Teses / dissertações sobre o tema "Stationary and stable solution"

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Universidade Federal de Sao Carlos
We address the question of existence of stationary stable solutions to a class of reaction-diffusion equations with spatial dependence in 2 and 3-dimensional bounded domains. The approach consists of proving the existence of local minimizer of the corres-ponding energy functional. For existence, it was enough to give sufficient conditions on the diffusion coefficient and on the reaction term to ensure the existence of isolated mi¬nima of the Γlimit functional of the energy functional family. In the second part we take the techniques developed in the first part to minimize functional in 2 and 3-dimensional rectangles, with and without constraint, solving in a more general form this problem, which was originaly proposed in 1989 by Robert Kohn and Peter Sternberg.
Na primeira parte deste trabalho, abordamos a existência de soluções estacioná-rias estáveis para uma classe de equações de reação-difusão com dependência espacial em domínios limitados 2 e 3-dimensionais. Esta abordagem foi feita via existência de míni¬mos locais dos funcionais de energia correspondentes. Para tal, foi suficiente encontrar condições no coeficiente de difusão e no termo de reação que garantam existência de míni¬mos isolados do funcional Γlimite da família de funcionais de energia. Na segunda parte, aproveitamos as técnicas desenvolvidas na primeira parte para minimizar funcionais em retângulos e paralelepípedos, com e sem vínculo, resolvendo de forma bem mais geral este problema, originalmente proposto em 1989 por Robert Kohn e Peter Sternberg.

The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift.

This work utilises the interactions between lanthanide complexes and anions in solution to explore the nature of coordination chemistry in the f-elements, and to define fundamental behaviour in paramagnetic complexes, as well as investigating the factors responsible for ensuring high lanthanide luminescence quantum yields. Chapter one describes characteristic lanthanide properties with a focus on luminescence and the current understanding of lanthanide complexes. Illustrating the response of luminescent lanthanide complexes to a range of analytes in aqueous solution. Chapter two explores the factors affecting luminescence quantum yield in arylacylDO3A complexes as well studying the pH behaviour of these species, showing that the whole energy transfer cascade involved in sensitisation of lanthanide luminescence must be considered when optimising the properties of lanthanide complexes. Chapter three describes the effect of fluoride binding in lanthanide tetra-amide complexes appended with fluorinated benzyl groups on the lanthanide crystal field, demonstrating that the effect of a strong axial donor on the overall ligand field can determine the nature of the magnetic anisotropy at the lanthanide centre. This in turn determines both the optical spectra and the NMR spectra of the complexes. The results obtained illustrate that the whole structure of the complex (and not just the donor set) need to be considered when defining the behaviour of the lanthanide complex. Chapter four investigates the interaction between fluoride and lanthanide complexes of the Lehn cryptand. In this case, the relatively symmetric donor set associated with the cryptand, combined with exchange between isomers, gives rise to small observed anisotropies in the absence of fluoride that are dramatically enhanced by fluoride binding. A range of fluoride responsive behaviour has been identified. Chapter five describes the synthesis and study of a group of halogenated phenacylDO3A lanthanide complexes. It is shown how such complexes respond to changes in cyanide concentration but are essentially inert towards fluoride as a consequence of the reduced residual charge on the lanthanide centre. The interaction with cyanide is assigned to the formation of a cyanohydrin which is assisted by the proximate lanthanide ion, which acts as a Lewis acid. Chapter six draws together the work described in earlier chapters. Chapter seven provides experimental procedures along with characterisation data for the compounds studied.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.
Includes bibliographical references (p. [149]-151).
by Kathryn A. Millis.
Ph.D.

This thesis investigates the possibility of approximating stationary solutions of stochastic differential equations using numerical methods. We consider a particular class of stochastic differential equations, which are known to generate random dynamical systems. The existence of stochastic stationary solution is proved using global attractor approach. Euler's numerical method, applied to the stochastic differential equation, is proved to generate a discrete random dynamical system. The existence of stationary solution is proved again using global attractor approach. At last we prove that the approximate stationary point converges in mean-square sense to the exact one as the time step of the numerical scheme diminishes.

The present thesis is devoted to the investigation of certain aspects of the large time behavior of the solutions of two nonlinear Schrödinger equations in dimension three in some suitable perturbative regimes. The first model consist in a Schrödinger equation with a concentrated nonlinearity obtained considering a {point} (or contact) interaction with strength $alpha$, which consists of a singular perturbation of the Laplacian described by a self adjoint operator $H_{alpha}$, and letting the strength $alpha$ depend on the wave function: $ifrac{du}{dt}= H_alpha u$, $alpha=alpha(u)$.It is well-known that the elements of the domain of a point interaction in three dimensions can be written as the sum of a regular function and a function that exhibits a singularity proportional to $|x - x_0|^{-1}$, where $x_0$is the location of the point interaction. If $q$ is the so-called charge of the domain element $u$, i.e. the coefficient of itssingular part, then, in order to introduce a nonlinearity, we let the strength $alpha$ depend on $u$ according to the law $alpha=-nu|q|^sigma$, with $nu > 0$. This characterizes the model as a focusing NLS with concentrated nonlinearity of power type. In particular, we study orbital and asymptotic stability of standing waves for such a model. We prove the existence of standing waves of the form $u (t)=e^{iomega t}Phi_{omega}$, which are orbitally stable in the range $sigma in (0,1)$, and orbitally unstable for $sigma geq 1.$ Moreover, we show that for $sigma in(0,frac{1}{sqrt 2}) cup left(frac{1}{sqrt{2}}, frac{sqrt{3} +1}{2sqrt{2}} right)$ every standing wave is asymptotically stable, in the following sense. Choosing an initial data close to the stationary state in the energy norm, and belonging to a natural weighted $L^p$ space which allows dispersive stimates, the following resolution holds: $u(t) =e^{iomega_{infty} t +il(t)} Phi_{omega_{infty}}+U_t*psi_{infty} +r_{infty}$, where $U_t$ is the free Schrödinger propagator,$omega_{infty} > 0$ and $psi_{infty}$, $r_{infty} inL^2(R^3)$ with $| r_{infty} |_{L^2} = O(t^{-p}) quadtextrm{as} ;; t right arrow +infty$, $p = frac{5}{4}$,$frac{1}{4}$ depending on $sigma in (0, 1/sqrt{2})$, $sigma in (1/sqrt{2}, 1)$, respectively, and finally $l(t)$ is a logarithmic increasing function that appears when $sigma in (frac{1}{sqrt{2}},sigma^*)$, for a certain $sigma^* in left(frac{1}{sqrt{2}}, frac{sqrt{3} +1}{2sqrt{2}} right]$. Notice that in the present model the admitted nonlinearities for which asymptotic stability of solitons is proved, are subcritical in the sense that it does not give rise to blow up, regardless of the chosen initial data. The second model is the energy critical focusing nonlinear Schrödinger equation $i frac{du}{dt}=-Delta u-|u|^4 u$. In this case we prove, for any $nu$ and $alpha_0$ sufficiently small, the existence of radial finite energy solutions of the form$u(t,x)=e^{ialpha(t)}lambda^{1/2}(t)W(lambda(t)x)+e^{iDeltat}zeta^*+o_{dot H^1} (1)$ as $tright arrow +infty$, where$alpha(t)=alpha_0ln t$, $lambda(t)=t^{nu}$,$W(x)=(1+frac13|x|^2)^{-1/2}$ is the ground state and $zeta^*$is arbitrarily small in $dot H^1$

