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Добірка наукової літератури з теми "Weakly nonlinear analysi"

Автор: Grafiati
Опубліковано: 14 березня 2023

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Статті в журналах з теми "Weakly nonlinear analysi"

1

Zheng, Kelong, Wenqiang Feng, and Chunxiang Guo. "Some New Nonlinear Weakly Singular Inequalities and Applications to Volterra-Type Difference Equation." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/912874.

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Some new nonlinear weakly singular difference inequalities are discussed, which generalize some known weakly singular inequalities and can be used in the analysis of nonlinear Volterra-type difference equations with weakly singular kernel. An application to the upper bound of solutions of a nonlinear difference equation is also presented.
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2

Cheng, Kelong, Chunxiang Guo, and Qingke Zeng. "On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/795456.

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Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.
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3

HUNTER, JOHN K. "SHORT-TIME EXISTENCE FOR SCALE-INVARIANT HAMILTONIAN WAVES." Journal of Hyperbolic Differential Equations 03, no. 02 (June 2006): 247–67. http://dx.doi.org/10.1142/s0219891606000781.

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We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations include ones that describe weakly nonlinear hyperbolic surface waves, such as nonlinear Rayleigh waves in elasticity.
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4

Spagnolo, Sergio, and Giovanni Taglialatela. "Analytic Propagation for Nonlinear Weakly Hyperbolic Systems." Communications in Partial Differential Equations 35, no. 12 (November 4, 2010): 2123–63. http://dx.doi.org/10.1080/03605300903440490.

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5

Christianson, Hans, Jeremy Marzuola, Jason Metcalfe, and Michael Taylor. "Nonlinear Bound States on Weakly Homogeneous Spaces." Communications in Partial Differential Equations 39, no. 1 (December 13, 2013): 34–97. http://dx.doi.org/10.1080/03605302.2013.845044.

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6

Rodriguez, Jesús, and Padraic Taylor. "Weakly nonlinear discrete multipoint boundary value problems." Journal of Mathematical Analysis and Applications 329, no. 1 (May 2007): 77–91. http://dx.doi.org/10.1016/j.jmaa.2006.06.024.

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7

Ibrahim, E. A., and S. P. Lin. "Weakly Nonlinear Instability of a Liquid Jet in a Viscous Gas." Journal of Applied Mechanics 59, no. 2S (June 1, 1992): S291—S296. http://dx.doi.org/10.1115/1.2899503.

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The weakly nonlinear instability of a viscous liquid jet emanated into a viscous gas contained in a coaxial vertical circular pipe is investigated as an initial-value problem. The linear stability theory predicted that the jet may become unstable either due to capillary pinching or due to interfacial stress fluctuation. The results of nonlinear stability analysis shows no tendency of supercritical stability for both of the linearly unstable modes. In fact, the nonlinear growth rate of the disturbance is faster than the exponential growth rate of the linear normal mode disturbance for the same flow parameters. Moreover, the most amplified linear normal mode disturbance evolves nonlinearly into a nonsinusoidal wave of shorter wavelength. No nonlinear instability is found for the linearly stable disturbances. Thus, while the linear theory is adequate for the prediction of the onset of jet breakup, nonlinear theory is required to describe the outcome of the jet breakup.
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8

Demenchuk, A. K. "Weakly irregular quasiperiodic solutions of nonlinear Pfaff systems." Differential Equations 44, no. 2 (February 2008): 186–91. http://dx.doi.org/10.1134/s0012266108020055.

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9

Dieter, Sabine. "Nonlinear degenerate curvature flows for weakly convex hypersurfaces." Calculus of Variations 22, no. 2 (February 2005): 229–51. http://dx.doi.org/10.1007/s00526-004-0279-4.

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10

Xu, Run. "Some new nonlinear weakly singular integral inequalities and their applications." Journal of Mathematical Inequalities, no. 4 (2017): 1007–18. http://dx.doi.org/10.7153/jmi-2017-11-76.

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Дисертації з теми "Weakly nonlinear analysi"

1

Lira, Sérgio Henrique Albuquerque. "Viscous Fingering In Complex Magnetic Fluids: Weakly Nonlinear Analysis, Stationary Solutions And Phase-field Models." Universidade Federal de Pernambuco, 2014. https://repositorio.ufpe.br/handle/123456789/12734.

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Submitted by Daniella Sodre (daniella.sodre@ufpe.br) on 2015-04-08T13:19:43Z No. of bitstreams: 2 TESE Sérgio Henrique Lira.pdf: 10473188 bytes, checksum: ad39baf570ad4b641f94987468e9d1d0 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5)
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CNPq; INCT-FCx.
Nesta Tese são empregadas técnicas analíticas e numéricas para investigar o fenômeno de formação de dedos viscosos entre fluidos imiscíveis confinados quando um destes fluidos é um fluido magnético complexo. Diferentes tipos de esquemas geométricos efetivamente bidimensionais foram investigados. Duas situações distintas são tomadas com relação à natureza da amostra de fluido magnético: um fluido newtoniano usual, e um fluido magneto-reológico que apresenta um yield stress dependente da intensidade do campo magnético. Equações governantes adequadas são derivadas para cada um dos casos. Para obter um entendimento analítico dos estágios iniciais da evolução temporal da interface foi empregada uma análise fracamente não-linear de modos acoplados. Este tipo de análise acessa a estabilidade de uma interface inicialmente perturbada e também revela a morfologia dos dedos emergentes. Em algumas circunstâncias soluções estacionárias podem ser encontradas mesmo na ordem não-linear mais baixa. Nesta situação é feita uma comparação de algumas destas soluções com soluções estáticas totalmente não-lineares obtidas através de um formalismo de vortex-sheet na condição de equilíbrio. Em seguida foi desenvolvido um modelo de phase-field aplicado a fluidos magnéticos que é capaz de simular numericamente a dinâmica totalmente não-linear do sistema. O modelo consiste em introduzir uma função auxiliar que reproduz uma interface difusa de espessura finita. Utilizando esta ferramenta também é possível estudar um complexo problema de dedos viscosos de origem biológica: o fluxo de actina como um fluido ativo dentro de um fragmento lamelar.
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2

Aberle, Marcus. "The nonlinear analysis of shear-weak gridshells." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621337.

