We present Lax pairs and functions called Lax functions corresponding to Calogero- Moser-Sutherland (CMS) systems. We present the Benjamin-Ono (BO) equation and a pole ansatz to the BO equation, constructed from a specific type of Lax function called a special Lax function corresponding to Rational and Trigonometric CMS systems. We present a generalization of the BO equation called the non-chiral Intermediate wave (ncILW) equation and show that a family of solutions to the ncILW equation can be constructed from the special Lax function corresponding to the hyperbolic CMS system. We present the Szegö equation on the circle and the real line. We obtain a family of solutions to the Szegö equation on the real line using a pole ansatz. Using numerical methods, we display solution plots to the BO equation and Szegö equation.

Daily demands for electrical power are met through sub-daily release of turbined water in the form of hydropeaking. Hydropeaking’s changes to stream flow are listed as a threat to biodiversity in river ecosystems as it causes rapid habitat alteration such as increased depth and velocity, affecting the species living downstream. The brown trout and landlocked salmon populations in Gullspång River, Sweden, are threatened and subjects to the hydropeaking regime. This study investigated the effects of hydropeaking in summertime (summer peaks) in Gullspång River on growth and survival of age 0 (fry) and age 1 (parr) brown trout and Atlantic salmon. The study used an individual-based model (inSTREAM 7.2-SD) to predict how different peak scenarios would affect the different species and age groups. A previous study’s parameters and model calibration for the study area were used, and I manipulated the flow time-series to create new flow time-series including three single peaking scenarios on different dates during summer, one multiple summer peak scenario as well as a no-peak (steady flow) scenario. The analysis focused on qualitative patterns in how the populations responded to the various flow scenarios. Age 0 salmon’s growth and survival were negatively affected by all peaking scenarios in comparison to the steady flow scenario, with the combined peaking scenario having the worst effect. Age 0 trout survival was either unaffected by single peaking (Scenario 1 & 2) or negatively affected (Scenario 3) and was also worst affected by the combined peaks compared to steady flow. Age 1 survival of both species was positively affected by the combined peaking but either unaffected (Scenario 1 & 2) or negatively (Scenario 3) affected by single peaks compared to the steady flow scenario. Age 1 growth followed a similar trend with highest growth rate in the combined peaks scenario and the lowest in the steady flow for both species. Results of the study may contribute to river management decisions regarding choice of peaking period depending on management goals regarding target species and life cycle stage. / Dagliga efterfrågan av elektricitet tillgodoses genom daglig korttidsreglering avvattenkraftverk där vatten flödar genom turbinerna. Korttidsreglering är listat somett av de större hoten mot den biologiska mångfalden i floders ekosystem då det ledertill snabba habitatförändringar som ökat djup och flödeshastighet, vilket påverkararterna som lever nedströms. Gullspångsälvens bestånd av öring och lax är hotadeoch utsätts för korttidsreglering som nyttjas i älven. Den här studien undersöktekorttidsregleringens påverkan under sommartid (sommartoppar) i Gullspångsälvenpå tillväxt och överlevnad hos ålder 0 (yngel) och ålder 1 (parr) öring och atlantlax.Studien använde en individbaserad modell (inSTREAM 7.2-SD) för att förutspå hurscenarion med olika toppar påverkar de olika arterna samt åldersgrupperna. Entidigare studies parametrar och kalibrering av modellen för studieområdet användesoch jag ändrade flödestidsserierna för att skapa nya flödestidsserier vilket1inkluderade tre enstaka sommartoppar vid olika datum under sommaren, ettkombinerat sommartoppscenario samt ett scenario utan topp (stadigt flöde).Analysen fokuserade på kvalitativa mönster bland populationernas respons till deolika flödestoppscenarion. 0-laxens tillväxt och överlevnad var negativt påverkad avalla flödestoppscenarion i jämförelse med det stadiga flödesscenariot, där detkombinerade flödesscenariot resulterade i en värsta påverkan. 0-öringens överlevnadvar antingen opåverkad (Scenario 1 & 2) eller negativt påverkad (Scenario 3) avenstaka flödestoppar samt också värst påverkad av det kombinerade flödesscenariot ijämförelse med det stadiga flödet. Överlevnaden hos ålder 1 av båda arter blevpositivt påverkad av det kombinerade flödescenariot men var antingen opåverkad(Scenario 1 & 2) eller negativt påverkad (Scenario 3) av de enstaka flödestopparnajämfört med det stadiga flödet. Tillväxten hos ålder 1 av båda arter följde ett liknandemönster där störst tillväxt uppmättes i det kombinerade scenariot och den lägstatillväxten i det stadiga flödesscenariot. Studiens resultat kan bidra tillförvaltningsbeslut gällande älvar när det kommer till utformningen av flödestoppar,beroende på vilka förvaltningsmål som finns för arter och dess livscykelstadium.

