Η παρούσα εργασία αφορά στη μελέτη Χαμιλτώνιων συστημάτων Ν μη γραμμικών ταλαντωτών, όπως είναι αυτό των Fermi Pasta και Ulam (FPU), με στόχο την βαθύτερη κατανόηση της δυναμικής των σχεδόν-περιοδικών τροχιών και του ρόλου των αντίστοιχων τόρων στο χώρο φάσεων, καθώς αυξάνουμε την ενέργεια Ε και τον αριθμό βαθμών ελευθερίας Ν του συστήματος. Το βασικό μας αποτέλεσμα είναι ότι υπάρχουν τόροι χαμηλής διάστασης, που προκύπτουν από τη συνέχεια των αντίστοιχων του γραμμικού συστήματος, οι οποίοι ευθύνονται για τις FPU επαναλήψεις και εμποδίζουν την ισοκατανομή της ενέργειας μεταξύ όλων των κανονικών τρόπων ταλάντωσης. Αναλύοντας ευστάθεια αυτών των τόρων, μπορέσαμε να δώσουμε μια πληρέστερη ερμηνεία στο Παράδοξο των FPU, συνδέοντας και συμπληρώνοντας έτσι δύο από τις επικρατέστερες ερμηνείες του εν λόγω φαινομένου. / The present work concerns the study of Hamiltonian systems of N nonlinear coupled oscillators, as it is the one by Fermi Pasta and Ulam (FPU), in order to understand the dynamics of quasi-periodic orbits and the role of their corresponding tori in phase space, as we increase the energy E and the number N of the degrees of freedom. Our fundamental result is that there exist tori of low dimension, that come from the continuation of the corresponding tori of the linear system, which are responsible for the FPU recurrences and prevent the system from equipartition of the energy among all normal modes. By investigating the stability of these tori, we achieved to provide a more complete explanation for the FPU paradox, connecting and supplementing in this way two of the most dominant approaches for this paradox.

The advancement in the eld of cold-atoms has generated a lot of interest in the condensed matter community. Cold-atom experiments can simulate clean, disor-der/impurity free systems very easily. In these systems, we have a control over various parameters like tuning the interaction between particles by the Feshbach resonance, tuning the hopping between lattice sites by laser intensity and so on. As a result, these systems can be used to mimic various theoretical models, which was hindered because of various experimental limitations. Thus, we have an ex-perimental tool in which we can start with a simple theoretical model and later tune the model experimentally and theoretically to simulate the real materials. This will be helpful in studying the physics of the real materials as we can control interactions as well as the impurities can also be taken care of. But the advance-ment in the eld of cold atoms has seen a roadblock for the fermions in optical lattices. The super uid and anti-ferromagnetic phases has not been achieved for fermions in optical lattices due to the \cooling problem" (entropy issues). In this thesis, we have addressed the issue of the \cooling problem" for fermions in optical lattice systems and studied the system with determinant quantum Monte Carlo technique. We start by giving a general idea of cold-atoms and optical lat-tice potentials, and a brief review of the experimental work going on in the cold-atomic systems. Experimental limitations like \fermionic cooling problem" have been discussed in some detail. Then we proposed a bilayer band-insulator model to circumvent the \entropy problem" and simultaneously increasing the transi-tion temperature for fermions in optical lattices. We have studied the attractive Hubbard model, which is the minimal model for fermions in optical lattices. The techniques that we have used to study the model are mean- eld theory, Gaussian uctuation theory and determinant quantum Monte Carlo numerical technique. . Chapter-1 : provides a general introduction to the ultra-cold atoms, optical lattice and Feshbach resonance. In this chapter we have discussed about cold-atom experiments in optical lattice systems. Here, we have brie y discussed the control over various parameters in the experiments. The goal of these experiments is to realize or mimic many many-body Hamiltonians in experiments, which until now was just a theoretical tool to describe various many-body physics. In the end we give a brief idea for introducing disorder in the cold-atom experiments discuss the limitations of these experiments in realizing the \interesting" super uid and anti-ferromagnetic phases of fermionic Hubbard model in optical lattices. Chapter-2 : gives a brief idea of \Determinant Quantum Monte-Carlo" (DQM C) technique that has been used to study these systems. In this chapter we will discuss the DQM C algorithm and the observables that can be calculated. We will discuss certain limitation of the DQM C algorithm like numerical instability and sign problem. We will brie y discuss how sign problem doesn't occur in the model we studied. Chapter-3 : discusses the way by which we can bypass the \cooling problem" (high entropy