A class of Petrov-Galerkin finite element methods is proposed for the numerical solution of the n dimensional stationary convection-diffusion equation. After an initial review of the literature we describe this class of methods and present both asymptotic and nonasymptotic error analyses. Links are made with the classical Galerkin finite element method and the cell vertex finite volume method. We then present numerical results obtained for a selection of these methods applied to some standard test problems. We also describe extensions of these methods which enable us to solve accurately for derivative values of the solution.

The paper considers systems of linear first-order ODEs with a randomly perturbed system matrix and stationary additive noise. For the description of the long-term behavior of such systems it is necessary to study their stationary solutions. We deal with conditions for the existence of stationary solutions as well as with their representations and the computation of their moment functions. Assuming small perturbations of the system matrix we apply perturbation techniques to find series representations of the stationary solutions and give asymptotic expansions for their first- and second-order moment functions. We illustrate the findings with a numerical example of a scalar ODE, for which the moment functions of the stationary solution still can be computed explicitly. This allows the assessment of the goodness of the approximations found from the derived asymptotic expansions.

In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions.

In this thesis, we study the existence of stationary solutions for two cases. One is for random difference equations. For this, we prove the existence and uniqueness of the stationary solutions in a finite-dimensional Euclidean space Rd by applying the coupling method. The other one is for semi linear stochastic evolution equations. For this case, we follows Mohammed, Zhang and Zhao [25]'s work. In an infinite-dimensional Hilbert space H, we release the Lipschitz constant restriction by using Arzela-Ascoli compactness argument. And we also weaken the globally bounded condition for F by applying forward and backward Gronwall inequality and coupling method.

A ideia de transferência de spin, como forma de controle da magnetização, foi introduzida independentemente por Slonczewski e por Berger em 1996. Desde então, esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memorias magnéticas não voláteis e em osciladores de alta frequência. Devido _a complexidade do problema, a grande maioria das pesquisas teóricas sobre o assunto _e baseada em resultados numéricos. Porém, esses métodos podem dificultar a visualização das influências individuais dos diferentes termos envolvidos. Para isso, seria melhor a utilização de métodos analíticos, o que nos motiva a buscar por esses resultados. Nesse trabalho, apresentamos uma revisão sobre a teoria básica do efeito de transferência de spin e da dinâmica da magnetização. São revistas as principais equações que descrevem o comportamento da magnetização, as equações de Landau-Lifshitz e de Landau-Lifshitz-Gilbert, e comparadas suas componentes quando da inclusão do termo de transferência, analisando a melhor forma de incluir esse termo. É destacada a contribuição dada pelo termo de transferência na frequência de precessão da magnetização, que aparece ao se utilizar a equação de Landau-Lifshitz-Gilbert. Após essa revisão dos conceitos base, são buscadas soluções analíticas para a dinâmica da magnetização da camada livre de um sistema nanopilar em tricamada. Quatro casos são analisados: primeiro um sistema sem anisotropias e sem a inclusão do campo de Oersted, no segundo caso é incluído um termo de anisotropia e no terceiro novamente um sistema sem anisotropias, mas com a inclusão do campo de Oersted. Todas essas análises são feitas em uma aproximação de macrospin. Por último, uma aproximação de microspin com campo de Oersted. Nos três primeiros casos, é possível obter resultados analíticos e simular os resultados. São estimados o tempo de reversão e a frequência de precessão estável.
The idea of spin transfer as a way to control magnetization was introduced independently by Slonczewski and Berger in 1996. Since then, this e ect has been the subject of numerous studies, especially for potential applications in nonvolatile magnetic memories and high-frequency oscillators. Due to the complexity of the problem, the vast majority of theoretical research on this subject is based on numerical results. However, these methods might not display the in uences of individual terms involved. For this, it would be better to use analytical methods, which motivates us to search for these results. In this paper, we review the basic theory of spin transfer e ect and of magnetization dynamics. We review the main equations that describe the behavior of magnetization, the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations, and compare its components when inserting the spin torque term, analyzing the best way to include this term. The contribution of spin transfer on magnetization precession frequency, which appears when using the Landau-Lifshitz- Gilbert equation, is emphasized. After this review of basic concepts, analytical solutions for magnetization dynamics of the free layer in a tri-layer nanopillar are searched. Four cases are analyzed: rst a system without anisotropy and without the inclusion of the Oersted eld, in the second case an anisotropy term is considered and in the third case, again a system without anisotropy, but with the inclusion of Oersted eld. All these analisys are done in a macrospin approximation. Finally, a microspin approach including Oersted eld. In the rst three cases, it is possible to obtain analytical results and simulate these results. Reversal time and stable precession frequency values are estimated.