No description available.

No / Owing to unpredictable bed topography conditions in natural shallow flows, various numerical methods have been developed to improve the treatment of source terms in the shallow water equations. The surface gradient method is an attractive approach as it includes a numerically simple approach to model flows over topographically-varied channels. To further improve the performance of this method, this study deals with the numerical improvement of the shallow-flow source terms. The so-called surface gradient upwind method (SGUM) integrates the source term treatment in the inviscid discretization scheme. A finite volume model (FVM) with the monotonic upwind scheme for conservative laws is used. The Harten–Lax–van Leer-contact approximate Riemann solver is used to reconstruct the Riemann problem in the FVM. The proposed method is validated against published analytical, numerical, and experimental data, indicating that the SGUM is robust and treats the source terms in different flow conditions well.

Yes / Based on the common approach, the adaptation length in sediment transport is normally estimated in the temporal independence. However, this approach might not be theoretically justified as the process of reaching of the sediment transport equilibrium stage is affected by the flow conditions in time, especially for those fast sediment moving flows, such as scour-hole developing flow. In this study, the 2D shallow water formulation together with a sediment continuity-concentration (SCC) model were applied to flow with mobile sediment boundary. A time-varying approach was proposed to determine the sediment transport adaptation length to treat the flow sediment erosion-deposition rate. The proposed computational model was based on the Finite Volume (FV) method. The Monotone Upwind Scheme of Conservative Laws (MUSCL)-Hancock scheme was used with the Harten Lax van Leer-contact (HLLC) approximate Riemann solver to discretize the FV model. In the flow applications of this paper, a highly discontinuous dam-break fast sediment transport flow was used to calibrate the proposed time-varying sediment adaptation length model. Then the calibrated model was further applied to two separate experimental sediment transport flow applications documented in literature, i.e. a highly concentrated sediment transport flow in a wide alluvial channel and a sediment aggradation flow. Good agreements with the experimental data were presented by the proposed model simulations. The tests prove that the proposed model, which was calibrated by the discontinuous dam-break bed scouring flow, also performed well to represent the rapid bed change and the steady sediment mobility conditions. / The National Natural Science Foundation of China NSFC (Grant Number 20101311246), Major State Basic Research Development Program (973 program) of China (Grant Number 2013CB036402) and Open Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University of China (Grant Number SKLH-OF-1103).

Dans cette thèse nous étudions la dynamique engendrée par une famille de flots Hamiltoniens. Un tel système dynamique à plusieurs générateurs est aussi appelé ‘polysystème’. Motivés par des questions liées au phénomène de la diffusion d’Arnold, notre objectif est de construire des trajectoires du polysystème qui relient deux régions lointaines de l’espace des phases. La thèse est divisée en trois parties.Dans la première partie, nous considérons le polysystème engendré par les flots discrétisés d’une famille d’Hamiltoniens Tonelli. En utilisant une approche variationnelle issue de la théorie KAM faible, nous donnons des conditions suffisantes pour l’existence des trajectoires souhaitées.Dans la deuxième partie, nous traitons le cas d’un polysystème engendré par un couple de flots Hamiltoniens à temps continu, dont l’étude rentre dans le cadre de la théorie géométrique du contrôle. Dans ce contexte, nous montrons dans certains cas la transitivité d’un polysystème générique, à l’aide du théorème de transversalité de Thom.La dernière partie de la thèse est dédiée à obtenir une nouvelle version du théorème de transversalité de Thom s’exprimant en termes d’ensembles rectifiables de codimension positive. Dans cette partie il n’est pas question de polysystèmes, ni d’Hamiltoniens. Néanmoins, les résultats obtenus ici sont utilisés dans la deuxième partie de la thèse / In this thesis we study the dynamics generated by a family of Hamiltonian flows. Such a dynamical system with several generators is also called ‘polysystem’.Motivated by some questions related to the phenomenon of Arnold diffusion, our aim is to construct trajectories of the polysystem which connect two far-apart regions of the phase space.The thesis is divided into three parts.In the first part, we consider the polysystem generated by the time-onemaps of a family of Tonelli Hamiltonians. By using a variational approach falling within the framework of weak KAM theory, we give sufficient conditions for the existence of the desired trajectories.In the second part, we address the case of a polysystem generated by twocontinuous-time Hamiltonian flows. This problem fits into the framework of geometriccontrol theory. In this context, we show in some cases the transitivity of a generic polysystem, by means of Thom’s transversality theorem.The third and last part of the thesis is devoted to the proof of a newversion of Thom’s transversality theorem, formulated in terms of rectifiable sets of positive codimension. Neither polysystems nor Hamiltonians are explicitly involved in this part. However, the results obtained here are used in the second part of the thesis.