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3

Chen, Kewang. "Mathematical Analysis of Some Partial Differential Equations with Applications." ScholarWorks @ UVM, 2019. https://scholarworks.uvm.edu/graddis/1053.

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In the first part of this dissertation, we produce and study a generalized mathematical model of solid combustion. Our generalized model encompasses two special cases from the literature: a case of negligible heat diffusion in the product, for example, when the burnt product is a foam-like substance; and another case in which diffusivities in the reactant and product are assumed equal. In addition to that, our model pinpoints the dynamics in a range of settings, in which the diffusivity ratio between the burned and unburned materials varies between 0 and 1. The dynamics of temperature distribution and interfacial front propagation in this generalized solid combustion model are studied through both asymptotic and numerical analyses. For asymptotic analysis, we first analyze the linear instability of a basic solution to the generalized model. We then focus on the weakly nonlinear case where a small perturbation of a neutrally stable parameter is taken so that the linearized problem is marginally unstable. Multiple scale expansion method is used to obtain an asymptotic solution for large time by modulating the most linearly unstable mode. On the other hand, we integrate numerically the exact problem by the Crank-Nicolson method. Since the numerical solutions are very sensitive to the derivative interfacial jump condition, we integrate the partial differential equation to obtain an integral-differential equation as an alternative condition. The result system of nonlinear algebraic equations is then solved by the Newton’s method, taking advantage of the sparse structure of the Jacobian matrix. By a comparison of our asymptotic and numerical solutions, we show that our asymptotic solution captures the marginally unstable behaviors of the solution for a range of model parameters. Using the numerical solutions, we also delineate the role of the diffusivity ratio between the burned and unburned materials. We find that for a representative set of this parameter values, the solution is stabilized by increasing the temperature ratio between the temperature of the fresh mixture and the adiabatic temperature of the combustion products. This trend is quite linear when a parameter related to the activation energy is close to the stability threshold. Farther from this threshold, the behavior is more nonlinear as expected. Finally, for small values of the temperature ratio, we find that the solution is stabilized by increasing the diffusivity ratio. This stabilizing effect does not persist as the temperature ratio increases. Competing effects produce a “cross-over” phenomenon when the temperature ratio increases beyond about 0.2. In the second part, we study the existence and decay rate of a transmission problem for the plate vibration equation with a memory condition on one part of the boundary. From the physical point of view, the memory effect described by our integral boundary condition can be caused by the interaction of our domain with another viscoelastic element on one part of the boundary. In fact, the three different boundary conditions in our problem formulation imply that our domain is composed of two different materials with one condition imposed on the interface and two other conditions on the inner and outer boundaries, respectively. These transmission problems are interesting not only from the point of view of PDE general theory, but also due to their application in mechanics. For our mathematical analysis, we first prove the global existence of weak solution by using Faedo-Galerkin’s method and compactness arguments. Then, without imposing zero initial conditions on one part of the boundary, two explicit decay rate results are established under two different assumptions of the resolvent kernels. Both of these decay results allow a wider class of relaxation functions and initial data, and thus generalize some previous results existing in the literature.
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4

LUPO, Salvatore. "FORMAZIONE DI PATTERN PER IL PROCESSO DELL'ELETTRODEPOSIZIONE IN MODELLI DI TIPO REAZIONE-DIFFUSIONE." Doctoral thesis, Università degli Studi di Palermo, 2014. http://hdl.handle.net/10447/90863.

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5

Moulin, Johann. "On the flutter bifurcation in laminar flows : linear and nonlinear modal methods." Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAX093.