La composition isotopique (¹³C/¹²C) du CO₂ respiré par les feuilles et les racines dans l'obscurité et celle des substrats respiratoires putatifs, y compris les sucres solubles et les acides organiques (malate et citrate), l'activité de la PEPc ainsi que les échanges gazeux des feuilles ont été déterminés sur le haricot (Phaseolus vulgaris L.) et l’épinards (Spinacia oleracea L.) cultivés dans du sable avec différents rapports NH₄⁺: NO₃⁻ dans N fourni. Le CO₂ respiré par les feuilles était enrichi en ¹³C sous NO₃⁻ s’appauvrissant progressivement avec l’augmentation de la fraction de NH₄⁺ dans le N fourni, tandis que la composition isotopique du CO₂ issu de la respiration des racines restait inchangée quel que soit le rapport NH₄⁺: NO₃⁻. Nous avons suggéré qu'une plus grande quantité de pools enrichis en ¹³C fixés par la PEPc via la voie anaplérotique contribuait à la respiration foliaire sous NO₃⁻. Cependant, un effet similaire dans les racines attendu sous NH₄⁺ a été masqué en raison d'une refixation (par la PEPc) du CO₂ respiré (appauvrie en ¹³C). De manière inattendue, les modifications de la composition isotopique du C des métabolites individuels, leurs quantités, ainsi que l'activité de l’enzyme PEPc, présentaient des profils différents entre les deux espèces étudiées. Des expériences de double marquage (¹³C et ¹⁵N) sont nécessaires pour mieux comprendre l’impact de la plasticité métabolique du TCA sur l’écart isotopique entre le malate et le citrate et sur la composition isotopique du CO₂ respiré chez différentes espèces sous différentes formes d’azote
C-isotope composition of leaf- and root-respired CO₂ in the dark and that of putative respiratory substrates including soluble sugars and organic acids (malate and citrate), PEPc activity, as well as leaf gas exchanges were determined on bean (Phaseolus vulgaris L.) and spinach (Spinacia oleracea L.) plants grown in sand with varying ratios of NH₄⁺: NO₃⁻ in supplied N. Leaf-respired CO₂ was ¹³C enriched under NO₃⁻ nutrition and became progressively ¹³C depleted with increasing amount of NH₄⁺ in supplied N, while C-isotope composition of root-respired CO₂ remained unchanged across N-type gradient. We suggested that a higher amount of ¹³C enriched C-pools fixed by PEPc through anaplerotic pathway contributed to respired CO₂ in leaves under NO₃⁻ nutrition. However, a similar effect in roots expected under NH4+ nutrition was masked because of a rather ¹³C depleted C source (respired CO₂) refixation by PEPc. Unexpectedly, the changes in C-isotope composition of individual metabolites and their amounts as well as PEPc activity exhibited different patterns between the two species. Double labelling experiments (¹³C and ¹⁵N) are needed for better understanding the impact of metabolic plasticity of TCA on isotopic gap between malate and citrate and on C-isotope composition of respired CO₂ in different species under varying N-type nutrition

Dans ce travail de thèse, la synthèse de nanoparticules d'argent (Ag) est réalisée par une méthode simple, efficace et rapide basée sur la réduction du nitrate d'argent (AgNO3) dans un milieu organique (éthanol) sous chauffage par irradiation micro-ondes (MW) pendant quelques secondes en présence d'une émulsion aqueuse de copolymère latex. Les expériences ont été effectuées soit de manière séquentielle en faisant varier les paramètres expérimentaux les uns après les autres (approche classique) ou bien en moyennant la méthodologie des plans d'expérience qui sert à varier simultanément ces conditions expérimentales dans le but à la fois d'optimiser et d'évaluer l'impact de ces facteurs sur les propriétés physico-chimiques des particules produites. L'objectif est d'arriver à préparer un maximum de concentration en nanoparticules d'argent avec un minimum de concentration en copolymère latex et en AgNO3. Les nanoparticules préparées sont trouvées extrêmement stables en solution colloïdale avec des distributions de taille très étroites, ce qui confirme la qualité élevée et le diamètre uniforme des nanoparticules obtenues par l'approche de synthèse micro-ondes. Ceci pourrait être probablement dû à l'effet de stabilisation produit par les molécules du latex, qui est un bon environnement pour contrôler efficacement la croissance de nanoparticules métalliques d'argent. En tant que principal objectif d'une telle réalisation de la synthèse de nanoparticules d'argent par la méthode MW ouvre la voie à l'exploitation d'effets plasmoniques de surface dans des réactions photocatalytiques en utilisant des structures semi-conductrices bien définies (Bi2O3, In2O3, TiO2...)
In this thesis work, the synthesis of silver nanoparticles (Ag) is carried out by a simple, efficient and fast method based on the reduction of silver nitrate (AgNO3) in an organic medium (ethanol) under heating by micro irradiation (MW) for a few seconds in the presence of an aqueous emulsion of latex copolymer. The experiments were performed either by varying the experimental parameters one after the other (classical approach) or by means of the experimental design methodology which serves to vary simultaneously these experimental conditions in order to both optimize and evaluate the impact of these factors on the physicochemical properties of the nanoparticles. The main goal is to prepare a maximum concentration of silver nanoparticles with a minimum concentration of latex copolymer and AgNO3. The prepared nanoparticles were found to be extremely stable in colloidal solution with very narrow size distributions, which confirms the high quality and the uniform diameter of the nanoparticles obtained by the microwave synthesis approach. This could possibly be due to the stabilizing effect produced by the latex molecules, which is a good environment for effectively controlling the growth of metallic silver nanoparticles. As the main objective of such realization of the silver nanoparticle synthesis by the MW method opens the way to the exploration of surface plasmonic effects in photocatalytic reactions using well-defined semiconducting structures (Bi2O3 , In2O3, TiO2 ...)

