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Alavi, Seyed Ehsan. "Homogénéisation de milieux architecturés périodiques et quasi-périodiques vers des milieux continus généralisés". Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0305.
Pełny tekst źródłaThis thesis aims to revisit higher-order homogenization schemes towards higher-order or higher gradient continua, successively for periodic and quasi-periodic architected materials and composites, based on variational principles and an extension of Hill macrohomogeneity condition. Continuous homogenization methods are exposed in Part I for micropolar and micromorphic media, followed by an exposition of the alternative discrete homogenization method.We have extended these theoretical developments to the situation of quasi-periodic materials, which still have a regular microstructure. The common idea to the proposed periodic homogenization methods of continuous or discrete nature is to split the microscopic displacement into a homogeneous part representative of the kinematics of the adopted effective continuum and a fluctuation evaluated from a variational principle. In substance, the theoretical developments allow the elaboration of enriched continua (generalized continua) of micromorphic type and all sub continua obtained using suitable degeneration conditions. Numerical applications have been made for architected materials and inclusion-based composites prone to higher-order effects due to their inner architecture. On the theoretical framework, the performed developments remedy many existing limitations of existing higher-order homogenization schemes.In Part II, repetitive lattice materials' effective classical and higher-order mechanical properties have been evaluated based on discrete homogenization schemes. Following the idea of a phenomenological approach, consistent couple stress models of repetitive beam lattices have been elaborated. Enriched Cosserat media have been derived in the spirit of micromechanics, adopting Timoshenko beam models at a microlevel, and applying a continualization method towards a Cosserat effective substitution medium. The proposed continualization method proves to be accurate and computationally efficient compared to continuous homogenization schemes and fully resolved finite element simulations. One key outcome of the performed analyses is the quantification of edge effects in the response of lattice structures, relying on the surface formulation of the extended Hill macrohomogeneity condition.The theoretical background underlying quasi-periodic asymptotic homogenization in the framework of linearized anisotropic elasticity deserves the development of Part III. Different methodologies for evaluating the effective quasi-periodic properties have been elaborated, leading to the emergence of strain gradient effective media. Conformal transformations define a specific class of geometrical mappings, allowing for designing compatible architected materials with inner porosity gradient, making them suitable bone biomechanics candidates
Souadnia, Azzedine. "Dispersion permanente et transitoire en milieux poreux spatialement périodiques". Vandoeuvre-les-Nancy, INPL, 1999. http://www.theses.fr/1999INPL001N.
Pełny tekst źródłaCoatléven, Julien. "Analyse mathématique et numérique de quelques problèmes d'ondes en milieux périodiques". Palaiseau, Ecole polytechnique, 2011. http://pastel.archives-ouvertes.fr/docs/00/64/92/12/PDF/memoire.pdf.
Pełny tekst źródłaThe modeling of many interesting physical problems leads to partial differential equations, in a domain whose geometry and coefficients are functions periodic outside some regions, called scatterers, which are small with respect to the full domain of interest. The caracteristics of these problems often prevent us from applying classical homogeneization techniques, that is why we have developped new methods to restrict the computational domain to bounded domains. We have generalized the Lippmann-Schwinger equation approach, which allows us to treat bounded and structured unbounded scatterers, the main issue being that for a generic periodic media there is no analytic representation of the solution in the case without scatterers (i. E the Green function is unknown). Dirichlet-to-Neumann maps for periodic strips infinite in one direction play a key role in our approach. We treat two kinds of problems : time harmonic problems, for which the DtN maps for strip problems are known, and evolution problems, for which we present a method of derivation of these operators. In these two cases, we first treat the case of one bounded or unbounded scatterer, then we generalize the multiple scattering methods for homogeneous media to the case of periodic media, which allow us to handle several scatterers as wel
Dos, Reis Francisco. "Homogénéisation automatique de milieux discrets périodiques : applications aux mousses polymères et aux milieux auxétiques". Thesis, Vandoeuvre-les-Nancy, INPL, 2010. http://www.theses.fr/2010INPL050N/document.
Pełny tekst źródłaThe first achievement of this work is to construct a unified and effective continuum equivalent to a lattice of beams, in the elastic domain, using a Bernoulli beam model. An extension has been done to calculate the elastic domain resistance of such lattices and to build an algorithm for monitoring the constitutive law taking into account work hardening. The choice of the asymptotic expansions leads to a classical continuous or to a micropolar elastic continuum. We restrict in this last case our study to lattices with centro-symmetric unit cells. The numerical codes developed provide the stress-strain relationship and the effective mechanical moduli. A wide variety of trusses has been studied, either existing or original, including typical geometries of foams and various auxetic lattices, exhibiting negative contraction coefficients. The results were systematically compared with data from literature and verified by finite element simulations with a good agreement. The homogenization in the plastic range has been limited to stretching dominated lattices. The equilibrium equations of the discrete asymptotic homogenization have been used to automatically obtain the elastic resistance domain for several trusses, and a return-mapping algorithm for the follow up of the stress-strain relationship including hardening has been conceived and implemented in a dedicated code. An isotropic hardening elastoplastic model of the beam has been used. The application of the algorithm to the simulation of a loading-unloading cycle shows a good agreement between the homogenized lattice and finite element simulations
Van, Der Biest François. "Diffusion multiple et renversement du temps ultrasonore dans des milieux périodiques et désordonnés". Phd thesis, Université Paris-Diderot - Paris VII, 2005. http://tel.archives-ouvertes.fr/tel-00011354.