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L'instabilité de flottement a été le sujet de nombreuses études depuis le milieu du vingtième siècle à cause de ses applications critiques en aéronautique. Elle est classiquement décrite comme un instabilité linéaire en écoulement potentiel, mais les effets visqueux et nonlinéaires du fluide peuvent avoir un impact crucial.La première partie de cette thèse est consacrée au développement de méthodes théoriques et numériques pour l'analyse linéaire et nonlinéaire de la dynamique d'une ``section typique aéroélastique'' --- une plaque montée sur des ressorts de flexion et torsion --- plongée dans un écoulement laminaire bidimensionnel modélisé par les équations de Navier--Stokes incompressibles.D'abord, on développe une analyse faiblement nonlinéaire pour étudier le régime basse amplitude, puis, une approche d'équilibrage harmonique, connue comme la Méthode Spectrale en Temps (TSM), de façon à capturer des solutions de flottement plus fortement nonlinéaires. Le défi de la résolution numérique des équations TSM est relevé grâce au développement d'une approche parallèle en temps de type Newton--Krylov, combinée à un préconditionneur spécialement développé, dit ``bloc-circulant''.La seconde partie de la thèse est dédiée à l'étude physique de la bifurcation de flottement. On commence par revisiter le problème de stabilité linéaire en mettant en lumière, en particulier, les effets de viscosité.On poursuit avec l'étude des effets nonlinéaires fluides: les structures légères et les hauts nombres de Reynolds favorisent des bifurcations sous-critiques.On achève cette partie en étudiant l'apparition de modulations de basse fréquence sur des solutions périodiques de flottement. On explique ce comportement par une instabilité linéaire (Floquet) de cycle limite.La dernière partie de la thèse vise à initier l'extension des différentes méthodes évoquées précédemment pour le cas de configurations tridimensionnelles à grande échelle. En guise de premier pas vers cet objectif à long terme, on développe un outil open-source massivement parallèle capable de réaliser l'analyse de stabilité linéaire hydrodynamique (structure figée) d'écoulements tridimensionnels possédant plusieurs dizaines de millions de degrés de liberté
The flutter instability has been the focus of numerous works since the middle of the twentieth century, due to its critical application in aeronautics. Flutter is classically described as a linear instability using potential flow models, but viscous and nonlinear fluid effects may both crucially impact this aeroelastic phenomenon.The first part of this thesis is devoted to the development of theoretical and numerical methods for analyzing the linear and nonlinear dynamics of a ``typical aeroelastic section'' --- a heaving and pitching spring-mounted plate --- immersed in a two-dimensional laminar flow modeled by the incompressible Navier--Stokes equations.First, we develop a semi-analytical weakly nonlinear analysis to efficiently study the small amplitude regime. Second, we develop a harmonic balance-type method, known as the Time Spectral Method (TSM), in order to tackle highly-nonlinear periodic flutter solutions. The challenging task of solving the TSM equations is tackled via a time-parallel Newton--Krylov approach in combination with a new, so-called block-circulant preconditioner.The second part of the thesis focuses on the physical investigation of the flutter bifurcation. We start by revisiting the linear stability problem using a Navier--Stokes fluid model allowing to highlight, in particular, the effect of viscosity.We continue our route on the flutter bifurcation by investigating the effect of fluid nonlinearities: low solid-to-fluid mass ratios and increasing Reynolds numbers foster subcritical bifurcations.We conclude our study by investigating the appearance of low-frequency amplitude modulations on top of a previously established periodic flutter solution. We explain this behavior by a (Floquet) linear instability of periodic solutions.The last part of the thesis aims at initiating the extension of the different methods previously evoked to large-scale three-dimensional configurations. As a first step towards this long-term goal, we develop an open-source massively parallel tool, able to perform hydrodynamic (the structure is fixed) linear stability analysis of three-dimensional flows possessing several tens of millions of degrees of freedom
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6

Chekila, Abdelfateh. "Analyse non linéaire de la stabilité de l'écoulement de Poiseuille plan d'un fluide rhéofluidifiant." Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0022/document.

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L'objectif de cette thèse est d'analyser l'influence des non linéarités, du comportement rhéologique des fluides rhéofluidifiants, sur les conditions de stabilité et de transition vers la turbulence. Dans un premier temps, une analyse linéaire de stabilité avec une approche modale a été réalisée. Les résultats obtenus mettent clairement en évidence l'effet stabilisant de la rhéofluidification. Ensuite, une analyse faiblement non linéaire de stabilité a été menée en vue d'examiner l'influence de la perturbation de la viscosité sur la stabilité vis à vis de perturbations d'amplitude finie. L'analyse de la contribution des termes non linéaires d'inertie et visqueux montre que, contrairement aux termes d'inertie, les termes non linéaires visqueux ont tendance à accélérer l'écoulement et favoriser une bifurcation sur-critique. Les effets rhéofluidifiants tendent à réduire la dissipation visqueuse. Finalement, une analyse fortement non linéaire de stabilité a été conduite en utilisant les techniques de suivi de branches de solutions par des méthodes de continuation. Pour pouvoir traiter les termes visqueux fortement non linéaires, un code de calcul pseudo-spectral a été développé. Des solutions non linéaires d'équilibre ont été obtenues et caractérisées pour différentes valeurs des paramètres rhéologiques
The aim of this study is to understand the influence of the nonlinear rheological behaviour of the shear-thinning fluids on the flow stability and transition to turbulence. First, a linear stability analysis using modal approach was carried out. Results clearly highlight the stabilizing effect of shear-thinning. Then, as a first approach to take into account nonlinear effects of viscosity perturbation on the flow stability, a weakly nonlinear stability analysis is performed in the neighbourhood of the critical conditions. Results indicate that shear-thinning reduces the viscous dissipation and, in contrast to inertial terms, the nonlinear viscous terms tend to accelerate the flow and act in favour of supercritical bifurcation. Finally, a nonlinear stability analysis is done by following solution branches in the parameter space using continuation techniques. To deal with highly nonlinear viscous terms, a pseudo-spectral code is developed. Nonlinear equilibrium solutions was found and characterized for various values of the rheological parameters
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7

GRIFO', Gabriele. "Pattern formation in hyperbolic reaction-transport systems and applications to dryland ecology." Doctoral thesis, Università degli Studi di Palermo, 2023. https://hdl.handle.net/10447/580054.