state) to get a fermionic super uid state in the cold atom experi-ments. In this chapter we propose a model whose idea hinges on a low-entropy band-insulator state, which can be tuned to super uid state by tuning the on-site attractive interaction by Feshbach resonance. We show through Gaussian uctua-tion theory that the critical temperature achieved is much higher in our model as compared to the single-band Hubbard model. Through detailed variational Monte Carlo calculations, we have shown that the super uid state is indeed the most stable ground state and there is no other competing order. In the end we give a proposal for its realization in the ultra-cold atom optical lattice systems. Chapter-4 : discusses the DQM C study of the model proposed in chapter- 3. Here we have studied the various single-particle properties like momentum distribution, double occupancies which can be easily measured in cold-atom ex-periments. We also studied the pair-pair and the density-density correlations in detail through DQM C algorithm and mapped out the full T U phase diagram. We show that the proposed model doesn't favor the charge density wave for the interaction strengths we are interested in. Chapter-5 : gives a brief idea of the e ect of adding an on-site random disorder in our proposed bilayer-Hubbard model. We study the e ect of random disorder on various single-particle properties which can be easily veri ed in cold-atom ex-periments. We studied the suppression of the pair-pair correlations as we increase the disorder strength in our proposed model. We nd that the critical value of the interaction doesn't change in the weak-disorder limit. We estimated the critical disorder strength needed to destroy the super uid state and argued that the tran-sition from the super uid to Bose-glass phase in presence of disorder lies in the universality class of (d + 1) XY model. In the end, we give a schematic U V phase diagram for our system. Chapter-6 : We studied the bilayer attractive Hubbard model in different lattice geometry, the bilayer honeycomb lattice, both in presence and in absence of the on-site random disorder. We discussed how the pair-pair and density-density cor-relations behave in the presence and absence of disorder. Through the finite-size scaling analysis we see the co-existence of the super fluid and the charge density wave order at half- lling. An in nitesimal disorder destroys the CDW order com-pletely while the super uid phase found to be robust against weak-disorder. We estimated the critical interaction strength, the critical temperature and the critical disorder strength through nite-size scaling, and provide a putative phase diagram for the system considered.

Abstract An optical lattice is a periodic array produced by the superposition of two or more counter-propagating laser beams which interfere and create a spatial periodic intensity pattern. An important difference between a solid state crystalline lattice and an optically induced lattice is that the latter have a longer coherence time which permits the observation of coherent phenomenon such as Bloch oscillations. Recently, an interesting effect has been reported in the literature, which is the analogue of Rabi oscillations in two level systems driven by an external optical field: an optical beam composed by pair of frequencies, resonants with the high symmetry points of the Brillouin zone, propagating through an optical lattice exhibits oscillations of the Fourier ways between the frequencies due to the coupling with the lattice. Therefore, in the optical case the field plays the role of the matter, while the lattice plays the role of the driving field which couples the frequencies. Based in this result, the objective of this paper is to investigate the influence of self-defocusing in the optical Rabi oscillation. We have shown, through numerical calculation of the wave nonlinear equation, that in the self-defocusing optical lattice, these oscillations go disappearingare. The result of the disappearance of the oscillations of Fourier can be understood considering that self-defocusing promotes an addition of phases in the ways that were resonant - kB and kB, in different way, form that the basic difference between kB and - kB will not be plus a vector of the reciprocal net, and as consequence the oscillations of optic Rabi disappear, therefore the coupling with the net requires this condition in the resonant frequencies. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Resumo Uma rede opticamente induzida é um arranjo periódico produzido pela superposição de dois ou mais feixes de laser que ao interferirem criam um padrão de intensidade periódico espacial. Uma importante diferença entre uma rede cristalina no estado sólido e uma rede produzida opticamente é que a última apresenta um tempo de coerência longo, permitindo a observação de fenômenos coerentes tal como as oscilações de Bloch. Recentemente, um efeito interessante análogo às oscilações de Rabi em um sistema atômico de dois níveis impulsionado por um campo externo, foi publicado na literatura: um feixe óptico composto de um par de freqüências, ressonantes com os pontos de alta simetria da zona de Brillouin, propagando - se através de uma rede óptica exibe oscilações dos modos de Fourier entre as freqüências adequadas para o acoplamento com a rede. Portanto, no caso óptico o campo representa a matéria, enquanto a rede representa a intensidade do campo aplicado que acopla as freqüências. Baseado neste resultado, o objetivo desta dissertação é investigar a influência da auto - desfocalização nas oscilações ópticas de Rabi. Demonstraremos, através de cálculos numéricos da equação de onda não linear, que em uma rede opticamente induzida na presença da auto - desfocalização, essas oscilações vão desaparecendo. O resultado do desaparecimento das oscilações de Fourier pode ser compreendidoconsiderando que a auto - desfocalização promove um adicionamento de fases nos modos que eram ressonantes -kB e kB, de maneira diferente, de forma que a diferença básica entre kB e -kB não será mais um vetor da rede recíproca, e como conseqüência as oscilações de Rabi óptica desaparecem, pois o acoplamento com a rede requer esta condição nas freqüências ressonantes.

Doped semiconductor systems have for decades provided an excellent platform to study novel concepts in solid state physics such as quantum hall effect, metal-to-insulator transition (MIT), weak localization and many body interaction effects. Doped Si, in particular and doped Ge has been studied extensively to study MIT as a function of dopant concentration or uniaxial stress. Spin transport phenomena have also been probed in bulk doped Si. All the previous studies involved bulk doped semiconductors where the dopants are spread through the bulk of the material. However spatial confinement of dopants in one or more dimensions may lead to a range of exotic quantum phenomena such as an absence of Anderson localization in one and two dimensions, hole-mediated (Nagaoka) ferromagnetism and new modes of quantum transport, when the Fermi energy lies at or close to centre of the band. Since many of these phenomena are inherent to lower dimensions, it has been hard to observe these experimentally in bulk doped crystals of Si and Ge. Recent advances in the monolayer doping techniques with atoms that closely pack on a surface, has made it possible to design a new class of 2D electron systems (2DES) in elemental semiconductors, such as Si and Ge, where the dopant (P) atoms are confined within a few atomic planes. The uniqueness of these systems lies not merely in the planar doping profile in bulk semiconductors that allow versatile designs of nanodevices, such as 1D wires, tunnel gaps and quantum dots, but also that it is now possible to study the interplay of wavefunction overlap and commensurability effects in 2D with unprecedented control. From an application perspective as well these systems are technologically important as they are aimed at being the building blocks of a solid state quantum computer. This thesis deals with investigating the electrical transport properties, both average (resistance) and dynamic (noise) of doped semiconductor systems in 2D delta layers, 1D wires and 0D quantum dots. We find that the 2D δ-layers shows suppressed low frequency noise and the Hooge parameter of delta doped Si is about five to six orders of magnitude lower when compared to bulk doped Si in metallic regime. At low temperatures, the noise arises in these systems due to universal conductance fluctuations. For 1D wires as well we find that the Hooge parameter is one of the lowest among various 1D systems including carbon nanotubes. We identify that charge traps in the Si/SiO2 are responsible for causing noise in δ-doped systems. Then we study the noise and transport in 2D delta layers as a function of doping density (and hence carrier density and interaction). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P delta layers, suggesting a spontaneous breaking of time reversal symmetry driven by strong Coulomb interactions. At low doping density we observe metal-like dependence of resistance on temperature at low temperatures, raising the possibility of a metallic ground state in 2D at 0 K in doped semiconductors. Finally we probe the low density devices (with broken time reversal symmetry) using superconducting Al as ohmic contacts. Anomalous increase in resistance below the superconducting transition temperature of Al and magnetoresistance with a sharp peak at 0 T is observed. Additionally we find that when the Al is superconducting, there exists a non-local resistance in low doped devices.