Pełny tekst źródłaNous avons tout d'abord conçu et caractérisé des échantillons périodiques, autrement appelés "cristaux phononiques". Ces matériaux se comportent comme des filtres fréquentiels et présentent un grand intérêt technologique et théorique.
Nous avons étudié le temps de groupe à la traversée de monocristaux, qui révèle un effet analogue à l'effet tunnel en mécanique quantique. Dans une structure de type Fabry-Pérot constituée de deux cristaux phononiques, nous avons mis en évidence des résonances en transmission. L'étude du temps de groupe montre un phénomène de piégeage de l'onde dans la cavité, analogue de l'effet tunnel résonant. Les résultats obtenus sont confirmés par la modélisation numérique.
Par la suite, des expériences de Retournement Temporel dans les cristaux phononiques ont révélé une absence d'hyperfocalisation, caractéristique des milieux désordonnés.
Nous avons ensuite cherché à mettre en évidence la diffusion multiple en régime non-linéaire dans les nuages de bulles. A cet effet, nous avons conçu un dispositif expérimental qui nous a permis de générer des populations de bulles relativement stables et contrôlées. Plusieurs méthodes de caractérisation de la fonction de distribution du rayon des bulles ont été mises en oeuvre, et l'une d'elles nous a permis d'estimer la fraction volumique de bulles.
Les densités de bulles mises en jeu n'ont pas permis de mettre en évidence un régime de diffusion multiple fort, tandis que l'origine des non-linéarités observées reste incertaine.
Tizianel, Julian. "Ondes complexes au dessus de matériaux poreux et de structures périodiques". Le Mans, 1999. http://www.theses.fr/1999LEMA1011.
Pełny tekst źródłaArlaud, Elodie. "Modèles dynamiques réduits de milieux périodiques par morceaux : application aux voies ferroviaires". Thesis, Paris, ENSAM, 2016. http://www.theses.fr/2016ENAM0047/document.
Pełny tekst źródłaRailway tracks have evolved over years based on empirical results and their dynamic behavior still can be difficult to assess or to quantify. A numerical model can thus provide assistance in track design by assessing the mechanical performance of new structures, or allowing the diagnostic of existing track parts, as a complement to relevant in-situ measurements.The numerical model developed in this work combines a reduction strategy with numerical techniques used to solve the propagation equations in waveguides in the frequency / wave number domains. The peculiarity of the exposed methodology is the introduction of a model based on a periodic sub structuring of the track, keeping only a few wavelengths carefully chosen to solve dispersion equations. Based on this model reduction technique and its extension to time domain models with moving contact, the computational time and storage capacity required are greatly reduced. Thus, this model is efficient and useful for engineering purposes in railway tracks studies.Numerical validation of the reduction is carried out by building a complete reference model in the frequency domain. In parallel, measurement campaigns (receptance measurement and sleeper acceleration under passing trains) were performed on a transition zone between ballasted and slab tracks on a High Speed Line. These tests are compared to simulation results in both time and frequency domains on different areas of the transition. After successful validation, the model is used to improve understanding of the role of the substructure on the dynamic behavior.The final major development of this work is the introduction of a strategy to extend the reduction to piecewise periodic structures and the development of post-processing tools to highlight the dynamic effects generated by the transition zone
Nguyen, Trung Kien. "Homogénéisation numérique de structures périodiques par transformée de Fourier : matériaux composites et milieux poreux". Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00598465.
Pełny tekst źródłaTo, Viet Thanh. "Contributions au calcul analytique et numérique des propriétés homogénéisées des composites et des milieux poreux périodiques". Thesis, Paris Est, 2015. http://www.theses.fr/2015PEST1069/document.
Pełny tekst źródłaIn this work, we determine the macroscopic properties of thermal transfer and mass transport in periodic heterogeneous materials. All the results are established in the framework of periodic homogenization, for which, the macroscopic properties are deduced by solving elementary problems for the irreducible cell. Various contributions are provided, leading to the derivation of new closed-form expressions for the effective properties or by developing numerical tools. In the first part, we determine the nonlinear filtration properties of porous media. At the microscopic scale, the fluid flow obeys to the Navier-Stokes equation. By expanding the solution into power series, we obtain, after homogenization, a polynomial type macroscopic filtration law. All the constitutive coefficients of are determined by solving a hierarchy of cell problems by means of a numerical approach based on the Fast Fourier Transform algorithm. The problem of conductivity of periodic composites reinforced by spherical inclusions is thereafter considered by an analytic approach. We solve the Lippmann-Schwinger integral equation using Neumann series and a constant polarization in the inclusion. Closed-form estimate of the macroscopic conductivity are then obtain for different spatial configurations: cubic lattice and isotropic distribution of inclusions. In the last part, we determine the thermal transfer properties by conduction and convection of porous media fulfilled by a viscous fluid. Again, numerical tools based on FFT are considered to solve the unit cell problems and to compute the diffusivity tensor
Dumeige, Yannick. "Génération de second harmonique dans les milieux périodiques uni ou bidimensionnels à semiconducteurs III-V". Paris 11, 2002. http://www.theses.fr/2002PA112214.