Cette thèse est centrée autour de l'étude théorique et de l'analyse numérique des équations paraboliques non linéaires avec divers conditions aux limites. La première partie est consacrée aux équations paraboliques dégénérées mêlant des phénomènes non-linéaires de diffusion et de transport. Nous définissons des notions de solutions entropiques adaptées pour chacune des conditions aux limites (flux nul, Robin, Dirichlet). La difficulté principale dans l'étude de ces problèmes est due au manque de régularité du flux pariétal pour traiter les termes de bords. Ceci pose un problème pour la preuve d'unicité. Pour y remédier, nous tirons profit du fait que ces résultats de régularités sur le bord sont plus faciles à obtenir pour le problème stationnaire et particulièrement en dimension un d'espace. Ainsi par la méthode de comparaison "fort-faible" nous arrivons à déduire l'unicité avec le choix d'une fonction test non symétrique et en utilisant la théorie des semi-groupes non linéaires. L'existence de solution se démontre en deux étapes, combinant la méthode de régularisation parabolique et les approximations de Galerkin. Nous développons ensuite une approche directe en construisant des solutions approchées par un schéma de volumes finis implicite en temps. Dans les deux cas, on combine les estimations dans les espaces fonctionnels bien choisis avec des arguments de compacité faible ou forte et diverses astuces permettant de passer à la limite dans des termes non linéaires. Notamment, nous introduisons une nouvelle notion de solution appelée solution processus intégrale dont l'objectif, dans le cadre de notre étude, est de pallier à la difficulté de prouver la convergence vers une solution entropique d'un schéma volumes finis pour le problème de flux nul au bord. La deuxième partie de cette thèse traite d'un problème à frontière libre décrivant la propagation d'un front de combustion et l'évolution de la température dans un milieu hétérogène. Il s'agit d'un système d'équations couplées constitué de l'équation de la chaleur bidimensionnelle et d'une équation de type Hamilton-Jacobi. L'objectif de cette partie est de construire un schéma numérique pour ce problème en combinant des discrétisations du type éléments finis avec les différences finies. Ceci nous permet notamment de vérifier la convergence de la solution numérique vers une solution onde pour un temps long. Dans un premier temps, nous nous intéressons à l'étude d'un problème unidimensionnel. Très vite, nous nous heurtons à un problème de stabilité du schéma. Cela est dû au problème de prise en compte de la condition de Neumann au bord. Par une technique de changement d'inconnue et d'approximation nous remédions à ce problème. Ensuite, nous adaptons cette technique pour la résolution du problème bidimensionnel. A l'aide d'un changement de variables, nous obtenons un domaine fixe facile pour la discrétisation. La monotonie du schéma obtenu est prouvée sous une hypothèse supplémentaire de propagation monotone qui exige que la frontière libre se déplace dans les directions d'un cône prescrit à l'avance.

