase space of Λ-BMS and show that it reduces to the one of the generalized BMS group in the flat limit.
Doctorat en Sciences
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35

Michel, Jean-Luc. "Polysimplices in euclidean spaces and the enumeration of domino tilings of rectangles". Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209922.

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Nous étudions, dans la première partie de notre thèse, les polysimplexes d’un espace euclidien de dimension quelconque, c’est-à-dire les objets consistant en une juxtaposition de simplexes réguliers (de tétraèdres si la dimension est 3) accolés le long de leurs faces. Nous étudions principalement le groupe des symétries de ces polysimplexes. Nous présentons une façon de représenter un polysimplexe à l’aide d’un diagramme. Ceci fournit une classification complète des polysimplexes à similitude près. De plus, le groupe des symétries se déduit du groupe des automorphismes du diagramme. Il découle en particulier de notre étude qu’en dimension supérieure à 2, une telle structure ne possède jamais deux faces parallèles et ne contient jamais de circuit fermé de simplexes.

Dans la seconde partie de notre thèse, nous abordons un problème classique de combinatoire :l’énumération des pavages d’un rectangle mxn à l’aide de dominos. Klarner et Pollack ont montré qu’en fixant m la suite obtenue vérifie une relation de récurrence linéaire à coefficients constants. Nous établissons une nouvelle méthode nous permettant d’obtenir la fonction génératrice correspondante et la calculons pour m <= 16, alors qu’elle n’était connue que pour m <= 10.

Doctorat en Sciences
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36

Hussein, Hussein Ali El Damrany [Verfasser], Thomas C. [Akademischer Betreuer] [Gutachter] Nugent, Nikolai [Gutachter] Kuhnert y Muhammad Sharif [Gutachter] Akbar. "Organocatalyzed Reactions for Breaking Symmetry and Reduced Protecting Group Drug Synthesis / Hussein Ali El Damrany Hussein ; Gutachter: Thomas C. Nugent, Nikolai Kuhnert, Muhammad Sharif Akbar ; Betreuer: Thomas C. Nugent". Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2017. http://d-nb.info/1132813530/34.

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37

Lange, Florian [Verfasser], Holger [Akademischer Betreuer] Fehske, Holger [Gutachter] Fehske, Eric [Gutachter] Jeckelmann y Fabian [Gutachter] Heidrich-Meisner. "Density-matrix renormalization-group studies of spin, boson and fermion systems with symmetry-protected topological phases / Florian Lange ; Gutachter: Holger Fehske, Eric Jeckelmann, Fabian Heidrich-Meisner ; Betreuer: Holger Fehske". Greifswald : Universität Greifswald, 2019. http://d-nb.info/1199537756/34.

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38

Lange, Florian [Verfasser], Holger [Akademischer Betreuer] Fehske, Holger Gutachter] Fehske, Eric [Gutachter] Jeckelmann y Fabian [Gutachter] [Heidrich-Meisner. "Density-matrix renormalization-group studies of spin, boson and fermion systems with symmetry-protected topological phases / Florian Lange ; Gutachter: Holger Fehske, Eric Jeckelmann, Fabian Heidrich-Meisner ; Betreuer: Holger Fehske". Greifswald : Universität Greifswald, 2019. http://nbn-resolving.de/urn:nbn:de:gbv:9-opus-33484.

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39

Farias, Carlene Paula Silva de. "Competing orders in Uru2Si2: from ordered magnetism to spin liquid phases". PROGRAMA DE P?S-GRADUA??O EM F?SICA, 2017. https://repositorio.ufrn.br/jspui/handle/123456789/23653.