Pełny tekst źródłaPhase matching is indispensable to obtain efficient second order non-linear interactions. III-V semiconductors materials have optical properties which don't allow us to obtain phase matching by usual ways. Hence we must use artificial media like periodic structures to achieve chromatic or group velocity dispersion engineering. We fabricated and studied experimentally laminar periodic structures and more particularly AlGaAs/AlOx multilayers. This kind of periodic structures permit phase matching and a simultaneous increase in the density of optical modes which is favourable for the conversion efficiency in the second harmonic generation process. By comparing different structures, we established that the conversion efficiency grows faster than the fifth power of the number of unit cells. We also studied numerically periodic structures in the waveguided regime. In order to simulate their behaviour we developed a non-linear FDTD (Finite Difference Time Domain) code. Subsequently we used it to simulate the non-linear interactions in a 1D photonic crystal constituted by a planar waveguide periodically etched. We proposed a structure achieving a compromise between confinement and diffraction lasses. Finally we demonstrated numerically with our non-linear FDTD code that a 2D photonic crystal defect waveguide allows simultaneously the waveguiding of the two waves in non-linear interaction and the phase-matching condition
Hoang, Duc Hieu, i Duc Hieu Hoang. "Contribution à l'homogénéisation de matériaux hétérogènes viscoélastiques : milieux aléatoires et périodiques et prise en compte des interfaces". Phd thesis, Université Paris-Est, 2011. http://tel.archives-ouvertes.fr/tel-00682436.
Pełny tekst źródłaHoang, Duc Hieu. "Contribution à l'homogénéisation de matériaux hétérogènes viscoélastiques : milieux aléatoires et périodiques et prise en compte des interfaces". Thesis, Paris Est, 2011. http://www.theses.fr/2011PEST1086/document.
Pełny tekst źródłaPas de résumé en anglais
Fliss, Sonia. "Analyse mathématique et numérique de problèmes de propagation des ondes dans des milieux périodiques infinis localement perturbés". Phd thesis, Palaiseau, Ecole polytechnique, 2009. http://pastel.archives-ouvertes.fr/pastel-00503023/en/.
Pełny tekst źródłaBaït, Lyès. "Traitement synchrone en parallèle de signaux périodiques en basse et en haute fréquences : principe et applications". Paris 6, 2003. http://www.theses.fr/2003PA066012.
Pełny tekst źródłaAnfosso, Julien. "Propagation Acoustique dans des Milieux Granulaires de Billes de Verre et d'Acier". Phd thesis, Université Paris-Diderot - Paris VII, 2003. http://pastel.archives-ouvertes.fr/pastel-00000532.
Pełny tekst źródłaGolkin, Stanislav. "Simulation de la propagation d'ondes SH dans des structures périodiques et de la diffusion multiple d'ondes de volume en milieux aléatoires". Thesis, Bordeaux 1, 2012. http://www.theses.fr/2012BOR1A002/document.
Pełny tekst źródłaThe study is concerned with acoustic waves in elastic media with a different nature of in homogeneity consisting in either periodically continuous or piece wise variation of material properties, or in random sets of defects embedded into a homogeneous matrix, with a given statistical distribution. The scope of problems is topical in non-destructive testing and other applications of ultrasound.Theoretical methods describing involved acoustic phenomena (complex dispersion features, coherent wave in random media, ensemble average techniques) often rely on certain a priori assumptions which render numerical verification especially important.The thesis presents results of analytical modelling of the propagation of surface acoustic waves along periodic half-space, for which the dispersion spectrum is rather complex (discontinuous spectrum of propagation for the surface waves). A 2nd order FDTD numerical code has been developed in order to perform numerical experiments in the space and time domains, and to corroborate the analytical predictions in the frequency domain. A good agreement of simulated results with analytical modelling demonstrates applicability and consistency of the numerical tool. Finally, the code has been used for extracting numerically the coherent wave regime (mean wave over ensemble averaging of the positions of scatterers) for the acoustic propagation in different types of populations of randomly distributed scatterers. The results indicate ranges of validity of some multiple scattering analytical techniques
Toscano, Jérémy. "Contribution à l'homogénéisation des structures périodiques unidimensionnelles : application en biomécanique à la structure axonémale du flagelle et des cils vibratiles". Phd thesis, Université Paris-Est, 2009. http://tel.archives-ouvertes.fr/tel-00534570.
Pełny tekst źródłaDucasse, Romain. "Équations et systèmes de réaction-diffusion en milieux hétérogènes et applications". Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLEE054/document.