Cette thèse est principalement consacrée à l’étude du comportement en temps long de solutions de certaines équations aux dérivées partielles hamiltoniennes, du type i∂_t u=X_H (u), en particulier l’existence globale, la croissance des normes de Sobolev, la diffusion et l’approximation par la dynamique résonante.Dans ce contexte, nous considérons d’abord une perturbation de l’équation de Szegő cubique par un potentiel linéaire, i∂_t u=∏ |u|² u+α∫ u,α∈R, (α-Szegő) où ∏▒ désigne le projecteur de Szegő sur les fréquences positives. Pour α=0, cette équation est l’équation de Szegő cubique, étudiée récemment par Gérard et Grellier comme modèle mathématique d’équation non linéaire et non dispersive. Pour l’équation (α–Szegő), nous établissons le caractère bien posé et la complète intégrabilité, et étudions la dynamique des valeurs singulières des opérateurs de Hankel associés. En outre, nous montrons les propriétés suivantes pour cette équation, sur une classe de sous–variétés invariantes de dimensions finies arbitrairement grandes : si α<0, toute trajectoire est relativement compacte, et toute norme de Sobolev est bornée le long de cette trajectoire. Siα>0, il existe des trajectoires le long desquelles toutes les normes de Sobolev de régularité plus grande que ½ tendent exponentiellement vers l’infini en temps.Dans une seconde partie, nous étudions un système mixte Schrödinger–ondes sur le cylinder (x,y)∈R×T , i∂_t U+∂_xx U-|D_y |U=|U|² U,(WS)En adaptant une idée de Hani–Pausader–Tzvetkov–Visciglia, nous établissons une théorie du scattering modifiée reliant les petites solutions de cette équation et les petites solutions de l’équation de Szegő cubique. En combinant cette théorie du scattering avec un résultat récent de Gérard–Grellier, nous en déduisons l’existence de solutions globales de (WS) qui sont non bornées dans l’espace L_x² H_y^s (R×T) pour tout s>½ . / The main purpose of this Ph.D. thesis is to study the long time behavior of solutionsto some Hamiltonian PDEs, i∂_t u=X_H (u), including global existence, growth of high Sobolev norms, scattering and long time approximation by resonant dynamics.In this context, at first we consider the Szegő equation on the circle S1 perturbed bya linear potential, i∂_t u=∏ |u|² u+α∫ u,α∈R, (α-Szegő) where ∏ is the projector onto the non-negative frequencies. For α=0, it turns out tobe the cubic Szegő equation, which was recently introduced by Gérard and Grellier as amathematical toy model of a non-linear totally non dispersive equation.We study the global well-posedness, the integrability and the dynamics of the singularvalues of the related Hankel operators of the α –Szegő equation. Moreover, we establishthe following properties for this equation on a class of invariant submanifolds, with anarbitrary large dimension. For α<0, any trajectory is relatively compact, and all theSobolev norms are bounded on it. For α>0, there exist trajectories on which everySobolev norm of regularity s>½ , exponentially tends to infinity in time.Second, we study the wave-guide Schrödinger equation posed on the spatial domain(x,y)∈R×T ，i∂_t U+∂_xx U-|D_y |U=|U|² U,(WS)Adapting an idea by Hani–Pausader–Tzvetkov–Visciglia, we establish a modified scattering theory between small solutions to this equation and small solutions to the cubic Szegő equation. Combining this scattering theory with a recent result by Gérard–Grellier, we infer existence of global solutions to (WS) which are unbounded in the space L_x^2 H_y^s (R×T) for every s>½ .