Made available in DSpace on 2014-10-09T12:51:50Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:08:58Z (GMT). No. of bitstreams: 0 / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Made available in DSpace on 2014-10-09T12:51:50Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:08:58Z (GMT). No. of bitstreams: 0 / Zircônia 3YTZP apresenta propriedades excelentes à temperatura ambiente, mas estas propriedades são afetadas pelo aumento da temperatura pois esta age negativamente sobre o mecanismo de transformação de fase induzida por tensão, que fortalece a tenacidade da matriz. A adição de Si3N4 e SiC em uma matriz de 3YTZP é muito interessante porque conduz à formação de oxinitreto de silício, melhorando as propriedades mecânicas tais como dureza e tenacidade, mas esta adição está limitada por várias dificuldades que se apresentam durante o processamento e sinterização destes materiais. Neste trabalho foi estudada a obtenção, por sinterização sem pressão, do compósito Y-TZP/Si2N2O, partindo-se da adição de 20vol%Si3N4-SiC em uma matriz de zircônia dopada com 3mol% de Y2O3 - 3YTZP, utilizando-se Al2O3 e Y2O3 como aditivos de sinterização. A mistura foi moída e moldada por prensagem isostática a frio. Amostras foram sinterizadas a 1500º, 1600º e 1700ºC por 2h sem pressão e em atmosfera ambiente, utilizando-se um leito de nitreto de silício. Após sinterização, as amostras foram caracterizadas por difração de raios-X. Foram medidas a densidade, tenacidade, dureza e resistência mecânica à flexão em temperatura ambiente. A estrutura do material foi observada em microscopia eletrônica de varredura e de transmissão, com mapeamento químico, para verificar a homogeneidade e morfologia das fases do compósito. A formação de Si2N2O foi observada no material sinterizado devido à reação entre os pós adicionados. O material obtido apresentou aumento de tenacidade e dureza com o aumento de temperatura de sinterização. As amostras apresentaram boa resistência à oxidação a 1000ºC. / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Submitted by Marco Antonio Oliveira da Silva (maosilva@ipen.br) on 2016-12-21T16:28:43Z No. of bitstreams: 0 / Made available in DSpace on 2016-12-21T16:28:43Z (GMT). No. of bitstreams: 0 / O titanato de estrôncio (SrTiO3) possui estrutura cristalina do tipo perovsquita. Materiais com este tipo de estrutura são utilizados para diversas aplicações, tais como, sensores, atuadores, em células a combustível de óxido sólido, entre outros. Devido as suas interessantes propriedades físicas, o SrTiO3 vem sendo intensamente estudado, em especial com a introdução de dopantes. Portanto, neste trabalho foi investigada a influência de diferentes teores de Ca (1; 2,5 e 5% mol) e Pr (0,025; 0,050; 0,075 e 1% mol) na microestrutura e propriedades elétricas e dielétricas do SrTiO3, assim como o material sem aditivos (puro). Os resultados mostram que após a sinterização do SrTiO3 puro, a microestrutura consiste de grãos poligonais com tamanho médio micrométrico, além de texturas lisas e rugosas. A condutividade elétrica das amostras sintetizadas sinterizadas a 1450 e 1500ºC é máxima para 2 horas de patamar. Apenas as amostras de SrTiO3 contendo 1% em mol de Ca apresentam fase única. O tamanho médio de grãos das amostras contendo 1% em mol de Ca é 10,65 ± 0,28 µm e para teores acima deste valor ocorre crescimento significativo dos grãos. As medidas de condutividade elétrica mostraram que as amostras contendo a adição de 1% em mol de Ca possuem maior condutividade dos grãos em relação ao material puro. Para as amostras contendo teores de até 0,075% mol de Pr, pode-se observar alguns grãos lisos e outros rugosos e não há variação considerável do tamanho médio de grãos. As amostras contendo menor teor de Pr (0,025% mol) apresentam maior condutividade dos grãos e contornos de grãos. As amostras de SrTiO3 sintetizado sinterizadas a 1450ºC/10 h apresentaram permissividade elétrica colossal em temperatura ambiente em altas frequências. / Dissertação (Mestrado em Tecnologia Nuclear) / IPEN/D / Instituto de Pesquisas Energéticas e Nucleares - IPEN-CNEN/SP