This thesis is concerned with nonlinear analyses of BWR stability behaviour, contributing to a deeper understanding in this field. Despite negative feedback-coefficients of a BWR, there are operational points (OP) at which oscillatory instabilities occur. So far, a comprehensive and an in-depth understanding of the nonlinear BWR stability behaviour are missing, even though the impact of the significant physical parameters is well known. In particular, this concerns parameter regions in which linear stability indicators, like the asymptotic decay ratio, lose their meaning. Nonlinear stability analyses are usually carried out using integral (system) codes, describing the dynamical system by a system of nonlinear partial differential equations (PDE). One aspect of nonlinear BWR stability analyses is to get an overview about different types of nonlinear stability behaviour and to examine the conditions of their occurrence. For these studies the application of system codes alone is inappropriate. Hence, in the context of this thesis, a novel approach to nonlinear BWR stability analyses, called RAM-ROM method, is developed. In the framework of this approach, system codes and reduced order models (ROM) are used as complementary tools to examine the stability characteristics of fixed points and periodic solutions of the system of nonlinear differential equations, describing the stability behaviour of a BWR loop. The main advantage of a ROM, which is a system of ordinary differential equations (ODE), is the possible coupling with specific methods of the nonlinear dynamics. This method reveals nonlinear phenomena in certain regions of system parameters without the need for solving the system of ROM equations. The stability properties of limit cycles generated in Hopf bifurcation points and the conditions of their occurrence are of particular interest. Finally, the nonlinear phenomena predicted by the ROM will be analysed in more details by the system code. Hence, the thesis is not focused on rendering more precisely linear stability indicators like DR. The objective of the ROM development is to develop a model as simple as possible from the mathematical and numerical point of view, while preserving the physics of the BWR stability behaviour. The ODEs of the ROM are deduced from the PDEs describing the dynamics of a BWR. The system of ODEs includes all spatial effects in an approximated (spatial averaged) manner, e.g. the space-time dependent neutron flux is expanded in terms of a complete set of orthogonal spatial neutron flux modes. In order to simulate the stability characteristics of the in-phase and out-of-phase oscillation mode, it is only necessary to take into account the fundamental mode and the first azimuthal mode. The ROM, originally developed at PSI in collaboration with the University of Illinois (PSI-Illinois-ROM), was upgraded in significant points: • Development and implementation of a new calculation methodology for the mode feedback reactivity coefficients (void and fuel temperature reactivity) • Development and implementation of a recirculation loop model; analysis and discussion of its impact on the in-phase and out-of-phase oscillation mode • Development of a novel physically justified approach for the calculation of the ROM input data • Discussion of the necessity of consideration of the effect of subcooled boiling in an approximate manner With the upgraded ROM, nonlinear BWR stability analyses are performed for three OPs (one for NPP Leibstadt (cycle7), one for NPP Ringhals (cycle14) and one for NPP Brunsbüttel (cycle16) for which measuring data of stability tests are available. In this thesis, the novel approach to nonlinear BWR stability analyses is extensively presented for NPP Leibstadt. In particular, the nonlinear analysis is carried out for an operational point (OP), in which an out-of-phase power oscillation has been observed in the scope of a stability test at the beginning of cycle 7 (KKLc7_rec4). The ROM predicts a saddle-node bifurcation of cycles, occurring in the linear stable region, close to the KKLc7_rec4-OP. This result allows a new interpretation of the stability behaviour around the KKLc7_rec4-OP. The results of this thesis confirm that the RAM-ROM methodology is qualified for nonlinear BWR stability analyses
Die vorliegende Dissertation leistet einen Beitrag zum tieferen Verständnis des nichtlinearen Stabilitätsverhaltens von Siedewasserreaktoren (SWR). Trotz der Tatsache, dass in diesem technischen System nur negative innere Rückkopplungskoeffizienten auftreten, können in bestimmten Arbeitspunkten oszillatorische Instabilitäten auftreten. Obwohl relativ gute Kenntnisse über die signifikanten physikalischen Einflussgrößen vorliegen, fehlt bisher ein umfassendes Verständnis des SWR-Stabilitätsverhaltens. Das betrifft insbesondere die Bereiche der Systemparameter, in denen lineare Stabilitätsindikatoren, wie zum Beispiel das asymptotische Decay Ratio (DR), ihren Sinn verlieren. Die nichtlineare Stabilitätsanalyse wird im Allgemeinen mit Systemcodes (nichtlineare partielle Differentialgleichungen, PDG) durchgeführt. Jedoch kann mit Systemcodes kein oder nur ein sehr lückenhafter Überblick über die Typen von nichtlinearen Phänomenen, die in bestimmten System-Parameterbereichen auftreten, erhalten werden. Deshalb wurde im Rahmen der vorliegenden Arbeit eine neuartige Methode (RAM-ROM Methode) zur nichtlinearen SWR-Stabilitätsanalyse erprobt, bei der integrale Systemcodes und sog. vereinfachte SWR-Modelle (ROM) als sich gegenseitig ergänzende Methoden eingesetzt werden, um die Stabilitätseigenschaften von Fixpunkten und periodischen Lösungen (Grenzzyklen) des nichtlinearen Differentialgleichungssystems, welches das Stabilitätsverhalten des SWR beschreibt, zu bestimmen. Das ROM, in denen das dynamische System durch gewöhnliche Differentialgleichungen (GDG) beschrieben wird, kann relativ einfach mit leistungsfähigen Methoden aus der nichtlinearen Dynamik, wie zum Beispiel die semianalytische Bifurkationsanalyse, gekoppelt werden. Mit solchen Verfahren kann, ohne das DG-System explizit lösen zu müssen, ein Überblick über mögliche Typen von stabilen und instabilen oszillatorischen Verhalten des SWR erhalten werden. Insbesondere sind die Stabilitätseigenschaften von Grenzzyklen, die in Hopf-Bifurkationspunkten entstehen, und die Bedingungen, unter denen sie auftreten, von Interesse. Mit dem Systemcode (RAMONA5) werden dann die mit dem ROM vorhergesagten Phänomene in den entsprechenden Parameterbereichen detaillierter untersucht (Validierung des ROM). Die Methodik dient daher nicht der Verfeinerung der Berechnung linearer Stabilitätsindikatoren (wie das DR). Das ROM-Gleichungssystem entsteht aus den PDGs des Systemcodes durch geeignete (nichttriviale) räumliche Mittelung der PDG. Es wird davon ausgegangen, dass die Reduzierung der räumlichen Komplexität die Stabilitätseigenschaften des SWR nicht signifikant verfälschen, da durch geeignete Mittlungsverfahren, räumliche Effekte näherungsweise in den GDGs berücksichtig werden. Beispielsweise wird die raum- und zeitabhängige Neutronenflussdichte nach räumlichen Moden entwickelt, wobei für eine Simulation der Stabilitätseigenschaften der In-phase- und Out-of-Phase-Leistungsoszillationen nur der Fundamentalmode und der erste azimuthale Mode berücksichtigt werden muss. Das ROM, welches ursprünglich am Paul Scherrer Institut (PSI, Schweiz) in Zusammenarbeit mit der Universität Illinois (USA) entwickelt wurde, ist in zwei wesentlichen Punkten erweitert und verbessert worden: • Entwicklung und Implementierung einer neuen Methode zur Berechnung der Rückkopplungsreaktivitäten • Entwicklung und Implementierung eines Modells zur Beschreibung der Rezirkulationsschleife (insbesondere wurde der Einfluss der Rezirkulationsschleife auf den In-Phase-Oszillationszustand und auf den Out-of-Phase-Oszillationszustand untersucht) • Entwicklung einer physikalisch begründeten Methode zur Berechnung der ROM-Inputdaten • Abschätzung des Einflusses des unterkühlten Siedens im Rahmen der ROM-Näherungen Mit dem erweiterten ROM wurden nichtlineare Stabilitätsanalysen für drei Arbeitspunkte (KKW Leibstadt (Zyklus 7) KKW Ringhals (Zyklus 14) und KKW Brunsbüttel (Zyklus 16)), für die Messdaten vorliegen, durchgeführt. In der Dissertationsschrift wird die RAM-ROM Methode ausführlich am Beispiel eines Arbeitspunktes (OP) des KKW Leibstadt (KKLc7_rec4-OP), in dem eine aufklingende regionale Leistungsoszillation bei einem Stabilitätstest gemessen worden ist, demonstriert. Das ROM sagt die Existenz eines Umkehrpunktes (saddle-node bifurcation of cycles, fold-bifurcation) voraus, der sich im linear stabilen Gebiet nahe der Stabilitätsgrenze befindet. Mit diesem ROM-Ergebnis ist eine neue Interpretation der Stabilitätseigenschaften des KKLc7_rec4-OP möglich. Die Resultate der in der Dissertation durchgeführten RAM-ROM Analyse bestätigen, dass das weiterentwickelte ROM für die Analyse des Stabilitätsverhaltens realer Leistungsreaktoren qualifiziert wurde

Dans ce manuscrit de thèse nous présentons des nouveaux résultats concernant l'existence, la non-existence, la multiplicité et la régularité des solutions positives pour deux problèmes quasilinéaires elliptiques avec conditions de Dirichlet dans un domaine borné. Dans le chapitre 1 d'introduction, nous décrivons les deux problèmes que nous allons étudier et nous donnons les principaux résultats. Le premier, d'inconnue u, comporte un terme de source de gradient à croissance critique. Le second, d'inconnue v, contient un terme source d'ordre 0. Dans le chapitre 2 nous donnons des nouveaux résultats de régularité des solutions renormalisées utiles pour notre étude. A l'aide d'un changement d'inconnue, nous établissons un lien précis entre les problèmes en u et v. Le chapitre 3 est consacré à montrer ce lien et à donner une première application. Dans les chapitres 4 et 5 nous traitons de l'existence de solutions, la solution extrémale et sa régularité, l'existence d'une deuxième solution bornée du problème en v. Dans le chapitre 6 nous démontrons un résultat d'existence pour le problème en v avec des données mesures de Radon bornées quelconques. Dans le chapitre 7 nous obtenons des nouveaux résultats pour le problème en u en utilisant la connexion entre ces deux problèmes.