Pełny tekst źródłaThis thesis is dedicated to the study of reaction-diffusion equations and systems in heterogeneous media. It is divided into two parts. The first one is devoted to the study of reaction-diffusion equations in periodic media. We pay a particular attention to equations set on domains that are not the whole space $\mathbb{R}^{N}$, but periodic domains, with "obstacles". In a first chapter, we study how the geometry of the domain can influence the speed of invasion of solutions. After establishing a Freidlin-Gartner type formula, we construct domains where the speed of invasion is strictly less than the critical speed of fronts. We also give geometric criteria to ensure the existence of directions where the invasion occurs with the critical speed. In the second chapter, we give necessary and sufficient conditions to ensure that invasion occurs, and we construct domains where intermediate phenomena (blocking, oriented invasion) occur. The second part of this thesis is dedicated to the study of models describing the influence of lines with fast diffusion (a road, for instance) on the propagation of invasive species. Indeed, it was observed that some species, such as the tiger mosquito, invade faster than expected some areas along the road-network. We study two models : the first one describes the influence of a curved road on the propagation. We study in particular the case of two non-parallel roads. The second model describes the influence of a road on an ecological niche, in presence of climate change. The main result is that the effect of the road is ambivalent: if the niche is stationary, then effect of the road is deleterious. However, if the niche moves, because of a shifting climate, the road can actually help the population to persist. To study this model, we introduce a notion of generalized principal eigenvalue for KPP-type systems, and we derive a Harnack inequality, that is new for this type of systems
Temin, Gendron Pascale. "Approche numérique du comportement homogénéisé des composites à matrice métallique et renforts continus : validation expérimentale". Châtenay-Malabry, Ecole centrale de Paris, 1990. http://www.theses.fr/1990ECAP0163.
Pełny tekst źródłaRobert, Sébastien. "Propagation d'ondes cohérentes et résonances dans des milieux élastiques présentant des inclusions cylindriques périodiquement ou aléatoirement distribuées". Phd thesis, Université du Havre, 2004. http://tel.archives-ouvertes.fr/tel-00143062.
Pełny tekst źródłaBricault, Charlie. "Diminution des vibrations et du bruit rayonné d'une paroi par contrôle distribué". Thesis, Le Mans, 2017. http://www.theses.fr/2017LEMA1009/document.
Pełny tekst źródłaMaking the structure lighter is an important economic stake in the field of industrial activities such as automotive, aeronautic or naval, which gradually integrate composite materials in the manufacturing of structures. This reduction of the mass goes along with a stiffening of the matter implying acoustics and vibrations issues. Several methods exist to reduce vibrations or acoustic radiations of structures, but these methods increase the mass. In order to answer the problematic, we propose to change the dynamic behavior of structures with a periodic lattice of piezoelectric patches shunted with an electrical circuit whose the impedance can be controlled. Therefore, the control of the coupled behavior of the piezoelectric patches allows the control of vibrational wave's diffusion inside the structure and so to treat the structure-borne vibrations and airborne acoustics emission. The shunt method chosen is negative capacitance shunt which allows to modify the rigidity of a structure. This semi-passive method has several advantages: the implementation is simple, it is possible to integrate the patches directly inside the wall, it consumes a low amonte of electrical energy and its implementation is inexpensive
Vu, Quoc Huy. "Modélisation micromécanique du compotement d’un sol injecté". Paris 6, 2008. http://www.theses.fr/2008PA066099.
Pełny tekst źródłaTorres, Francis. "Études de la diffusion de particules ponctuelles (1) dans des milieux poreux périodiques et (2) dans des systèmes de rochets à fréquence finie par une méthode de calcul exact". Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/28028.
Pełny tekst źródłaFéjoz, Jacques. "Mouvements périodiques et quasi-périodiques dans le problème des n corps". Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2010. http://tel.archives-ouvertes.fr/tel-00702650.
Pełny tekst źródłaHamdi, Bilel. "Modélisation des circuits périodiques et quasi-périodiques alimentés par des sources arbitraires". Thesis, Toulouse, INPT, 2015. https://oatao.univ-toulouse.fr/25877/1/HAMDI_Bilel.pdf.
Pełny tekst źródłaPlanar antenna arrays are renowned for their high directivity and ease of implementation, which offers the possibility of having a controllable radiation pattern. However the global study taking into account the different EM couplings by a rigorous electromagnetic theory requires a large memory space and a considerable computation time. To overcome these drawbacks, we propose to introduce a new theoretical approach based on the Floquet theorem allowing the reduction of the EM analysis volume at the level of a single elementary cell (basic cell). We will focus our study on the determination of coupling terms in a distributed configuration in an almost-periodic frame and in particular for periodic and quasi-periodic antenna arrays fed by arbitrary sources. In this case, we will use Floquet mode decompositions (adapted to periodic structures) to extract the coupling matrix [S]. These decompositions are concepts established for a long time and a priori demonstrated by solid theoretical supports. Consequently, this modal analysis makes it possible to simplify considerably the resolution of the problem, especially when the radiating elements are strongly coupled. A single numerical method is adopted in order to model the proposed structure: the method of moments combined with the generalized equivalent circuit: MoM-GEC. Validation of the latter will be done by comparison with other exact numerical methods
Marchalant, Elise. "Analyse numérique de phénomènes de propagation d'ondes : problèmes périodiques et quasi périodiques". Paris 13, 2001. http://www.theses.fr/2001PA132017.