Submitted by Pedro Silva Filho (pfsilva@ipen.br) on 2017-11-22T14:03:18Z No. of bitstreams: 0 / Made available in DSpace on 2017-11-22T14:03:18Z (GMT). No. of bitstreams: 0 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Nas últimas décadas, o consumo de dispositivos eletrônicos e a alta demanda por armazenamento de dados tem mostrado grandes oportunidades para a criação de novas tecnologias que garantam as necessidades mundiais na área de computação e desenvolvimento. Alguns materiais multiferroicos tem sido amplamente estudados e o BiFeO3, considerado o único material multiferroico em temperatura ambiente, ganhou destaque como candidato para produção de dispositivos lógicos e de memória. O uso de técnicas de crescimento como a deposição por laser pulsado permitiu a produção de filmes finos de BiFeO3 com elevado controle de qualidade. Heteroestruturas de filmes multiferroicos de BiFeO3 e LaBiFeO3 foram crescidas com diferentes espessuras sobre substratos de SrTiO3(100), DyScO3(110) e SrTiO3/Si(100) para avaliação e teste de suas propriedades elétricas e magnéticas. Filmes ferromagnéticos de Co0,9Fe0,1 foram depositados por sputtering sobre os filmes multiferroicos para avaliação da interação interfacial entre ordenamentos magnéticos. Técnicas como fotolitografia foram utilizadas para padronização de microdispositivos gravados sobre as amostras. Tanto os filmes finos de BiFeO3 como os de LaBiFeO3 foram crescidos epitaxialmente sobre os substratos já cobertos com uma camada buffer de SrRuO3 usado como contato elétrico inferior. A estrutura cristalina romboédrica das ferritas de bismuto foi confirmada pelos dados de difração de raios X, bem como a manutenção de tensão estrutural causada pela rede cristalina do substrato para amostras de 20 nm. Os valores de coeficiente do tensor piezelétrico d33 foram da ordem de 0,15 V (∼ 60 kV.cm-2) para amostras com 20 nm de espessura enquanto que os valores de voltagem coerciva para as análises de histerese elétrica foram da ordem de 0,5 V para as mesmas amostras. A relação de coercividade elétrica com a espessura corresponde ao perfil encontrado na literatura pela relação E≈d-2/3. As amostras de CoFe/BFO e CoFe/LBFO depositadas em diferentes substratos apresentam acoplamento interfacial entre ordenamento ferromagnético e antiferromagnético com momento ferromagnético de rede. / Tese (Doutorado em Tecnologia Nuclear) / IPEN/T / Instituto de Pesquisas Energéticas e Nucleares - IPEN-CNEN/SP / CAPES:99999.009511/2014-08 / CNPq:146622/2013-2

Un graphe métrique G(X;D) est un graphe dont l’ensemble des sommets est l’ensemble X des points d’un espace métrique (X; d), et dont les arêtes relient les paires fx; yg de sommets telles que d(x; y) 2 D. Dans cette thèse, nous considérons deux problèmes qui peuvent être interprétés comme des problèmes de graphes métriques dans Rn. Premièrement, nous nous intéressons au célèbre problème d’empilements de sphères, relié au graphe métrique G(Rn; ]0; 2r[) pour un rayon de sphère r donné. Récemment, Venkatesh a amélioré d’un facteur log log n la meilleure borne inférieure connue pour un empilement de sphères donné par un réseau, pour une suite infinie de dimensions n. Ici nous prouvons une version effective de ce résultat, dans le sens où l’on exhibe, pour la même suite de dimensions, des familles finies de réseaux qui contiennent un réseaux dont la densité atteint la borne de Venkatesh. Notre construction met en jeu des codes construits sur des corps cyclotomiques, relevés en réseaux grâce à un analogue de la Construction A. Nous prouvons aussi un résultat similaire pour des familles de réseaux symplectiques. Deuxièmement, nous considérons le graphe distance-unité G associé à une norme k_k. Le nombre m1 (Rn; k _ k) est défini comme le supremum des densités réalisées par les stables de G. Si la boule unité associée à k _ k pave Rn par translation, alors il est aisé de voir que m1 (Rn; k _ k) > 1 2n . C. Bachoc et S. Robins ont conjecturé qu’il y a égalité. On montre que cette conjecture est vraie pour n = 2 ainsi que pour des régions de Voronoï de plusieurs types de réseaux en dimension supérieure, ceci en se ramenant à la résolution de problèmes d’empilement dans des graphes discrets. / A distance graph G(X;D) is a graph whose set of vertices is the set of points X of a metric space (X; d), and whose edges connect the pairs fx; yg such that d(x; y) 2 D. In this thesis, we consider two problems that may be interpreted in terms of distance graphs in Rn. First, we study the famous sphere packing problem, in relation with thedistance graph G(Rn; (0; 2r)) for a given sphere radius r. Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor log log n for infinitely many dimensions n. We prove an effective version of this result, in the sense that we exhibit, for the same set of dimensions, finite families of lattices containing a lattice reaching this bound. Our construction uses codes over cyclotomic fields, lifted to lattices via Construction A. We also prove a similar result for families of symplectic lattices. Second, we consider the unit distance graph G associated with a norm k _ k. The number m1 (Rn; k _ k) is defined as the supremum of the densities achieved by independent sets in G. If the unit ball corresponding with k _ k tiles Rn by translation, then it is easy to see that m1 (Rn; k _ k) > 1 2n . C. Bachoc and S. Robins conjectured that the equality always holds. We show that this conjecture is true for n = 2 and for several Voronoï cells of lattices in higher dimensions, by solving packing problems in discrete graphs.

Bien que la dynamique des réseaux périodiques non-linéaires ait été investiguée dans les domainestemporel et fréquentiel, il existe un réel besoin d’identifier des relations pratiques avec lephénomène de la localisation d’énergie en termes d’interactions modales et topologies de bifurcation.L’objectif principal de cette thèse consiste à exploiter le phénomène de la localisation pourmodéliser la dynamique collective d’un réseau périodique de résonateurs non-linéaires faiblementcouplés.Un modèle analytico-numérique a été développé pour étudier la dynamique collective d’unréseau périodique d’oscillateurs non-linéaires couplés sous excitations simultanées primaire et paramétrique,où les interactions modales, les topologies de bifurcations et les bassins d’attraction ontété analysés. Des réseaux de pendules et de nano-poutres couplés électrostatiquement ont étéinvestigués sous excitation extérieure et paramétrique, respectivement. Il a été démontré qu’enaugmentant le nombre d’oscillateurs, le nombre de solutions multimodales et la distribution desbassins d’attraction des branches résonantes augmentent. Ce modèle a été étendu pour investiguerla dynamique collective des réseaux 2D de pendules couplés et de billes sphériques en compressionsous excitation à la base, où la dynamique collective est plus riche avec des amplitudes de vibrationplus importantes et des bandes passantes plus larges. Une deuxième investigation de cettethèse consiste à identifier les solitons associés à la dynamique collective d’un réseau périodique etd’étudier sa stabilité. / Although the dynamics of periodic nonlinear lattices was thoroughly investigated in the frequencyand time-space domains, there is a real need to perform profound analysis of the collectivedynamics of such systems in order to identify practical relations with the nonlinear energy localizationphenomenon in terms of modal interactions and bifurcation topologies. The principal goal ofthis thesis consists in exploring the localization phenomenon for modeling the collective dynamicsof periodic arrays of weakly coupled nonlinear resonators.An analytico-numerical model has been developed in order to study the collective dynamics ofa periodic coupled nonlinear oscillators array under simultaneous primary and parametric excitations,where the bifurcation topologies, the modal interactions and the basins of attraction havebeen analyzed. Arrays of coupled pendulums and electrostatically coupled nanobeams under externaland parametric excitations respectively were considered. It is shown that by increasing thenumber of coupled oscillators, the number of multimodal solutions and the distribution of the basinsof attraction of the resonant solutions increase. The model was extended to investigate the collectivedynamics of periodic nonlinear 2D arrays of coupled pendulums and spherical particles underbase excitation, leading to additional features, mainly larger bandwidth and important vibrationalamplitudes. A second investigation of this thesis consists in identifying the solitons associated tothe collective nonlinear dynamics of the considered arrays of periodic structures and the study oftheir stability.