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Pattern formation and modulation is an active branch of mathematics, not only from the perspective of fundamental theory but also for its huge applications in many fields of physics, ecology, chemistry, biology, and other sciences. In this thesis, the occurrence of Turing and wave instabilities, giving rise to stationary and oscillatory patterns, respectively, is theoretically investigated by means of two-compartment reaction-transport hyperbolic systems. The goal is to elucidate the role of inertial times, which are introduced in hyperbolic models to account for the finite-time propagation of disturbances, in stationary and transient dynamics, in supercritical and subcritical regimes. In particular, starting from a quite general framework of reaction-transport model, three particular cases are derived. In detail, in the first case, the occurrence of stationary patterns is investigated in one-dimensional domains by looking for the inertial dependence of the main features that characterize the formation and stability process of the emerging patterns. In particular, the phenomenon of Eckhaus instability, in both supercritical and subcritical regimes, is studied by adopting linear and multiple-scale weakly-nonlinear analysis and the role played by inertia during the transient regime, where an unstable patterned state evolves towards a more favorable stable configuration through sequences of phase-slips, is elucidated. Then, in the second topic, the focus is moved to oscillatory periodic patterns generated by wave (or oscillatory Turing) instability. This phenomenon is studied by considering 1D two-compartment hyperbolic reaction-transport systems where different transport mechanisms of the species here involved are taken into account. In these cases, by using linear and weakly nonlinear stability analysis techniques, the dependence of the non-stationary patterns on hyperbolicity is underlined at and close to the criticality. In particular, it is proven that inertial effects play a role, not only during transient regimes from the spatially-homogeneous steady state toward the patterned state but also in altering the amplitude, the wavelength, the migration speed, and even the stability of the travelling waves. Finally, in the last case, the formation and stability of stationary patterns are investigated in bi-dimensional domains. To this aim, a general class of two-species hyperbolic reaction-transport systems is deduced following the guidelines of Extended Thermodynamics theory. To characterize the emerging Turing patterns, linear and weakly nonlinear stability analysis on the uniform steady states are addressed for rhombic and hexagonal planform solutions. In order to gain some insight into the above-mentioned dynamics, the previous theoretical predictions are corroborated by numerical simulations carried out in the context of dryland ecology. In this context, patterns become a relevant tool to identify early warning signals toward desertification and to provide a measure of resilience of ecosystems under climate change. Such ecological implications are discussed in the context of the Klausmeier model, one of the easiest two-compartment (vegetation biomass and water) models able to describe the formation of patterns in semi-arid environments. Therefore, it will be also here discussed how the experimentally-observed inertia of vegetation affects the formation and stability of stationary and oscillatory periodic vegetation patterns.
Pattern formation and modulation is an active branch of mathematics, not only from the perspective of fundamental theory but also for its huge applications in many fields of physics, ecology, chemistry, biology, and other sciences. In this thesis, the occurrence of Turing and wave instabilities, giving rise to stationary and oscillatory patterns, respectively, is theoretically investigated by means of two-compartment reaction-transport hyperbolic systems. The goal is to elucidate the role of inertial times, which are introduced in hyperbolic models to account for the finite-time propagation of disturbances, in stationary and transient dynamics, in supercritical and subcritical regimes. In particular, starting from a quite general framework of reaction-transport model, three particular cases are derived. In detail, in the first case, the occurrence of stationary patterns is investigated in one-dimensional domains by looking for the inertial dependence of the main features that characterize the formation and stability process of the emerging patterns. In particular, the phenomenon of Eckhaus instability, in both supercritical and subcritical regimes, is studied by adopting linear and multiple-scale weakly-nonlinear analysis and the role played by inertia during the transient regime, where an unstable patterned state evolves towards a more favorable stable configuration through sequences of phase-slips, is elucidated. Then, in the second topic, the focus is moved to oscillatory periodic patterns generated by wave (or oscillatory Turing) instability. This phenomenon is studied by considering 1D two-compartment hyperbolic reaction-transport systems where different transport mechanisms of the species here involved are taken into account. In these cases, by using linear and weakly nonlinear stability analysis techniques, the dependence of the non-stationary patterns on hyperbolicity is underlined at and close to the criticality. In particular, it is proven that inertial effects play a role, not only during transient regimes from the spatially-homogeneous steady state toward the patterned state but also in altering the amplitude, the wavelength, the migration speed, and even the stability of the travelling waves. Finally, in the last case, the formation and stability of stationary patterns are investigated in bi-dimensional domains. To this aim, a general class of two-species hyperbolic reaction-transport systems is deduced following the guidelines of Extended Thermodynamics theory. To characterize the emerging Turing patterns, linear and weakly nonlinear stability analysis on the uniform steady states are addressed for rhombic and hexagonal planform solutions. In order to gain some insight into the above-mentioned dynamics, the previous theoretical predictions are corroborated by numerical simulations carried out in the context of dryland ecology. In this context, patterns become a relevant tool to identify early warning signals toward desertification and to provide a measure of resilience of ecosystems under climate change. Such ecological implications are discussed in the context of the Klausmeier model, one of the easiest two-compartment (vegetation biomass and water) models able to describe the formation of patterns in semi-arid environments. Therefore, it will be also here discussed how the experimentally-observed inertia of vegetation affects the formation and stability of stationary and oscillatory periodic vegetation patterns.
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8

Abatangelo, N. "Large Solutions for Fractional Laplacian Operators." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/320258.