Pełny tekst źródłaWang, Kang. "Structure électronique et stabilité des cristaux quasi-périodiques". Paris 11, 1989. http://www.theses.fr/1989PA112150.
Pełny tekst źródłaHutridurga, Ramaiah Harsha. "HOMOGÉNÉISATION ET DISPERSION POUR DES ÉCOULEMENTS COMPLEXES EN MILIEU POREUX ET APPLICATIONS". Phd thesis, Ecole Polytechnique X, 2013. http://pastel.archives-ouvertes.fr/pastel-00866253.
Pełny tekst źródłaVigué, Pierre. "Solutions périodiques et quasi-périodiques de systèmes dynamiques d'ordre entier ou fractionnaire : applications à la corde frottée". Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0306/document.
Pełny tekst źródłaThe continuation of periodic and quasi-periodic solutions is performed on several models derived from the violin. The continuation for a one degree-of-freedom model with a regularized friction shows, compared with Coulomb friction, the persistence of limit cycle bifurcations (a maximum bow speed and a minimum normal force allowing Helmholtz motion) and of global properties of the solution branch (increase of amplitude with respect to the bow speed, decrease of frequency with respect to the normal force). The Harmonic Balance Method is assessed on this regularized friction system and shows interesting convergence properties (the error is low, monotone and rapidly decreasing). For two modes the continuation shows higher register solutions with a plausible stability. A stronger inharmonicity can greatly modify the bifurcation diagram. A new method is proposed for the continuation of quasi-periodic solutions. It couples a two-pulsations HBM with the Asymptotic Numerical Method. We have taken great care to deal efficiently with large systems of unknowns. A model of friction that takes into account temperature of the contact zone is reformulated with a fractional derivative. We then propose a method of continuation of periodic solutions for differential systems that contain fractional operators. Their definition is usually restricted to causal solutions, which prevents the existence of periodic solutions. Having chosen a specific definition of fractional operators to avoid this issue we establish a sufficient condition on asymptotically attractive cycles in the causal framework to be solutions of our framework
Hassouani, Youssef El. "Contribution à l'étude des structures phononiques et photoniques unidimensionnelles périodiques et quasi-périodiques : super-réseaux solide-fluide et guides monomodes". Lille 1, 2007. https://pepite-depot.univ-lille.fr/LIBRE/Th_Num/2007/50376-2007-215.pdf.
Pełny tekst źródłaThis thesis presents a contribution to the study of propagation and localization of acoustic and electromagnetic waves in one-dimensional phononic and photonic crystals. We are mainly interested in acoustic wave propagation in solid-fluid periodic multi-layered media and electromagnetic wave propagation in quasi-periodic monomode waveguides. Our goal was to propose new materials that exhibit large forbidden bands and to study the effect of the presence of inhomogeneities in these structures such as : a free surface, an interface with a homogeneous medium or a defect layer (cavity). These results are obtained using a detailed analytical calculation of the Green's functions which enabled us to determine the dispersion relations, local and total densities of states, transmission and reflection coefficients as weIl as the corresponding phase times. Ln the case of acoustic waves of sagittal polarization in solid-fluid superlattices, we highlighted the existence and the behaviour of the surface and interface modes; in particular we have shown a general ruIe on the existence of these modes. Also, we have shown that these systems can present omnidirectional band gaps where aIl incident angles are reflected (acoustic mirrors) as weIl as a selective transmission through defect and interface modes (acoustic filters). Ln the case of electromagnetic waves in quasi-periodic (Fibonacci) monomode waveguides constituted of coaxial cables, we highlighted sorne properties related to these systems such as: the self-similarity of the transmission spectrum with a scaling factor in the case of a single Fibonacci sequence. Also, it was shown that these systems can present in sorne regions of frequencies, subluminal and superluminal velocities. Ln the case of periodic Fibonacci sequences, we have shown some properties related to the allowed bands such as the fragmentation of the frequency spectra according to a power law as weIl as the existence of two types of surface modes. The surface and bulk modes in these Structures can exhibit particular behaviours related to multifractal systems. AIl these results are obtained from the measurement of the amplitude and the phase of the transmission coefficient through these photonic crystals when the latter are either inserted horizontally between two guides or placed vertically on a guide. The experimental and theoretical results are in~ood agreement
Zhao, Lei. "Solutions quasi-périodiques et solutions de quasi-collision du problème spatial des trois corps". Paris 7, 2013. http://www.theses.fr/2013PA077166.