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The main objective of this thesis is to investigate the competing ordered phases in the metallic heavy fermion compound URu2Si2, which displays a bodycentered tetragonal lattice. We first provide a study case of the competition between antiferromagnetic (AF) and spin liquid phases. The antiferromagnetic state is study with spin-wave theory. Whereas the spin liquid analysis has been carried out in an algebraic spin liquid representation. In the second part, we describe an effective theory for Raman scattering experiments at these particular phases. We provide insight about the hidden order phase displayed by the heavy fermion compound URu2Si2.
L?objectif central de cette th?se est d??tudier des phases ordonn?es en comp?tition dans des mat?riaux magn?tiques pr?sentant une structure cristalline t?tragonale centr?e. Ce travail est divis? en deux parties principales. Dans la premi?re, nous pr?sentons les r?sultats de notre ?tude de la comp?tition entre des ?tats ordonn?s antiferromagn?tiques et des phases liquides de spin. Nous montrons comment ces derni?res peuvent ?tre stabilis?es par la frustration g?om?trique et par une g?n?ralisation de la sym?trie de spin au groupe SU(n). Les ?tats antiferromagn?tiques sont d?crits par une th?orie d?onde de spin et l?analyse de liquide de spin est effectu?e par une repr?sentation fermionique des op?rateurs de spin. Dans la deuxi?me partie, nous d?crivons une th?orie effective pour d?rcrire des exp?riences de diffusion Raman. Nous fournissons un aper?u de la phase d?ordre cach? affich?e par le compos? de fermions lourds URu2Si2.

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40

Chassaniol, Arthur. "Contributions à l'étude des groupes quantiques de permutations". Thesis, Clermont-Ferrand 2, 2016. http://www.theses.fr/2016CLF22709/document.

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Dans cette thèse nous étudions le groupe quantique d’automorphismes des graphes finis, introduit par Banica et Bichon. Dans un premier temps nous montrerons un théorème de structure du groupe quantique d’automorphismes du produit lexicographique de deux graphes finis réguliers, qui généralise un résultat classique de Sabidussi. Ce théorème donne une condition nécessaire et suffisante pour que ce groupe quantique s’exprime comme le produit en couronne libre des groupes quantiques d’automorphismes de ces deux graphes. Dans un deuxième temps, nous expliciterons certaines améliorations de résultats de Banica, Bichon et Chenevier permettant d’obtenir des critères de non symétrie quantique sur les graphes, à l’aide des outils développés par les auteurs susmentionnés.Enfin, pour poursuivre ces recherches, nous développerons une autre méthode utilisant la dualité de Tannaka-Krein et inspirée de l’étude des groupes quantiques compacts orthogonaux par Banica et Speicher. Celle-ci nous permettra, à l’aide d’une étude orbitale approfondie des graphes sommets-transitifs, d’énoncer une condition suffisante pour qu’un graphe ait des symétries quantiques ; condition qui a vocation à être aussi nécessaire mais ceci reste une conjecture à ce stade
In this thesis we study the quantum automorphism group of finite graphs, introduces by Banica and Bichon. First we will prove a theorem about the structure of the quantum automorphism group of the lexicographic product of two finite regular graphs. It is a quantum generalization of a classical result of Sabidussi. This theorem gives a necessary and sufficient condition for this quantum group to be discribe as the free wreath product of the quantum automorphism groups of these two graphs. Then, we will give some improvement of Banica, Bichon and Chenevier results, to obtain a quantum non-symmetry criteria on graphs, using tools developped by the above authors. Finally, to continue this research, we will describe another method using Tannaka-Krein duality and inspired by the study of orthogonal compact groups by Banica and Speicher. This will enable us, with a thorough orbital study of vertex-transitive graphs, to state a sufficient condition for a graph to have quantum symmetries ; condition which is intended to be also necessary but this remains conjecture at this point

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41

Pedone, M. (Matteo). "Algebraic methods for constructing blur-invariant operators and their applications". Doctoral thesis, Oulun yliopisto, 2015. http://urn.fi/urn:isbn:9789526208770.