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The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the boundary of the prescribed domain. We first remark the existence of a large class of harmonic functions with a boundary blow-up and we characterize them in terms of a new notion of degenerate boundary trace. Via some integration by parts formula, we then provide a weak theory of Stampacchia's sort to extend the linear theory to a setting including these functions: we study the classical questions of existence, uniqueness, continuous dependence on the data, regularity and asymptotic behaviour at the boundary. Afterwards we develop the theory of semilinear problems, by adapting and generalizing some sub- and supersolution methods. This allows us to build the fractional counterpart of large solutions in the elliptic PDE theory of nonlinear equations, giving sufficient conditions for the existence. The thesis is concluded with the definition and the study of a notion of nonlocal directional curvatures.
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9

Filippini, Andrea Gilberto. "Free surface flow simulation in estuarine and coastal environments : numerical development and application on unstructured meshes." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0404/document.

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Over the last decades, there has been considerable attention in the accurate mathematical modeling and numerical simulations of free surface wave propagation in near-shore environments. A physical correct description of the large scale phenomena, which take place in the shallow water region, must account for strong nonlinear and dispersive effects, along with the interaction with complex topographies. First, a study on the behavior in nonlinear regime of different Boussinesq-type models is proposed, showing the advantage of using fully-nonlinear models with respect to weakly-nonlinear and weakly dispersive models (commonly employed). Secondly, a new flexible strategy for solving the fully-nonlinear and weakly-dispersive Green-Naghdi equations is presented, which allows to enhance an existing shallow water code by simply adding an algebraic term to the momentum balance and is particularly adapted for the use of hybrid techniques for wave breaking. Moreover, the first discretization of the Green-Naghdi equations on unstructured meshes is proposed via hybrid finite volume/ finite element schemes. Finally, the models and the methods developed in the thesis are deployed to study the physical problem of bore formation in convergent alluvial estuary, providing the first characterization of natural estuaries in terms of bore inception
Ces dernières décennies, une attention particulière a été portée sur la modélisation mathématique et la simulation numérique de la propagation de vagues en environnements côtiers. Une description physiquement correcte des phénomènes à grande échelle, qui apparaissent dans les régions d'eau peu profonde, doit prendre en compte de forts effets non-linéaires et dispersifs, ainsi que l'interaction avec des bathymétries complexes. Dans un premier temps, une étude du comportement en régime non linéaire de différents modèles de type Boussinesq est proposée, démontrant l'avantage d'utiliser des modèles fortement non-linéaires par rapport à des modèles faiblement non-linéaires et faiblement dispersifs (couramment utilisés). Ensuite, une nouvelle approche flexible pour résoudre les équations fortement non-linéaires et faiblement dispersives de Green-Naghdi est présentée. Cette stratégie permet d'améliorer un code "shallow water" existant par le simple ajout d'un terme algébrique dans l'équation du moment et est particulièrement adapté à l'utilisation de techniques hybrides pour le déferlement des vagues. De plus, la première discrétisation des équations de Green-Naghdi sur maillage non structuré est proposée via des schémas hybrides Volume Fini/Élément Fini. Finalement, les modèles et méthodes développés dans la thèse sont appliqués à l'étude du problème physique de la formation du mascaret dans des estuaires convergents et alluviaux. Cela a amené à la première caractérisation d'estuaire naturel en terme d'apparition de mascaret
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Ricchiuti, Amelia Lavinia. "Design and fabrication of customized fiber gratings to improve the interrogation of optical fiber sensors." Doctoral thesis, Universitat Politècnica de València, 2016. http://hdl.handle.net/10251/66343.