Pełny tekst źródłaThis thesis generalizes to the spatial three-body problem in the lunar case some studies about several familles of quasiperiodic motions in the planar circular restricted three-body problem and in the planar three-body problem. As discovered by Harrington, if we develop the perturbing function of the system averaged over the fast angles in the powers of the ratio of the semi major axes, then the truncation at the first non-trivial order is integrable. This is the quadrupolar system. In a classical article, Lidov and Ziglin studied the dynamics of this system. We start by proving the existence of some quasi periodic solutions of the spatial three-body problem by applying KAM theorems to this system. We then prove the existence of a family of quasi-periodic almost-collision solutions: These are solutions along which two bodies become arbitrarily close to one another but never collide: the lower limit of their distance is zero but the upper limit is strictly positive. After a change of time, these solutions are quasi-periodic in a regularized system. Such solutions were first discovered in the planar circular restricted three-body problem by Chenciner and Llibre, and afterwards, in the planar three-body problem by Féjoz. We show the existence of a positive measure of such solutions in the spatial three-body problem, which confirms rigorously a prediction of Marchai. The proof goes through the application of an equivariant KAM theorem to a regularization of the problem, here the Kustaanheimo-Stiefel regularization, and, as in Féjoz's work, it requires understanding the relation between the regularization and averaging
Degand, Christophe. "Modélisation de structures quasi-périodiques et croissance de quasi-cristaux de la phase icosaédrique Al6CuLi3". Paris 6, 1992. http://www.theses.fr/1992PA066449.
Pełny tekst źródłaHutridurga, Ramaiah Harsha. "Homogénéisation et dispersion pour des écoulements complexes en milieu poreux et applications". Phd thesis, Palaiseau, Ecole polytechnique, 2013. https://theses.hal.science/index.php?halsid=b5dg7470uitq63omogbminqdg3&view_this_doc=pastel-00866253&version=1.
Pełny tekst źródłaOur work is a contribution to the understanding of transport of solutes in a porous medium. It has applications in groundwater contaminant transport, CO2 sequestration, underground storage of nuclear waste, oil reservoir simulations. We derive expressions for the effective Taylor dispersion taking into account convection, diffusion, heterogeneous geometry of the porous medium and reaction phenomena. Microscopic phenomena at the pore scale are upscaled to obtain effective behaviour at the observation scale. Method of two-scale convergence with drift from the theory of homogenization is employed as an upscaling technique. In the first part of our work, we consider reactions of mass exchange type, adsorption/desorption, at the fluid-solid interface of the porous medium. Starting with coupled convection-diffusion equations for bulk and surface concentrations of a single solute, coupled via adsorption isotherms, at a microscopic scale we derive effective equations at the macroscopic scale. We consider the microscopic system with highly oscillating coefficients in a strong convection regime i. E. , large Péclet regime. The presence of strong convection in the microscopic model leads to the induction of a large drift in the concentration profiles. Both linear and nonlinear adsorption isotherms are considered and the results are compared. In the second part of our work we generalize our results on single component flow to multicomponent flow in a linear setting. In the latter case, the effective parameters are obtained using Factorization principle and two-scale convergence with drift. The behaviour of effective parameters with respect to Péclet number and Damköhler number are numerically studied. Freefem++ is used to perform numerical tests in two dimensions
Rodriguez, Jérôme. "Études spectro-temporelles de microquasars en rayons X : oscillations quasi-périodiques et couplage accrétion-éjection". Paris 6, 2002. http://www.theses.fr/2002PA066320.
Pełny tekst źródłaBen, Slimene Jihed. "Réductibilité et théorie de Floquet pour des systèmes différenciels non linéaires". Phd thesis, Université Panthéon-Sorbonne - Paris I, 2013. http://tel.archives-ouvertes.fr/tel-00952406.
Pełny tekst źródłaMoreau, Gabriel. "Homogénéisation de structures discrètes en élasticité et en incrémental : applications aux modélisations continues linéaires et non-linéaires de treillis quasi-périodiques". Grenoble INPG, 1996. https://tel.archives-ouvertes.fr/tel-01762234.
Pełny tekst źródłaAmaral, Souto Hélio Pédro. "Diffusion-dispersion en milieu poreux : étude numérique du tenseur de dispersion pour quelques arrangements périodiques bidimensionnels ordonnés et désordonnés". Vandoeuvre-les-Nancy, INPL, 1993. http://docnum.univ-lorraine.fr/public/INPL_T_1993_AMARAL_SOUTO_H_P.pdf.
Pełny tekst źródłaKhayamian, Chiara. "Periodic and Quasi-Periodic Solutions of some Non-Linear Hamiltonian PDE's". Thesis, Avignon, 2017. http://www.theses.fr/2017AVIG0418/document.
Pełny tekst źródłaThe aim of this thesis is the research of periodic and quasi-periodic solutions for some non-linear hamiltonian PDEs
Galière, Julien. "Conception et réalisation de filtres transversaux à résonateurs diélectriques quasi-planaires en bande Ka pour des applications spatiales". Limoges, 2002. http://www.theses.fr/2002LIMO0062.
Pełny tekst źródłaNadin, Grégoire. "Equations de réaction-diffusion et propagation en milieu hétérogène". Paris 6, 2008. http://www.theses.fr/2008PA066491.
Pełny tekst źródłaDebraux, Laurent. "Analyse et contrôle de l'équation de Duffing et des phénomènes de ferrorésonance dans les lignes électriques : calcul des bassins d'attraction : continuation des tores invariants et solutions quasi-périodiques". Compiègne, 1990. http://www.theses.fr/1990COMPD320.