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Abstract Image acquisition devices are always subject to physical limitations that often manifest as distortions in the appearance of the captured image. The most common types of distortions can be divided into two categories: geometric and radiometric distortions. Examples of the latter ones are: changes in brightness, contrast, or illumination, sensor noise and blur. Since image blur can have many different causes, it is usually not convenient and also computationally expensive to develop ad hoc algorithms to correct each specific type of blur. Instead, it is often possible to extract a blur-invariant representation of the image, and utilize such information to make algorithms that are insensitive to blur. The work presented here mainly focuses on developing techniques for the extraction and the application of blur-invariant operators. This thesis contains several contributions. First, we propose a generalized framework based on group theory to constructively generate complete blur-invariants. We construct novel operators that are invariant to a large family of blurs occurring in real scenarios: namely, those blurs that can be modeled by a convolution with a point-spread function having rotational symmetry, or combined rotational and axial symmetry. A second important contribution is represented by the utilization of such operators to develop an algorithm for blur-invariant translational image registration. This algorithm is experimentally demonstrated to be more robust than other state-of-the-art registration techniques. The blur-invariant registration algorithm is then used as pre-processing steps to several restoration methods based on image fusion, like depth-of-field extension, and multi-channel blind deconvolution. All the described techniques are then re-interpreted as a particular instance of Wiener deconvolution filtering. Thus, the third main contribution is the generalization of the blur-invariants and the registration techniques to color images, by using respectively a representation of color images based on quaternions, and the quaternion Wiener filter. This leads to the development of a blur-and-noise-robust registration algorithm for color images. We observe experimentally a significant increase in performance in both color texture recognition, and in blurred color image registration
Tiivistelmä Kuvauslaitteet ovat aina fyysisten olosuhteiden rajoittamia, mikä usein ilmenee tallennetun kuvan ilmiasun vääristyminä. Yleisimmät vääristymätyypit voidaan jakaa kahteen kategoriaan: geometrisiin ja radiometrisiin distortioihin. Jälkimmäisestä esimerkkejä ovat kirkkauden, kontrastin ja valon laadun muutokset sekä sensorin kohina ja kuvan sumeus. Koska kuvan sumeus voi johtua monista tekijöistä, yleensä ei ole tarkoitukseen sopivaa eikä laskennallisesti kannattavaa kehittää ad hoc algoritmeja erityyppisten sumeuksien korjaamiseen. Sitä vastoin on mahdollista erottaa kuvasta sumeuden invariantin edustuma ja käyttää tätä tietoa sumeudelle epäherkkien algoritmien tuottamiseen. Tässä väitöskirjassa keskitytään esittämään, millaisia eri tekniikoita voidaan käyttää sumeuden invarianttien operaattoreiden muodostamiseen ja sovellusten kehittämiseen. Tämä opinnäyte sisältää useammanlaista tieteellistä vaikuttavuutta. Ensiksi, väitöskirjassa esitellään ryhmäteoriaan perustuva yleinen viitekehys, jolla voidaan generoida sumeuden invariantteja. Konstruoimme uudentyyppisiä operaattoreita, jotka ovat monenlaiselle kuvaustilanteessa ilmenevälle sumeudelle invariantteja. Kyseessä ovat ne rotationaalisesti (ja/tai aksiaalisesti) symmetrisen sumeuden lajit, jotka voidaan mallintaa pistelähteen hajaantumisen funktion (PSF) konvoluutiolla. Toinen tämän väitöskirjan tärkeä tutkimuksellinen anti on esitettyjen sumeuden invarianttien operaattoreiden hyödyntäminen algoritmin kehittelyssä, joka on käytössä translatorisen kuvan rekisteröinnissä. Tällainen algoritmi on tässä tutkimuksessa osoitettu kokeellisesti johtavia kuvien rekisteröintitekniikoita robustimmaksi. Sumeuden invariantin rekisteröinnin algoritmia on käytetty esiprosessointina tässä tutkimuksessa useissa kuvien restaurointimenetelmissä, jotka perustuvat kuvan fuusioon, kuten syväterävyysaluelaajennus ja monikanavainen dekonvoluutio. Kaikki kuvatut tekniikat ovat lopulta uudelleen tulkittu erityistapauksena Wienerin dekonvoluution suodattimesta. Näin ollen tutkimuksen kolmas saavutus on sumeuden invarianttien ja rekisteröintiteknikoiden yleistäminen värikuviin käyttämällä värikuvien kvaternion edustumaa sekä Wienerin kvaternion suodatinta. Havaitsemme kokeellisesti merkittävän parannuksen sekä väritekstuurin tunnistuksessa että sumean kuvan rekisteröinnissä

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42

Altafini, Claudio. "Geometric control methods for nonlinear systems and robotic applications". Doctoral thesis, Stockholm : Tekniska högsk, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3151.