Après une présentation des notations usuelles de la théorie des graphes, on étudie l'ensemble des fonctions harmoniques sur les graphes, c'est à dire des fonctions dont le laplacien est nul. Ces fonctions forment un espace vectoriel et sur un graphe uniformément localement fini, on montre que cet espace vectoriel est soit de dimension un, soit de dimension infinie. Lorsque le graphe comporte une infinité de cycles, ce résultat tombe en défaut et on exhibe des exemples qui montrent qu'il existe un graphe sur lequel les harmoniques forment un espace vectoriel de dimension n, pour tout n. Un exemple de graphe périodique est également traité. Ensuite, toujours pour le laplacien, on étudie plus précisément sur les arbres uniformément localement finis les valeurs propres dont l'espace propre est de dimension infini. Dans ce cas, il est montré que l'espace propre contient un sous-espace isomorphe à l'ensemble des suites réelles bornées. Une inégalité concernant le spectre est donnée dans le cas spécial où les arêtes sont de longueur un. Des exemples montrent que ces inclusions sont optimales. Dans le chapitre suivant, on étudie le comportement asymptotique des valeurs propres pour des opérateurs elliptiques d'ordre 2 quelconques sous des conditions de Kirchhoff dynamiques. Après réécriture du problème sous la forme d'un opérateur de Sturm-Liouville, on écrit le problème de façon matricielle. Puis on trouve une équation caractéristique dont les zéros correspondent aux valeurs propres. On en déduit une formule pour l'asymptotique des valeurs propres. Dans le dernier chapitre, on étudie la stabilité de solutions stationnaires pour certains problèmes de réaction-diffusion où le terme de non linéarité est polynomial
After a quick presentation of usual notations for the graph theory, we study the set of harmonic functions on graphs, that is, the functions whose laplacian is zero. These functions form a vectorial space. On a uniformly locally finite tree, we shaw that this space has dimension one or infinity. When the graph has an infinite number of cycles, this result change and we describe some examples showing that there exists a graph on which the harmonic functions form a vectorial space of dimension n, for all n. We also treat the case of a particular periodic graph. Then, we study more precisely the eigenvalues of infinite dimension. In this case, the eigenspace contains a subspace isomorphic to the set of bounded sequences. An inequality concerning the spectral is given when edges length is equal to one. Examples show that these inclusions are optimal. We also study the asymptotic behavior of eigenvalues for elliptic operators under dynamical Kirchhoff node conditions. We write the problem as a Sturm-Liouville operator and we transform it in a matrix problem. Then we find a characteristic equation whose zeroes correspond to eigenvalues. We deduce a formula for the asymptotic behavior. In the last chapter, we study the stability of stationary solutions for some reaction-diffusion problem whose the non-linear term is polynomial

Cette thèse porte principalement sur l'étude des solutions de certaines équations aux dérivées partielles elliptiques via l'indice de Morse, y compris des solutions stables, i.e. quand l'indice de Morse est égal à zéro. Elle comporte deux parties indépendantes.Dans la première partie, sous des hypothèses sur-linéaires et sous-critiques sur f, on établit d'abord une estimation explicite de la norme L [infini] des solutions de -Δu = f(u) avec u = 0 sur le bord, via leurs indices de Morse. On propose une approche plus transparente et plus souple que le travail de Yang [1998], ce qui nous permet de traiter des non linéarités très proches de la croissance critique. Les résultats obtenus nous ont motivé de travailler sur des équations polyharmoniques (-Δ)ku = f(x; u) avec notamment k = 2 et 3. Avec des hypothèses semblables à Yang [1998] sur f et des conditions au bord convenables, on obtient pour la première fois des estimations explicites de solution des équations polyhamoniques, via l'indice de Morse. Dans la seconde partie, on considère un système de Lane-Emden-Δu = ρ(x)vp; -Δv = ρ(x)u θ ; u; v > 0; dans RN; avec 1 < p< θ et un poids radial ρ strictement positif. Nous montrons la non-existence de solution stable en petites dimensions N. Nos résultats améliorent les travaux précédents de Cowan & Fazly [2012]; Fazly [2012]; Hu [2015], et fournissent notamment des résultats du type Liouville pour solution stable, en petites dimensions N, valables pour tout 1 < ρ min(4 3 ; θ)
The main concern of this thesis deals with the study of solutions of several elliptic partial differential equations via the Morse index, including the stable solutions, i.e. when the Morse index is zero. The thesis has two independent parts. In the first part, under suplinear and subcritical assumptions on f, we establish firstly some explicit estimation for the L1 norms of solutions to -Δu = f(u) avec u = 0 on the boundary, via its Morse index. We propose an approach more transparent and easier than the work of Yang [1998], which allow us to treat some nonlinearities very close to the critical growth. These results motivated us to consider the polyharmonic equations (-Δ)ku = f(x; u) with especially k = 2 and 3. With the hypothesis on f similar to Yang [1998] and appropriate boundary conditions, we obtain for the _rst time some explicit estimations of solution via its Morse index, for the polyharmonic equations.In the second part, we consider a Lane-Emden system -Δu = ρ(x)vp; -Δv = ρ(x)u_; u; v > 0; in RN; with 1 < p< θ and a radial positive weight ρ. We prove the non-existence of stable solution in small dimension case. Our results improve the previous works Cowan & Fazly [2012]; Fazly [2012]; Hu [2015], especially we prove some general Liouville type results for stable solutions in small dimension which hold true for any 1 < ρ min(4 3 ; θ)