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[EN] Fiber grating sensors and devices have demonstrated outstanding capabilities in both telecommunications and sensing areas, due to their well-known advantageous characteristics. Therefore, one of the most important motivations lies in the potential of customized fiber gratings to be suitably employed for improving the interrogation process of optical fiber sensors and systems. This Ph.D. dissertation is focused on the study, design, fabrication and performance evaluation of customized fiber Bragg gratings (FBGs) and long period gratings (LPGs) with the double aim to present novel sensing technologies and to enhance the response of existing sensing systems. In this context, a technique based on time-frequency domain analysis has been studied and applied to interrogate different kind of FBGs-based sensors. The distribution of the central wavelength along the sensing structures has been demonstrated, based on a combination of frequency scanning of the interrogating optical pulse and optical time-domain reflectometry (OTDR), allowing the detection of spot events with good performance in terms of measurand resolution. Moreover, different customized FBGs have been interrogated using a technology inspired on the operation principle of microwave photonics (MWP) filters, enabling the detection of spot events using radio-frequency (RF) devices with modest bandwidth. The sensing capability of these technological platforms has been fruitfully employed for implementing a large scale quasi-distributed sensor, based on an array of cascaded FBGs. The potentiality of LPGs as fiber optic sensors has also been investigated in a new fashion, exploiting the potentials of MWP filtering techniques. Besides, a novel approach for simultaneous measurements based on a half-coated LPG has been proposed and demonstrated. Finally, the feasibility of FBGs as selective wavelength filters has been exploited in sensing applications; an alternative approach to improve the response and performance of Brillouin distributed fiber sensors has been studied and validated via experiments. The performance of the reported sensing platforms have been analyzed and evaluated so as to characterize their impact on the fiber sensing field and to ultimately identify the use of the most suitable technology depending on the processing task to be carried out and on the final goal to reach.
[ES] Los sensores y dispositivos en fibra basados en redes de difracción han mostrado excepcionales capacidades en el ámbito de las telecomunicaciones y del sensado, gracias a sus excelentes propiedades. Entre las motivaciones más estimulantes destaca la posibilidad de fabricar redes de difracción ad-hoc para implementar y/o mejorar las prestaciones de los sensores fotónicos. Esta tesis doctoral se ha enfocado en el estudio, diseño, fabricación y evaluación de las prestaciones de redes de difracción de Bragg (FBGs) y de redes de difracción de periodo largo (LPGs) personalizadas con el fin de desarrollar nuevas plataformas de detección y a la vez mejorar la respuesta y las prestaciones de los sensores fotónicos ya existentes. En este contexto, una técnica basada en el análisis tiempofrecuencia se ha estudiado e implementado para la interrogación de sensores en fibra basados en varios tipos y modelos de FBGs. Se ha analizado la distribución de la longitud de onda central a lo largo de la estructura de sensado, gracias a una metodología que conlleva el escaneo en frecuencia del pulso óptico incidente y la técnica conocida como reflectometria óptica en el dominio del tiempo (OTDR). De esta manera se ha llevado a cabo la detección de eventos puntuales, alcanzando muy buenas prestaciones en términos de resolución de la magnitud a medir. Además, se han interrogado varias FBGs a través de una técnica basada en el principio de operación de los filtros de fotónica de microondas (MWP), logrando así la detección de eventos puntuales usando dispositivos de radio-frecuencia (RF) caracterizados por un moderado ancho de banda. La capacidad de sensado de estas plataformas tecnológicas ha sido aprovechada para la realización de un sensor quasi-distribuido de gran alcance, formado por una estructura en cascada de muchas FBGs. Por otro lado, se han puesto a prueba las capacidades de las LPGs como sensores ópticos según un enfoque novedoso; para ello se han aprovechados las potencialidades de los filtros de MWP. Asimismo, se ha estudiado y demostrado un nuevo método para medidas simultáneas de dos parámetros, basado en una LPG parcialmente recubierta por una película polimérica. Finalmente, se ha explotado la viabilidad de las FBGs en cuanto al filtrado selectivo en longitud de onda para aplicaciones de sensado; para ello se ha propuesto un sistema alternativo para la mejora de la respuesta y de las prestaciones de sensores ópticos distribuidos basados en el scattering de Brillouin. En conclusión, se han analizado y evaluado las prestaciones de las plataformas de sensado propuestas para caracterizar su impacto en el ámbito de los sistemas de detección por fibra y además identificar el uso de la tecnología más adecuada dependiendo de la tarea a desarrollar y del objetivo a alcanzar.
[CAT] Els sensors i dispositius en fibra basats en xarxes de difracció han mostrat excepcionals capacitats en l'àmbit de les telecomunicacions i del sensat, gràcies a les seus excel¿lents propietats. Entre les motivacions més estimulants destaca la possibilitat de fabricar xarxes de difracció ad-hoc per a implementar i/o millorar les prestacions de sensors fotònics. Esta tesi doctoral s'ha enfocat en l'estudi, disseny, fabricació i avaluació de les prestacions de xarxes de difracció de Bragg (FBGs) i de xarxes de difracció de període llarg (LPGs) personalitzades per tal de desenvolupar noves plataformes de detecció i al mateix temps millorar la resposta i les prestacions dels sensors fotònics ja existents. En este context, una tècnica basada en l'anàlisi temps-freqüència s'ha estudiat i implementat per a la interrogació de sensors en fibra basats en diversos tipus i models de FBGs. S'ha analitzat la distribució de la longitud d'ona central al llarg de l'estructura de sensat, gràcies a una metodologia que comporta l'escaneig en freqüència del pols òptic incident i la tècnica coneguda com reflectometria òptica en el domini del temps (OTDR). D'esta manera s'ha dut a terme la detecció d'esdeveniments puntuals, aconseguint molt bones prestacions en termes de resolució de la magnitud a mesurar. A més, s'han interrogat diverses FBGs a través d'una tècnica basada en el principi d'operació dels filtres de fotònica de microones (MWP), aconseguint així la detecció d'esdeveniments puntuals utilitzant dispositius de ràdio-freqüència (RF) caracteritzats per un moderat ample de banda. La capacitat de sensat d'aquestes plataformes tecnològiques ha sigut aprofitada per a la realització d'un sensor quasi-distribuït a llarga escala, format per una estructura en cascada de moltes FBGs. D'altra banda, s'han posat a prova les capacitats de les LPGs com a sensors òptics segons un enfocament nou; per a això s'han aprofitat les potencialitats dels filtres de MWP. Així mateix, s'ha estudiat i demostrat un nou mètode per a mesures simultànies de dos paràmetres, basat en una LPG parcialment recoberta per una pel¿lícula polimèrica. Finalment, s'ha explotat la viabilitat de les FBGs pel que fa al filtrat selectiu en longitud d'ona per a aplicacions de sensat; per això s'ha proposat un sistema alternatiu per a la millora de la resposta i de les prestacions de sensors òptics distribuïts basats en el scattering de Brillouin. S'han analitzat i avaluat les prestacions de les plataformes de sensat propostes per a caracteritzar el seu impacte en l'àmbit dels sistemes de detecció per fibra i a més identificar l'ús de la tecnologia més adequada depenent de la tasca a desenvolupar i de l'objectiu a assolir.
Ricchiuti, AL. (2016). Design and fabrication of customized fiber gratings to improve the interrogation of optical fiber sensors [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/66343
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Книги з теми "Weakly nonlinear analysi"

1

1959-, Fitzmaurice N., ed. Nonlinear waves and weak turbulence with applications in oceanography and condensed matter physics. Boston: Birkhäuser, 1993.

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2

Jeribi, Aref, and Bilel Krichen. Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications. Taylor & Francis Group, 2015.

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3

Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications. Taylor & Francis Group, 2015.

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4

Jeribi, Aref, and Bilel Krichen. Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications. Taylor & Francis Group, 2015.