Pełny tekst źródłaFerroresonance on electric transmission lines are related to magnetic saturation of iron cores in transformers, this non-linearity is used to generate subharmonics, quasiperiodic or even chaotic motions. Non distributed parameter models for electric lines can be written as ordinary differential equations with periodic excitation as for instance Duffing’s equation. We start in chapter 1 with some theoretic preliminaries, then in chapters 2, 3 and 4 we study periodic solutions, we develop algorithms to search subharmonics and we deal with control of singular points. Chapter 5 is concerned with the computation of domains of attractions for non-transient states. Chapters 6 and 7 are devoted to the continuation of paths of invariant torus that emanate from a torus bifurcation. The algorithm is original and consists in following invariant circles using local charts that we adapt at each step. This program has been used to compute quasi periodic solutions for an electric line model using Poincaré mapping. We can think about further and numerous developments
Desoyer, Thierry. "Etudes numérique et expérimentale de l'évolution de cavités autour d'inclusions en milieu elastoplastique quasi-périodique : relation avec un modèle d'endommagement ductile". Poitiers, 1987. http://www.theses.fr/1987POIT2294.
Pełny tekst źródłaRoussel-Prioleau, Hélène. "Réflectivité d'un milieu stratifié chargé par des distributions périodiques d'inclusions bidimensionnelles : comparaison des modélisations par équation intégrale de domaine et par matrice de transition". Paris 6, 1993. http://www.theses.fr/1993PA066634.
Pełny tekst źródłaAmenoagbadji, Pierre. "Wave propagation in quasi-periodic media". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAE020.
Pełny tekst źródłaThe goal of this thesis is to develop efficient numerical methods for the solution of the time-harmonic wave equation in quasiperiodic media, in the spirit of methods previously developed for periodic media. The goal is to use as in quasiperiodic homogenization the idea that an elliptic PDE with quasiperiodic coefficients can be interpreted as the cut of a higher-dimensional PDE which is elliptically degenerate, but with periodic coefficients. The periodicity property allows to use adapted tools, but the non-elliptic aspect makes the mathematical and numerical analysis of the PDE delicate. One application concerns transmission problems between periodic half-spaces (typically photonic crystals) when (1) the interface does not cut the periodic half-spaces in a direction of periodicity, or (2) when the periodic media have noncommensurate periods along the interface
GUIDONI, Luca. "Quasicristaux optiques : refroidissement et piégeage d'atomes de césium dans un potentiel lumineux quasi-périodique". Phd thesis, Université Pierre et Marie Curie - Paris VI, 1998. http://tel.archives-ouvertes.fr/tel-00004625.
Pełny tekst źródłaNous décrivons comment obtenir des potentiels lumineux quasi-périodiques et nous expliquons comment nous avons refroidi et piégé des atomes de césium dans des réseaux optiques incommensurables, dans des super-réseaux optiques (potentiels lumineux modulés à grande échelle) et dans des quasicristaux
optiques avec une symétrie rotationnelle d'ordre cinq.
Nous avons caractérisé ces nouveaux systèmes physiques par des techniques de temps de vol, de spectroscopie pompe-sonde, de diffraction de Bragg et d'imagerie directe. Nous avons ainsi obtenu des informations sur la température cinétique, sur
le mouvement des atomes dans les puits de potentiel lumineux, sur la distribution de densité atomique (ordre à grande échelle) et sur les propriétés de transport des réseaux optiques quasi-périodiques.
Dans une dernière partie de la thèse, nous avons effectué une étude
numérique par simulation Monte-Carlo semi-classique des réseaux optiques périodiques et quasi-périodiques à trois dimensions. Les résultats de ces simulations sur la température, la localisation et les propriétés de transport sont en bon accord qualitatif avec les expériences. Ces simulations ont permis d'améliorer notablement la compréhension du comportement des atomes dans ce nouveau type de réseau optique.
Jacques, Jean-Nicolas. "Culture : vers une autonomie du champ? : La revue culturelle Las Moradas (1947-1949) d’Emilio Adolfo Westphalen (1911-2001) : étude socio-anthropologique d’une revue culturelle et d’un groupe d’avant-garde du champ artistique péruvien du milieu du XXe siècle". Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAH039.
Pełny tekst źródłaLas Moradas, a cultural review in the peruvian 1940
Metzger, Florian. "Exposants de Lyapunov d’opérateurs de Schrödinger ergodiques". Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066127/document.