This thesis focuses mainly on the Maximum Independent Set (MIS) problem. Some related graph theoretical combinatorial problems are also considered. As these problems are generally NP-hard, we study their complexity in hereditary graph classes, i.e. graph classes defined by a set F of forbidden induced subgraphs. We revise the literature about the issue, for example complexity results, applications, and techniques tackling the problem. Through considering some general approach, we exhibit several cases where the problem admits a polynomial-time solution. More specifically, we present polynomial-time algorithms for the MIS problem in: + some subclasses of $S_{2;j;k}$-free graphs (thus generalizing the classical result for $S_{1;2;k}$-free graphs); + some subclasses of $tree_{k}$-free graphs (thus generalizing the classical results for subclasses of P5-free graphs); + some subclasses of $P_{7}$-free graphs and $S_{2;2;2}$-free graphs; and various subclasses of graphs of bounded maximum degree, for example subcubic graphs. Our algorithms are based on various approaches. In particular, we characterize augmenting graphs in a subclass of $S_{2;k;k}$-free graphs and a subclass of $S_{2;2;5}$-free graphs. These characterizations are partly based on extensions of the concept of redundant set [125]. We also propose methods finding augmenting chains, an extension of the method in [99], and finding augmenting trees, an extension of the methods in [125]. We apply the augmenting vertex technique, originally used for $P_{5}$-free graphs or banner-free graphs, for some more general graph classes. We consider a general graph theoretical combinatorial problem, the so-called Maximum -Set problem. Two special cases of this problem, the so-called Maximum F-(Strongly) Independent Subgraph and Maximum F-Induced Subgraph, where F is a connected graph set, are considered. The complexity of the Maximum F-(Strongly) Independent Subgraph problem is revised and the NP-hardness of the Maximum F-Induced Subgraph problem is proved. We also extend the augmenting approach to apply it for the general Maximum Π -Set problem. We revise on classical graph transformations and give two unified views based on pseudo-boolean functions and αff-redundant vertex. We also make extensive uses of α-redundant vertices, originally mainly used for $P_{5}$-free graphs, to give polynomial solutions for some subclasses of $S_{2;2;2}$-free graphs and $tree_{k}$-free graphs. We consider some classical sequential greedy heuristic methods. We also combine classical algorithms with αff-redundant vertices to have new strategies of choosing the next vertex in greedy methods. Some aspects of the algorithms, for example forbidden induced subgraph sets and worst case results, are also considered. Finally, we restrict our attention on graphs of bounded maximum degree and subcubic graphs. Then by using some techniques, for example ff-redundant vertex, clique separator, and arguments based on distance, we general these results for some subclasses of $S_{i;j;k}$-free subcubic graphs.

碩士
國立暨南國際大學
應用化學系
108
Organic field-effect transistors (OFETs) are attracting ever increasing attention because of their applications for low-cost, large-area, and flexible electronics. To realize the low-cost and large-area organic electronics, OSCs should be processed from solution using the techniques such as spin coating, casting, printing, and bar coating. In this study we have successfully investigated by solution processed OFET. Thin films were prepared by bar coating a dichlorobenzene solution of different derivatives on trichloro(phenyl)silane treated SiO2/Si wafers. The highest mobility of devices was 3.01×10-2 cm2/Vs obtained. X-ray diffractometer (XRD) and atomic force microscope (AFM) to investigate thin film of morphology at different coating speeds and different substrate temperatures. Also we investigated the reasons for the inability to measure the transfer efficiency of Benzodithiophene derivatives (BPBDT-C8) and Pyromellitic Diimide derivatives (PyDTI-C8, PyDTI-C6C2, PyDTI-C2C3F7). In addition, this study has successfully used to control of solvent vapor for control crystal growth to fabricate NDAM-C2C6 single crystal device. The highest mobility was obtained with devices 0.43 cm2/Vs. This study also discusses the reasons why BPBDT-C8 crystals grown by solvent diffusion cannot be measurable device.

Half of the sun’s power lies in the infrared. As a result, the optimal bandgaps for solar cells in both the single-junction and even the tandem architectures lie beyond 850 nm. However, progress in low-cost, large-area, physically-flexible solar cells has instead been made in organic and polymer materials possessing absorption onsets in the visible. Recent advances have been achieved in solution-cast infrared photovoltaics through the use of colloidal quantum dots. Here we report stable solution-processed photovoltaic devices having 3.6% power conversion efficiency in the infrared. The use of a strongly-bound bidentate linker, benzenedithiol, ensures device stability over weeks. We investigate in detail the physical mechanisms underlying the operation of this class of device. We find that diffusion of electrons and holes over hundreds of nanometers through our PbSe colloidal quantum dot solid is chiefly responsible for the high external quantum efficiencies obtained in this new class of devices.

碩士
國立交通大學
統計學研究所
105
By studying the sub-density of the M/G/2/3 queuing system,$f_1(s)$、$f_2(s,t)$、$f_3(s,t)$,which respectively stand for the density function of the system in a steady state when the system has 1,2,3 people and they are has been serving for s, (s ,t), (s, t) unit of time, we can find the density function of the system and other special values (e.g.stationary probability). In this study, we find the analytical solution of the M/M/2/3, the numerical solution and the approximate solution of M/G/2/3 where the approximate solution can be expressed as the linear combination of several known functions and have good efficiency and approximation. We then try to extend the algorithm to M/G/2 /K and discuss possible approaches to M/G/C/K calculations. The structure of this paper is as follows. In the first chapter, we review the similar literature and introduce the method used in this study. In chapter 2, we discuss the situation of M/M/2/3, and solve the density function and the stationary probability. The third chapter to explore the M/G/2/3 situation, and lists the numerical algorithm and approximate algorithm. The fourth chapter lists the experimental results. The fifth chapter will be extended to M/G/2/K and discuss the case of M/G/C/K. In the end, the chapter sixth is the conclusion.

碩士
國立臺灣大學
物理學研究所
105
Van der Waals heterostructures composed of two-dimensional transition metal Dichalcogenides (TMDs) layers have recently emerged as a new class of materials, where quantum coupling between stacked atomically thin two-dimensional layers. Theory predicts that stacked TMDs heterostructures form type II semiconductor heterojunctions that facilitate efficient electron-hole separation for light harvesting. It has been reported that ultrafast hole transfer occurs in WS2/MoS2 heterostructure only within 50 fs. In this thesis, we integrate the WS2/MoS2 heterostructure into organic solar cells as hole transfer layer (HTL). By chemically exfoliation, we can get the solution of few-layers and monolayers TMDs nanosheets. With these solutions, solution-processed HTLs can be achieved. We found that power conversion efficiency of the device based on WS2/MoS2 HTL is large than the ones based on WS2 and MoS2 HTLs. The improved performance of devices indicates that carrier collections are more efficient. Besides, the devices based on TMDs (WS2, MoS2, and WS2/MoS2) HTLs were highly stable while they were stored in ambient air due to their chemical inert.