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5

FITZMAURICE, GURARIE, MCCAUGHAN, and WOYCZYNSKI. Weak Turbulance and Nonlinear Waves with Applications to Geophysics and Oceanography (Progress in Nonlinear Differential Equations and Their Applications). Birkhauser, 1993.

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6

Nonlinear waves and weak turbulence with applications in oceanography and condensed matter physics. Boston: Birkhauser, 1993.

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7

Deterministic Extraction From Weak Random Sources. Springer, 2010.

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8

Gabizon, Ariel. Deterministic Extraction from Weak Random Sources. Springer, 2010.

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9

Gabizon, Ariel. Deterministic Extraction from Weak Random Sources. Springer, 2012.

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10

Gabizon, Ariel. Deterministic Extraction from Weak Random Sources. Springer, 2010.

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Частини книг з теми "Weakly nonlinear analysi"

1

Hunter, John K. "Interacting Weakly Nonlinear Hyperbolic and Dispersive Waves." In Microlocal Analysis and Nonlinear Waves, 83–111. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4613-9136-4_7.

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2

Giaquinta, M., G. Modica, and J. Souček. "Some Regularity Properties of Locally Weakly Invertible Maps." In Nonlinear Analysis and Continuum Mechanics, 45–59. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-2196-8_5.

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3

Slimani, N., A. Makhoute, and M. Tlidi. "Weakly Nonlinear Analysis and Localized Structures in Nonlinear Cavities with Metamaterials." In Springer Proceedings in Physics, 153–66. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24871-4_11.

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4

Wolf, Joerg. "Hölder Continuity of Weak Solutions to Certain Nonlinear Parabolic Systems in Two Space Dimensions." In Applied Nonlinear Analysis, 531–46. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/0-306-47096-9_36.

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Alliot, Frédéric, and Cherif Amrouche. "On the Regularity and Decay of the Weak Solutions to the Steady-State Navier-Stokes Equations in Exterior Domains." In Applied Nonlinear Analysis, 1–18. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/0-306-47096-9_1.

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Dizès, Stéphane Le, Patrick Huerre, J. M. Chomaz, and Peter A. Monkewitz. "Nonlinear Stability Analysis of Slowly-Diverging Flows: Limitations of the Weakly Nonlinear Approach." In Bluff-Body Wakes, Dynamics and Instabilities, 147–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-662-00414-2_34.

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Neustupa, Jiří, and Patrick Penel. "Regularity of a Suitable Weak Solution to the Navier-Stokes Equations as a Consequence of Regularity of One Velocity Component." In Applied Nonlinear Analysis, 391–402. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/0-306-47096-9_26.

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Fečkan, Michal. "Galerkin-Averaging Method in Infinite-Dimensional Spaces for Weakly Nonlinear Problems." In Nonlinear Analysis and its Applications to Differential Equations, 269–79. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0191-5_18.

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Pesch, W., W. Decker, Q. Feng, M. Kaiser, L. Kramer, and A. Weber. "Weakly Nonlinear Analysis of Pattern Formation in Nematic Liquid Crystals." In Nematics, 291–301. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3428-6_22.

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Sohr, Hermann. "A Special Class of Weak Solutions of the Navier-Stokes Equations in Arbitrary Three-dimensional Domains." In Topics in Nonlinear Analysis, 621–42. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8765-6_27.

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Тези доповідей конференцій з теми "Weakly nonlinear analysi"

1

Lee, Jung Lyul, and Chan Sung Park. "A Weakly Nonlinear Wave Model of Practical Use." In Fourth International Symposium on Ocean Wave Measurement and Analysis. Reston, VA: American Society of Civil Engineers, 2002. http://dx.doi.org/10.1061/40604(273)91.

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2

Hermann, J. A. "Analysis of The Thick Medium Z-Scan." In Nonlinear Optics. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.tud17.

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An analytic solution of the propagation equation for a symmetrical optical beam has been obtained, in the situation where the beam is focused within an optically nonlinear medium having a thickness greater than the depth of focus. Previous related work by the author has concentrated upon finding solutions, in continued-fraction format, within the strongly self-focusing/defocusing limit [1]. In the present work, an expression is derived for the transmitted electric field envelope in the weakly nonlinear case. The result is described in terms of a linear superposition of Gaussian-Laguerre modes, the coefficients of which depend only upon the linear component of the accumulated optical phase on the optic axis. The medium that has been explored possesses a Kerr-type susceptibility with refractive and absorptive components.
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3

Jakobsen, P. K., S. G. Wenden, J. V. Moloney, and A. C. Newell. "Optical turbulence in wide gain section lasers: An analogy with large aspect ratio fluids." In Nonlinear Optics. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.tuc4.

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The close synergism between experiment and theory for Rayleigh-Benard fluid convection has led to the development of sophisticated theoretical models which accurately predict the onset of widely diverse pattern forming turbulent convection. Close to threshold a multiple scales weakly nonlinear analysis yields a universal class of amplitude equations which accurately predict the formation of roll, hexagon, defect patterns and various instabilities of the underlying roll solutions. An elegant study by Busse of the nonlinear regime established that turbulent patterns and stable rolls could coexist beyond the first instability threshold.
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4

Diogo, Teresa, Pedro Lima, Magda Rebelo, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Extrapolation Methods for a Nonlinear Weakly Singular Volterra Integral Equation." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497874.

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5

Balachandran, Balakumar, and Khalil A. Khan. "Spectral Analyses of Nonlinear Interactions." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0304.

