This paper studies the relationship between the degree of compactness of the pile structure foundation and how it will tilt under different wave condition. In the lab experiment setup, we use a periodic force generated by a magnetic coil to simulate the wave force impending on a scaled down model pile. With this setup, forces with different periods and magnitudes are used to find out the critical wave condition under which the pile will tilt, and it relationship with the results, engineering aspect of setting up a pile structure in the sea will have a better reference in the design stage.

La première partie de cette thèse concerne l'étude du problème de Cauchy pour l'équation de KdV quasi-linéaire.On établit un théorème d'existence locale obtenu grâce à des propriétés structurelles et des techniques de jauge qui permettent de compenser les pertes de dérivées apparentes dans les estimations a priori.Dans la seconde partie, les propriétés de stabilité orbitale co-périodique et modulationnelle sont explorées numériquement en exploitant des critères algébriques tous établis à partir d'une même intégrale d'action et de ses dérivées secondes. Notre méthode utilise des quadratures numériques suivies de différences finies afin de calculer la matrice hessienne de l'intégrale d'action. Le comportement asymptotique de cette matrice nous pousse à prêter beaucoup d'attention à l'étude des ondes de grande période ou de faible amplitude. Les résultats numériquesprésentés fournissent de nombreuses informations en lien avec des questions ouvertes.On effectue également des simulations directes sur le système d' ÉDP original pour étudier à la fois le comportement des ondes périodiques sous différents types de perturbations, et les solutions de problèmes de Cauchy avec donnée initiale discontinue. Pour ces derniers, on s'attend à observer des chocs dispersifs, dont la compréhension est basée sur le problème de Gurevich-Pitaevskii, où les équations modulées à la Whitham sont utilisées pour approcher la zone oscillante des chocs. On compare des simulations directes aux solutions idéales du problème de Gurevich-Pitaevskii, en commençant par la célèbre équation de KdV / The first part of this manuscript presents a well-posedness result for a quasilinear version of the KdV equation.The proof takes advantage of structural properties and gauge techniques to deal with apparent loss of derivativesin a priori estimates.In the second part, we investigate the modulational and orbital coperiodic stability of periodic waves by computingalgebraic criteria involving the same abbreviated action integral and its second order derivatives. Our methoduses numerical integrations followed by finite differences to compute the Hessian matrix of the action integral.We pay attention to the asymptotic behavior of this matrix in the large period and small amplitude limits. Thenumerical results about stability give some new insight on several analytical open questions.Finally, direct numerical computations are done on the original system of PDEs to study the behavior of periodictraveling waves under various kinds of perturbations and the solutions of Cauchy problem with discontinuousinitial data. For the latter, we expect dispersive shock waves to arise. The building block for understandingdispersive shocks is known as the Gurevich-Pitaevskii problem, in which modulated equations 'a la Whitham'are used as an approximate model for the oscillatory zone. We compare direct numerical simulations to idealizedsolutions of Gurevich-Pitaevskii problems, starting with the famous KdV equation

In this dissertation, we study integrodifference equations in patchy landscapes. Specifically, we provide a framework for linking individual dispersal behavior with population-level dynamics in patchy landscapes by integrating recent advances in modeling dispersal into an integrodifference equation. First, we formulate a random-walk model in a patchy landscape with patch-dependent diffusion, settling, and mortality rates. We incorporate mechanisms for individual behavior at an interface which, in general, results in the probability-density function of the random walker being discontinuous at an interface. We show that the dispersal kernel can be characterized as the Green's function of a second-order differential operator and illustrate the kind of (discontinuous) dispersal kernels that arise from our approach. We examine the dependence of obtained kernels on model parameters. Secondly, we analyze integrodifference equations in patchy landscapes equipped with discontinuous kernels. We obtain explicit formulae for the critical-domain-size problem, as well as, explicit formulae for the analogous critical size of good patches on an infinite, periodic, patchy landscape. We examine the dependence of obtained formulae on individual behavior at an interface. Through numerical simulations, we observe that, if the population can persist on an infinite, periodic, patchy landscape, its spatial profile can evolve into a discontinuous traveling periodic wave. We derive a dispersion relation for the speed of the wave and illustrate how interface behavior affects invasion speeds. Lastly, we develop a strategic model for the spread of the emerald ash borer and its interaction with host trees. A thorough literature search provides point estimates and interval ranges for model parameters. Numerical simulations show that the spatial profile of an emerald ash borer invasion evolves into a pulse-like solution that moves with constant speed. We employ Latin hypercube sampling to obtain a plausible collection of parameter values and use a sensitivity analysis technique, partial rank correlation coefficients, to identify model parameters that have the greatest influence on obtained speeds. We illustrate the applicability of our framework by exploring the effectiveness of barrier zones on slowing the spread of the emerald ash borer invasion.

In this dissertation, we study integrodifference equations in patchy landscapes. Specifically, we provide a framework for linking individual dispersal behavior with population-level dynamics in patchy landscapes by integrating recent advances in modeling dispersal into an integrodifference equation. First, we formulate a random-walk model in a patchy landscape with patch-dependent diffusion, settling, and mortality rates. We incorporate mechanisms for individual behavior at an interface which, in general, results in the probability-density function of the random walker being discontinuous at an interface. We show that the dispersal kernel can be characterized as the Green's function of a second-order differential operator and illustrate the kind of (discontinuous) dispersal kernels that arise from our approach. We examine the dependence of obtained kernels on model parameters. Secondly, we analyze integrodifference equations in patchy landscapes equipped with discontinuous kernels. We obtain explicit formulae for the critical-domain-size problem, as well as, explicit formulae for the analogous critical size of good patches on an infinite, periodic, patchy landscape. We examine the dependence of obtained formulae on individual behavior at an interface. Through numerical simulations, we observe that, if the population can persist on an infinite, periodic, patchy landscape, its spatial profile can evolve into a discontinuous traveling periodic wave. We derive a dispersion relation for the speed of the wave and illustrate how interface behavior affects invasion speeds. Lastly, we develop a strategic model for the spread of the emerald ash borer and its interaction with host trees. A thorough literature search provides point estimates and interval ranges for model parameters. Numerical simulations show that the spatial profile of an emerald ash borer invasion evolves into a pulse-like solution that moves with constant speed. We employ Latin hypercube sampling to obtain a plausible collection of parameter values and use a sensitivity analysis technique, partial rank correlation coefficients, to identify model parameters that have the greatest influence on obtained speeds. We illustrate the applicability of our framework by exploring the effectiveness of barrier zones on slowing the spread of the emerald ash borer invasion.