碩士
國立成功大學
機械工程學系
106
Hydroxypropyl methylcellulose (HPMC) is a kind of biopolymer with the character-istics of biodegradability, environment friendly, great mechanical properties and tribological properties. Therefore, it is suitable to develop as substituted materials of plastic. However, HPMC deforms easily when it bears the loading, causing real con-tact area and the adhesive force between HPMC and counter(AISI52100) increase, so that the HPMC film is easily damaged due to adhesive wear, and leading to lose efficacy on wear resistance. Hence, nanoparticles(NPs) Al, Cu, Al2O3, CuO have been used as fillers, by means of procedure, nano- suspension with dispersant (Span80) were prepared, and mixed with HPMC solution to prepare composite solu-tions and composite films. The study examined the basic properties (quality analysis, thickness, surface roughness, morphology), load capacity and macro-scale tribologi-cal behaviors. Results showed that Span80 could provide steric stabilization, and dispersed the NPs effectively in suspension. After suspension mixed with HPMC so-lution, HPMC made composite solution more stable. The load capacity of composite film remarkably enhanced, especially Cu/HPMC composite film. In terms of tribo-logical behaviors, the NPs Al and Cu occur deformation after wear test of low load-ing, the wear resistances had rose. Spherical CuO and sphere-like Al2O3 occurred rolling effect as third-body at interface during the test, so that the coefficient of fric-tion and wear rate decreased significantly. Since HPMC is soluble in water and or-ganic solvents (ethanol, and so on), the composite solution could be separated into additive and solution easily by appropriate pore size of filters, preventing pollution and recycling limited resources.

Internal gravity waves (GWs) are an important component of the atmospheric dynamics, significantly affecting the middle atmosphere by momentum and energy transport and deposition. In order to be able to improve global circulation models, in which the majority of the GW spectrum is not resolved, it is necessary to quantify their effects as precise as possible. We study GWs in a high-resolution simulation of the WRF model around Southern Andes, Antarctic Peninsula and South Georgia Island. We analyse a Gaussian high-pass filter method for separation of GWs from the basic flow. To overcome an observed problem of dependence of the method on a cutoff parameter, we propose an improved method that determines the parameter at each time step from the horizontal kinetic energy spectrum. The differences between the methods are further examined using the horizontal kinetic energy spectrum, vertical potential energy spectrum and forcing to the divergence equation evaluated by the active wind method, which is a recent theory-based method that divides the flow into a balanced flow and a perturbation field. The results suggest that the high-pass filter method does not produce correct results for time periods with strong wave activity.

In this thesis, we first propose a new scalar auxiliary variable (SAV) approach for general dissipative nonlinear systems. This new approach is half computational cost of the original SAV approach, can be extended to high order unconditionally energy stable backward differentiation formula (BDF) schemes and not restricted to the gradient flow structure. Rigorous error estimates for this new SAV approach are conducted for the Allen-Cahn and Cahn-Hilliard type equations from the BDF1 to the BDF5 schemes in a unified form. As an application of this new approach, we construct high order unconditionally stable, fully discrete schemes for the incompressible Navier-Stokes equation with periodic boundary condition. The corresponding error estimates for the fully discrete schemes are also reported. Secondly, by combining the new SAV approach with functional transformation, we propose a new method to construct high-order, linear, positivity/bound preserving and unconditionally energy stable schemes for general dissipative systems whose solutions are positivity/bound preserving. We apply this new method to second order equations: the Allen-Cahn equation with logarithm potential, the Poisson-Nernst-Planck equation and the Keller-Segel equations and fourth order equations: the thin film equation and the Cahn-Hilliard equation with logarithm potential. Ample numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.

This thesis focuses mainly on the Maximum Independent Set (MIS) problem. Some related graph theoretical combinatorial problems are also considered. As these problems are generally NP-hard, we study their complexity in hereditary graph classes, i.e. graph classes defined by a set F of forbidden induced subgraphs. We revise the literature about the issue, for example complexity results, applications, and techniques tackling the problem. Through considering some general approach, we exhibit several cases where the problem admits a polynomial-time solution. More specifically, we present polynomial-time algorithms for the MIS problem in: + some subclasses of $S_{2;j;k}$-free graphs (thus generalizing the classical result for $S_{1;2;k}$-free graphs); + some subclasses of $tree_{k}$-free graphs (thus generalizing the classical results for subclasses of P5-free graphs); + some subclasses of $P_{7}$-free graphs and $S_{2;2;2}$-free graphs; and various subclasses of graphs of bounded maximum degree, for example subcubic graphs. Our algorithms are based on various approaches. In particular, we characterize augmenting graphs in a subclass of $S_{2;k;k}$-free graphs and a subclass of $S_{2;2;5}$-free graphs. These characterizations are partly based on extensions of the concept of redundant set [125]. We also propose methods finding augmenting chains, an extension of the method in [99], and finding augmenting trees, an extension of the methods in [125]. We apply the augmenting vertex technique, originally used for $P_{5}$-free graphs or banner-free graphs, for some more general graph classes. We consider a general graph theoretical combinatorial problem, the so-called Maximum -Set problem. Two special cases of this problem, the so-called Maximum F-(Strongly) Independent Subgraph and Maximum F-Induced Subgraph, where F is a connected graph set, are considered. The complexity of the Maximum F-(Strongly) Independent Subgraph problem is revised and the NP-hardness of the Maximum F-Induced Subgraph problem is proved. We also extend the augmenting approach to apply it for the general Maximum Π -Set problem. We revise on classical graph transformations and give two unified views based on pseudo-boolean functions and αff-redundant vertex. We also make extensive uses of α-redundant vertices, originally mainly used for $P_{5}$-free graphs, to give polynomial solutions for some subclasses of $S_{2;2;2}$-free graphs and $tree_{k}$-free graphs. We consider some classical sequential greedy heuristic methods. We also combine classical algorithms with αff-redundant vertices to have new strategies of choosing the next vertex in greedy methods. Some aspects of the algorithms, for example forbidden induced subgraph sets and worst case results, are also considered. Finally, we restrict our attention on graphs of bounded maximum degree and subcubic graphs. Then by using some techniques, for example ff-redundant vertex, clique separator, and arguments based on distance, we general these results for some subclasses of $S_{i;j;k}$-free subcubic graphs.