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Abstract Signals pertaining to motions of nonlinearly coupled oscillators are studied using higher-order spectral analyses. The analyses is used to understand the role of phase coupling in nonlinear interactions between two or more Fourier components. For certain motions of weakly nonlinear systems, analytical approximations are obtained for relevant higher-order spectra and coherence functions. Numerical studies are conducted to verify analytical predictions and to illustrate the usefulness of spectral analyses for different cases.
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6

Hattori, Y., Y. Fukumoto, and K. Fujimura. "Instability of an elliptical flow: weakly nonlinear analysis." In FLUID STRUCTURE INTERACTION/MOVING BOUNDARIES 2007. Southampton, UK: WIT Press, 2007. http://dx.doi.org/10.2495/fsi070181.

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7

Slimani, N., A. Makhoute, and M. Tlidi. "Weakly nonlinear analysis and localised structures in nonlinear cavities with metamaterials." In SPIE Photonics Europe, edited by Krassimir Panajotov, Marc Sciamanna, Angel Valle, and Rainer Michalzik. SPIE, 2016. http://dx.doi.org/10.1117/12.2229874.

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Gutschmidt, Stefanie, and Oded Gottlieb. "Internal Resonances in Microbeam Arrays Subject to Electrodynamical Parametric Excitation." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35017.

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The dynamic response of parametrically excited microbeam arrays is governed by nonlinear effects which directly influence their performance. To date, documented theoretical models consist of lumped-mass systems which do not resolve the spatio-temporal interaction of the individual elements and reproduce measured array response only qualitatively. A consistent nonlinear continuum model is derived using the extended Hamilton’s principle to capture the salient dynamic features of an array of N nonlinearly coupled microbeams. The nonlinear dynamic equations of motion are solved analytically using the asymptotic multiple-scales method for the weakly nonlinear system. Stability analysis of the resulting coexisting solutions enables construction of a comprehensive bifurcation structure for the system. Analytically obtained results for the weakly nonlinear limit of two coupled microbeams are verified numerically.
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Fitch, J., A. Norman, and M. A. Moore. "Alkahest III: automatic analysis of periodic weakly nonlinear ODEs." In the fifth ACM symposium. New York, New York, USA: ACM Press, 1986. http://dx.doi.org/10.1145/32439.32446.

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10

De Angelis, C., and M. Santagiustina. "Induced nonlinear modulational instability in high birefringence fibers: a quantitative study." In Nonlinear Guided-Wave Phenomena. Washington, D.C.: Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.tub.6.

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Modulational instability (MI) refers to the growth of an initial weak perturbation at the expense of a plane wave in a dispersive or diffractive nonlinear medium [1]. In the context of optical fibers, temporal MI in the anomalous group-velocity dispersion (GVD) regime has been extensively studied in recent years for its potential application in high-repetition rate ultrashort pulse train generation [2] and ultrafast optical switching [3]. The domain of MI may be extended to the normal GVD regime by means of a feedback loop [4] or exploiting cross-phase modulation (XPM) [5,6]. In the latter case, the simultaneous presence of two copropagating beams can also lead to a more complex behaviour in comparison with the scalar case [7]. The aim of this paper is to give a quantitative understanding of the nonlinear dynamics (i.e. past the early stage of exponential sidebands growth) of MI induced by XPM between linearly polarized beams copropagating along the principal axes of a high-birefringence fiber, both weakly perturbed. At first, for the sake of clarity, we will recall the well known linear stability analysis of the system and then introduce a finite dimensional truncation leading to an intricate system of Ordinary Differential Equations (ODE’s). Finally, introducing some approximations supported by numerical results and physical considerations, we will obtain an exactly solvable set of ODE's, which is analogous to the one derived in [7] for a different initial condition.
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Звіти організацій з теми "Weakly nonlinear analysi"

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Muhlestein, Michael, and Carl Hart. Numerical analysis of weak acoustic shocks in aperiodic array of rigid scatterers. Engineer Research and Development Center (U.S.), October 2020. http://dx.doi.org/10.21079/11681/38579.

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Nonlinear propagation of shock waves through periodic structures have the potential to exhibit interesting phenomena. Frequency content of the shock that lies within a bandgap of the periodic structure is strongly attenuated, but nonlinear frequency-frequency interactions pumps energy back into those bands. To investigate the relative importance of these propagation phenomena, numerical experiments using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation are carried out. Two-dimensional propagation through a periodic array of rectangular waveguides is per-formed by iteratively using the output of one waveguide as the input for the next waveguide. Comparison of the evolution of the initial shock wave for both the linear and nonlinear cases is presented.
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SEISMIC PERFORMANCE OF SPATIAL STEEL BEAM-COLUMN CONNECTIONS. The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.125.

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This paper presents a finite element analysis for spatial beam-column connections in steel frame to better understand the structural behavior of spatial connections. After the simulation and validation of experimental results, a total of 7 refined 3D models, including beam-to-column connections at different positions in the steel frame, were created and analyzed cyclically through the nonlinear finite element program ABAQUS to investigate the spatial coupling effect. The momentrotation relationships and TI index distribution across the width of beam flanges, were discussed in detail to elucidate the mechanical performance interaction between strong-axis and weak-axis connections. Results showed that there is obvious interaction between two beams in strong-axis or weak-axis connections, and the plane exterior connections has better hysteresis performance. While the interaction of strong-axis connection and weak-axis connection slightly affected each other’s hysteresis performance, and thus the coupling effect of spatial connections is not evident.
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