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43

Kasouha, Abeir Mikhail. "Symmetric representations of elements of finite groups". CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2605.

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This thesis demonstrates an alternative, concise but informative, method for representing group elements, which will prove particularly useful for the sporadic groups. It explains the theory behind symmetric presentations, and describes the algorithm for working with elements represented in this manner.

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44

Manriquez, Adam. "Symmetric Presentations, Representations, and Related Topics". CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/711.

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The purpose of this thesis is to develop original symmetric presentations of finite non-abelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J1, the Mathieu group M12, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2*60 : (2 x A5), 2*60 : A5, 2*56 : (23 : 7), and 2*28 : (PGL(2,7):2), respectively. We have also discovered the groups 24 : A5, 34 : S5, PSL(2,31), PSL(2,11), PSL(2,19), PSL(2,41), A8, 34 : S5, A52, 2• A52, 2 : A62, PSL(2,49), 28 : A5, PGL(2,19), PSL(2,71), 24 : A5, 24 : A6, PSL(2,7), 3 x PSL(3,4), 2• PSL(3,4), PSL(3,4), 2• (M12 : 2), 37:S7, 35 : S5, S6, 25 : S6, 35 : S6, 25 : S5, 24 : S6, and M12 as homomorphic images of the permutation progenitors 2*60 : (2 x A5), 2*60 : A5, 2*21 : (7: 3), 2*60 : (2 x A5), 2*120 : S5, and 2*144 : (32 : 24). We have given original proof of the 2*n Symmetric Presentation Theorem. In addition, we have also provided original proof for the Extension of the Factoring Lemma (involutory and non-involutory progenitors). We have constructed S5, PSL(2,7), and U(3,5):2 using the technique of double coset enumeration and by way of linear fractional mappings. Furthermore, we have given proofs of isomorphism types for 7 x 22, U(3,5):2, 2•(M12 : 2), and (4 x 2) :• 22.

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45

Potanka, Karen Sue. "Groups, Graphs, and Symmetry-Breaking". Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36630.

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A labeling of a graph G is said to be r-distinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an r-distinguishing labeling on G is called the distinguishing number of G. The distinguishing set of a group Gamma, D(Gamma), is the set of distinguishing numbers of graphs G in which Aut(G) = Gamma. It is shown that D(Gamma) is non-empty for any finite group Gamma. In particular, D(D_n) is found where D_n is the dihedral group with 2n elements. From there, the generalized Petersen graphs, GP(n,k), are defined and the automorphism groups and distinguishing numbers of such graphs are given.
Master of Science

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46

Silva, de Farias Carlene Paula. "Competing Orders in URu2Si2 : from ordered magnetism to spin liquid phases". Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0569/document.

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L’objectif central de cette thèse est d’étudier des phases ordonnées en compétition dans des matériaux magnétiques présentant une structure cristalline tétragonale centrée.Ce travail est divisé en deux parties principales. Dans la première, nous présentons les résultats de notre étude de la compétition entre des états ordonnés antiferromagnétiques et des phases liquides de spin. Nous montrons comment ces dernières peuvent être stabilisées par la frustration géométrique et par une généralisation de la symétrie de spinau groupe SU(n). Les états antiferromagnétiques sont décrits par une théorie d’onde despin et l’analyse de liquide de spin est effectuée par une représentation fermionique des opérateurs de spin. Dans la deuxième partie, nous décrivons une théorie effective pour dércrire des expériences de diffusion Raman. Nous fournissons un aperçu de la phase d’ordre caché affichée par le composé de fermions lourds URu2Si2
The main objective of this thesis is to investigate the competing ordered phases in the metallic heavy fermion compound URu2Si2, which displays a body-centered tetragonallattice. We first provide a study case of the competition between antiferromagnetic(AF) and spin liquid phases. The antiferromagnetic state is study with spin-wave theory. Whereas the spin liquid analysis has been carried out in an algebraic spin liquid representation.In the second part, we describe an effective theory for Raman scattering experiments at these particular phases. We provide insight about the hidden order phase displayed by the heavy fermion compound URu2Si2

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47

Rai, Suranjana, Jagdish Rai y Andreas Cap@esi ac at. "Group--Theoretical Structure of the Entangled States of N Identical". ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi904.ps.