Les systèmes dynamiques qui évoluent sur un grand intervalle de temps (dynamique moléculaire, prédiction astronomique, turbulence...) occupent une place importante dans le domaine de la science de l'ingénieur. Leur résolution numérique constitue, jusqu'à l'heure actuelle, un défi. En effet, la simulation de la solution nécessite un solveur non seulement rapide mais aussi qui respecte les propriétés physiques du problème, pour garantir la stabilité. Dans cette thèse, on se propose d'étudier, vis-à-vis de cette problématique, un schéma d'intégration temporelle basée sur la décomposition de la solution en série temporelle, suivie de la technique de resommation de Borel des séries divergentes. On analyse alors la rapidité du schéma sur des problèmes modèles. Ensuite, on montre sa capacité à préserver la structure des équations (symplecticité, iso-spectralité, conservation de l'énergie...) à un ordre arbitrairement élevé. Par la suite, on applique le schéma à la résolution d'équations aux dérivées partielles issues de la mécanique, dont les équations de la chaleur, de Burgers et de Navier-Stokes bidimensionnelles. Pour cela, on associe le schéma à une méthode de discrétisation par éléments finis en espace. Enfin, dans le but de rendre l'algorithme plus robuste, on s'intéresse à la représentation de la somme de Borel par une série de factorielle généralisée. / Dynamical systems which evolve in a large time interval (molecular dynamic, astronomical prediction, turbulence…) take an important place in engineering science. Their numerical resolution has so far constituted a challenge. Indeed, the simulation of the solution requires a solver which is not only fast but also respects the physical properties of the problem, to ensure the stability. In this thesis, we propose to study, regarding this issue, a time integration scheme based on the decomposition of the solution into time series, followed by Borel's resummation technique of divergent series. We analyse the speed of scheme on model problems. Next, we show its capability to preserve the structure of the equation (symplecticity, iso-spectrality, conservation of energy…) up to an arbitrary high order. Thereafter, we use the scheme to resolve partial differential equations coming from mechanics, including the two-dimensional heat equation, Burger’s equation and the Navier-Stokes equation. To this aim, we choose a finite element method for space discretisation. Finally, and in order to make the algorithm more robust, we are interested in the representation of the Borel sum by a generalized factorials series.

Ma thèse vise en premier ressort à étudier toutes les questions juridiques concernant la ‘question arménienne’.D’abord, le sujet de l’existence des éléments du crime de génocide en 1915 au niveau du droit international conventionnel a été notre première question à étudier. Ensuite, il était indispensable d’étudier la nature du crime commis envers les Arméniens ottomans en 1915.En plus, est-ce que l’Etat Turc actuel peut-il être responsable d’un crime commis par l’Empire ottoman, selon le principe de la succession d’Etats en droit international, surtout que l’Etat Turc n’était créé qu’en 1923 ? Et en cas de l’existence de cette responsabilité, est-ce que l’Arménie a droit à l’action en responsabilité, surtout qu’au moment de la perpétration du crime, il n’y avait pas un Etat Arménien ? Les victimes étaient des ressortissants de l’Empire ottoman mais d’origine arménienne. Donc il faudra étudier la qualité de l’Arménie pour agir en justice, par des moyens judiciaires ou extrajudiciaires, vis-à-vis surtout du principe de la non-rétroactivité des traités, surtout que dans notre cas, le crime a été perpétré en 1915, alors que la Convention sur le génocide n’a été promulguée qu’en 1948.En fait, notre thèse vise en dernier ressort à rapprocher les deux pays et mettre fin réellement au conflit entre eux, à percevoir ce qui les rassemblent et non ce qui les divisent, et trouver une solution équitable et objective pour les deux pays afin de contribuer à mettre fin à leur litige historique, et cela à travers une étude réaliste, impartiale et basée sur la logique et la nature des choses et des circonstances du fait existantes. / The main purpose of my thesis is to study all the legal issues concerning the 'Armenian question'.First, the existence of the elements of the crime of genocide in 1915 at the conventional international law, made our first question to consider. Then, it was necessary to study the nature of the crime committed against the Ottoman Armenians in 1915.In addition, can Turkey be responsible for a crime committed by the Ottoman Empire, according to the principle of succession of States in international law, especially that the Turkish state was created in 1923?And in case of such responsibility, has Armenia the right to maintain a lawsuit against Turkey, especially at the time of the crime, there was no Armenian state?The victims were citizens of the Ottoman Empire but of Armenian descent.Also, the quality of Armenia to take legal action, by judicial or extrajudicial processes, must be studied, regarding especially to the principle of non-retroactivity of treaties, especially that in our case, the crime was committed in 1915, while the Genocide Convention was enacted in 1948.In fact, our thesis aims ultimately to bring the two countries closer and actually try to help reach the end of the conflict between them, perceive what gather them and not what divides them, and find a fair and objective solution for both countries, in order to help put an end to their historic dispute, and that through a realistic and impartial study, based on logic and the nature of things and the circumstances of the existing.