Pełny tekst źródłaIn this thesis we are interested in the Lyapunov exponent of ergodic Schrödinger cocycles. These cocycles occur in the analysis of solutions to the Schrödinger equation where the potential is defined with ergodic dynamics. We study two distinct aspects related to the the Lyapunov exponent for different kinds of dynamics. First we focus on a large deviation theorem for quasi-periodic cocycles and then for potentials defined by the doubling map. We prove that estimates of Bourgain & Goldstein type are granted if an upper estimate involved in the theorem is true on a strip of the complex plane. Then we establish a new technique to prove this upper bound in the quasi-periodic setting, based on subharmonic arguments suggested by Avila, Jitomirskaya & Sadel. We adapt afterwards the method to the doubling map and prove a large deviation theorem for the inverse branches of this dynamics. In the second part, we establish an asymptotic development similar to the results of Figotin & Pastur and Sadel & Schulz-Baldes for the Lyapunov exponent of Schrödinger cocycles at small coupling when the potential is a mixture of quasi-periodic and random. The analysis distinguishes the cases when the energy is either diophantine or resonant with respect to the frequency of the quasi-periodic part of the potential
Belhadj, Mohamed. "Vers une modélisation mathématique de la filtration des globules blancs du sang". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2005. http://tel.archives-ouvertes.fr/tel-00011977.
Pełny tekst źródłaDans la première partie, nous définissons des modèles mathématiques qui réprésentent les principaux phénomènes physiques qui entrent en jeu dans le procédé de la filtration.
La deuxième partie est dédiée à l'analyse mathématique de systèmes d'équations aux dérivées partielles modélisant le procédé de la filtration. Tout d'abord, nous considérons un système d'équations semi-linéaires de type hyperbolique-parabolique avec une diffusion anisotrope dégénérée. Nous étudions ce problème avec une théorie $L^{1}$; nous considérons en particulier l'existence et l'unicité de solutions faibles ainsi que d'autres propriétés comme le principe du maximum; puis nous établissons la limite quand la constante de réaction devient grande. Nous montrons que le système converge vers une équation non linéaire parabolique-hyperbolique qui généralise le problème de Stefan. Nous étudions également, par des techniques de l'homogénéisation, la filtration au travers de milieux poreux fibrés. Le réseau des fibres étudié est celui utilisé par M. Briane dans le cadre d'une étude sur la conduction thermique des tissus biologiques. Nous dérivons et justifions l'équation de Darcy ainsi que la forme du tenseur de perméabilité pour un tel milieu fibreux. Les résultats théoriques concernant la perméabilité sont illustrés par quelques simulations numériques. Finalement, nous considérons le cas où le diamètre des fibres tend vers zéro. En appliquant des résultats de G. Allaire à notre cas, nous justifions rigoureusement la forme du terme dominant dans les formules de perméabilité efficace utilisées en ingénierie. Ces résultats sont également confirmés par un calcul numérique direct de la perméabilité, dans lequel la petitesse du diamètre des fibres rend nécessaire le recours à des approximations de précision élevée.
La définition des méthodes numériques efficaces pour approximer la solution des modèles mathématiques est envisagée dans la troisième partie. Précisément, concernant les équations de Darcy, nous avons utilisé la méthode des éléments finis mixtes hybrides. Pour la résolution de l'équation du transport, nous avons implémenté une méthode numérique utilisant des volumes finis pour la discrétisation du terme convection/réaction associé à une approximation mixte hybride pour la discrétisation du terme dispersif.
Zokimila, Pierre. "Modélisation numérique du comportement thermomécanique de réseaux de galeries souterraines pour le stockage des déchets radioactifs : Approche par homogénéisation". Phd thesis, 2005. http://tel.archives-ouvertes.fr/tel-00010925.
Pełny tekst źródłaLa formation géologique hôte sera soumise à des chargements mécanique et thermique dus respectivement au creusement des ouvrages de stockage et au dégagement de chaleur des colis de déchets stockés. Ces chargements thermomécaniques vont engendrer une modification de la distribution des contraintes dans la couche hôte et les déformations des ouvrages ainsi que l'extension des zones endommagées (EDZ) pourraient provoquer des instabilités locales et globales.
Les objectifs de ce travail consistent en l'élaboration de techniques de calculs pour optimiser la modélisation numérique du comportement thermoélastique des ouvrages à grande échelle et en l'évaluation de la perturbation thermomécanique induite par le stockage sur la formation géologique hôte. Dans cette optique, après une présentation de l'état des connaissances sur les aspects thermomécaniques des roches liés au stockage souterrain, des modélisations numériques 2D et 3D du comportement thermoélastique d'ouvrage individuel et d'un réseau de galeries ont été réalisées par une approche discrète. Toutefois, cette approche classique est pénalisante pour l'étude du comportement global d'installations de stockage. Pour pallier à cela, une approche de modélisation numérique, basée sur la technique d'homogénéisation des milieux périodiques, a été proposée. Des formulations ainsi que des procédures numériques ont été élaborées pour déterminer le comportement thermoélastique effectif d'une structure hétérogène équivalente. Le modèle, obtenu par cette méthode, a été validé avec des méthodes d'homogénéisation existantes telles que le modèle auto-cohérent, ainsi que les bornes de Hashin-Shtrikman. La comparaison du comportement thermoélastique effectif avec le comportement thermoélastique réel de référence a montré une bonne cohérence des résultats. Pour une application au stockage profond, les coefficients thermoélastiques effectifs d'un réseau de galeries circulaires ont pu être déterminés en 2D pour différentes dimensions de l'entraxe des galeries.