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48

Hill, David Edward. "The Jantzen-Shapovalov form and Cartan invariants of symmetric groups and Hecke algebras /". view abstract or download file of text, 2007. http://proquest.umi.com/pqdweb?did=1400959351&sid=1&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2007.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 107-108). Also available for download via the World Wide Web; free to University of Oregon users.

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49

Salam, M. A. "Symmetric functions and the symmetric group Sn". Thesis, University of Canterbury. Physics, 1991. http://hdl.handle.net/10092/8161.

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A simple method for the embedding On → Sn of ordinary and spin irreps in both n-dependent notation and an n-independent reduced notation is given. Basic spin irreps and ordinary irreps are combined using the properties of Q-functions and raising operators in order to give a complete set of branching rules of On → Sn for spin irreps. The modification rules for Q-functions given by Morris are redefined to yield a complete and unambiguous set of rules. Properties of shifted tableaux have been explored in order to improve the algorithm for the calculation of Q-function outer products. A simple technique has been established for finding out the highest and lowest partitions in the expansion of Q-function outer products. Using these techniques and Young's raising operators, the Kronecker product for Sn spin irreps has been completed. A number of properties of Young's raising operator as applied to S-functions and Schur's Q-functions are noted. The order of evaluating the action of inverse raising operators is found to require careful specification and the maximum power of the operators δij is determined. The operation of inverse raising operator on a partition λ is found to be the same as for its conjugate λ. A new definition of Shifted Lattice Property that can efficiently remove all the dead tableaux in the Q-function analogue of the Littlewood-Richardson rule is introduced. A simple combinatorial analogue of raising and inverse raising operators is given. The q-deformation of symmetric functions is introduced leading to q-analogues of many well-known relationships in the theory of symmetric functions. A q-analogue of the spin and ordinary characters of Sn is given by making use of a method that closely parallels that of quantum groups. This formalism leads to a very simple technique for the construction of twisted and untwisted q-vertex operators. An isomorphism between the space of q-vertex operators and the ring of q-deformed Hall-Littlewood symmetric functions has been found.

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50

Correa, Diego Paolo Ferruzzo. "Symmetric bifurcation analysis of synchronous states of time-delay oscillators networks". Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/3/3139/tde-29122014-180651/.

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In recent years, there has been increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry, patterns can emerge in these networks; as a consequence, a part of the system might repeat itself, and properties of this symmetric subsystem represent the whole dynamics. In this thesis, an analysis of a second order N-node time-delay fully connected network is made. This study is carried out using symmetry groups. The existence of multiple eigenvalues forced by symmetry is shown, as well as the possibility of uncoupling the linearization at equilibria, into irreducible representations due to the symmetry. The existence of steady-state and Hopf bifurcations in each irreducible representation is also proved. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. A finite set of frequencies ω is also determined, which might correspond to Hopf bifurcations in each case for critical values of the delay. Although we restrict our attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal.
Nos últimos anos, tem havido um crescente interesse em estudar redes de osciladores acopladas com retardo de tempo uma vez que estes ocorrem em muitas aplicações da vida real. Em muitos casos, simetria e padrões podem surgir nessas redes; em consequência, uma parte do sistema pode repetir-se, e as propriedades deste subsistema simétrico representam a dinâmica da rede toda. Nesta tese é feita uma análise de uma rede de N nós de segunda ordem totalmente conectada com atraso de tempo. Este estudo é realizado utilizando grupos de simetria. É mostrada a existência de múltiplos valores próprios forçados por simetria, bem como a possibilidade de desacoplamento da linearização no equilíbrio, em representações irredutíveis. É também provada a existência de bifurcações de estado estacionário e Hopf em cada representação irredutível. São usados três modelos diferentes para analisar a dinâmica da rede: o modelo de fase completa, o modelo de fase, e o modelo de diferença de fase. É também determinado um conjunto finito de frequências ω, que pode corresponder a bifurcações de Hopf em cada caso, para valores críticos do atraso. Apesar de restringir a nossa atenção para nós de segunda ordem, os resultados podem ser estendido para redes de ordem superior, desde que o tempo de atraso nas conexões entre nós permanece igual.

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