The global mean temperature is predicted to increase by up to 5 °C during this century. For fish, being ectotherms, temperature is one of the most important environmental factors, influencing them in a number of different ways, including effects on physiological traits, timing of life history events and behavior. Atlantic salmon has been shown to grow faster after being incubated at warmer temperatures. One possible explanation for this could be that the increased incubation temperature causes decreased metabolic rates. The aim of this project was to examine whether this is true. Atlantic salmon eggs were incubated in three different temperature regimes: natural temperature conditions, heated water and a mixed temperature treatment, where eggs were incubated in increased temperature until the beginning of January and after that subjected to natural temperature conditions. Ventilation rate, a proxy for metabolism, was measured for fish from each treatment group, as well as fish length and weight. The results revealed significantly lower ventilation rates of the fish from the heated temperature treatment, but not of the fish from the mixed temperature treatment. This suggests that an increased incubation temperature causes lowered rates of metabolism in Atlantic salmon, and that the change occurs later than early January. Because of differences in size and life stage between fish from the different groups however, the results are uncertain and call for further investigations. A lowered metabolic rate will affect the fish’s behavior. A further development might therefore be to study fish survival in the wild in relation to a fish’s metabolic rate. / Jordens medeltemperatur beräknas öka med upp till 5 °C det här århundradet. För fiskar, som är ektotermer, är temperatur en av de viktigaste abiotiska faktorerna och påverkar dem på en mängd olika sätt, bland annat genom förändring av fysiologiska attribut, tidpunkter för steg i livscykeln och beteende. Lax har visats växa snabbare efter att ha blivit inkuberade i varmare vattentemperatur. En möjlig förklaring till det kan vara att en förhöjd inkuberingstemperatur orsakar en lägre metabolism. Det här projektet syftade till att undersöka om så är fallet. Ägg från lax inkuberades i tre olika temperaturförhållanden: naturliga temperaturförhållanden, förhöjd temperatur och en blandad temperaturbehandling, där ägg inkuberades i förhöjd temperatur till början av januari, varefter de utsattes för naturliga temperaturförhållanden. Gälslagsfrekvens, som fungerar som en indikator för metabolism, mättes på fisk från varje behandlingsgrupp, samt fiskarnas längd och vikt. Resultaten visade signifikant lägre gälslagsfrekvenser hos fiskarna från behandlingen med förhöjd temperatur, men inte hos fiskarna från behandlingen med blandad temperatur. Detta indikerar att en förhöjd inkuberingstemperatur orsakar en lägre metabolism hos lax, och att förändringen sker senare än tidiga januari. På grund av skillnader i storlek och livsstadier hos fiskarna från de olika grupperna är resultaten dock osäkra, vilket gör att ytterligare studier behövs. En lägre ämnesomsättning påverkar fiskars beteende. En uppföljning kan därför vara att studera fiskars överlevnad i det vilda i relation till deras metabolism.