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This thesis concerns the applications and analysis of the Heterogeneous Multiscale methods (HMM) for Multiscale Elliptic and Hyperbolic Partial Differential Equations. We have gathered the main contributions in two papers. The first paper deals with the cell-boundary error which is present in multi-scale algorithms for elliptic homogenization problems. Typical multi-scale methods have two essential components: a macro and a micro model. The micro model is used to upscale parameter values which are missing in the macro model. Solving the micro model requires, on the other hand, imposing boundary conditions on the boundary of the microscopic domain. Imposing a naive boundary condition leads to $O(\varepsilon/\eta)$ error in the computation, where $\varepsilon$ is the size of the microscopic variations in the media and $\eta$ is the size of the micro-domain. Until now, strategies were proposed to improve the convergence rate up to fourth-order in $\varepsilon/\eta$ at best. However, the removal of this error in multi-scale algorithms still remains an important open problem. In this paper, we present an approach with a time-dependent model which is general in terms of dimension. With this approach we are able to obtain $O((\varepsilon/\eta)^q)$ and $O((\varepsilon/\eta)^q  + \eta^p)$ convergence rates in periodic and locally-periodic media respectively, where $p,q$ can be chosen arbitrarily large.      In the second paper, we analyze a multi-scale method developed under the Heterogeneous Multi-Scale Methods (HMM) framework for numerical approximation of wave propagation problems in periodic media. In particular, we are interested in the long time $O(\varepsilon^{-2})$ wave propagation. In the method, the microscopic model uses the macro solutions as initial data. In short-time wave propagation problems a linear interpolant of the macro variables can be used as the initial data for the micro-model. However, in long-time multi-scale wave problems the linear data does not suffice and one has to use a third-degree interpolant of the coarse data to capture the $O(1)$ dispersive effects apperaing in the long time. In this paper, we prove that through using an initial data consistent with the current macro state, HMM captures this dispersive effects up to any desired order of accuracy in terms of $\varepsilon/\eta$. We use two new ideas, namely quasi-polynomial solutions of periodic problems and local time averages of solutions of periodic hyperbolic PDEs. As a byproduct, these ideas naturally reveal the role of consistency for high accuracy approximation of homogenized quantities. / <p>QC 20130926</p>

京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第20755号 / 医博第4285号 / 新制||医||1024(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 伊佐 正, 教授 宮本 享, 教授 井上 治久 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

The dissertation gives a rigorous study of surface waves on water of finite depth subjected to gravitational force. As for `water', it is an inviscid and incompressible fluid of constant density and the flow is irrotational. The fluid is bounded above by a free surface separating the fluid from the air above (assumed to be a vacuum) and below by a rigid flat bottom. Then, the governing equations for the motion of the fluid flow are called Euler equations. If the initial fluid flow is prescribed at time zero, i.e., mathematically the initial condition for the Euler equations is given, the long-time existence of a unique solution for the Euler equations is still an open problem, even if the initial condition is small (or initial flow is almost motionless). The dissertation tries to make some progress for proving the long-time existence and show that the time interval of the existence is exponentially long, called almost global well-posedness, if the initial condition is small and satisfies some conditions. The main ideas for the study are from the corresponding almost global well-posedness result for surface waves on water of infinite depth. / Doctor of Philosophy / This dissertation concerns the mathematical study of surface waves on water of finite depth under gravitational force. Mathematically, water is considered as a fluid of constant density that has no viscosity and is incompressible. It is also assumed that any portion of the corresponding fluid flow is not rotating. Furthermore, the water is bounded above by a free surface separating the water from the air above and below by a rigid horizontal flat bottom. A natural question to ask is whether the water surface will keep smooth and will not break as time progresses, if a small disturbance on the flat free surface and the tranquil water-body is initially created. The dissertation tries to make some progress on this question by showing that under some mathematical and technical assumptions, the water surface remains smooth and will not break for a very long time by using the mathematical equations derived from the laws of physics.

The aim of this thesis is to analyze the factors that affect the accessibility of scientific data and results at the Luleå University of Technology (LTU). This work also attempts to improve the accessibility of scientific data at LTU. To this end, first, accessibility is measured by a questionnaire and compared with some theory in the field and certain main factors for a satisfactory accessibility.Second, a survey is given about the causes and factors for better accessibility in accordance with standards and theory. Considering the expectations of students and staff, who are the first users of scientific data as a part of their studies and research, following some frameworks and standards certainly is necessary.Furthermore, the thesis contains a study to find out any plan to save and preserve some related metadata of scientific data. This is another scope of this thesis that can increase access for users for a long time. This research figures out some standards and frameworks according to reliable previous research by other authors. If these are adopted by the university, accessibility of scientific data will be obtained without the problems that users mention in the questionnaire. / <p>Validerat; 20140210 (global_studentproject_submitter)</p>

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Välfärdsjobb är en relativt ny typ av insats som används i flera kommuner i Sverige. Den går ut på att personer som har levt länge med försörjningsstöd ska få en tidsbegränsad anställning med kollektivavtalsenlig lön för att komma närmare den reguljära arbetsmarknaden. Uppsala har börjat ge insatsen under hösten 2013 och där startade intresset för att genomföra en undersökning. Den har ett barnperspektiv för att belysa barns situation. För att besvara frågeställningarna har en kvalitativ innehållsanalys använts. Materialet har bestått av en utvärdering, en delrapport och en rad olika kommunala texter. De kodades och kategoriserades utifrån barndomssociologiska begrepp och Jahodas (1982) teori om arbetets latenta och manifesta effekter. Dessa delades upp i underrubriker som passade ihop med datamaterialet. Kommunerna som använts är Malmö, Sigtuna, Sundsvall, Uppsala, Botkyrka och Ludvika. De inkluderade kommunerna är positiva till resultaten av insatsen välfärdsjobb. Malmö har fortsatt använda sig av den sedan år 2005 och Sigtuna redovisar stora ekonomiska vinster av insatsen. Personerna som deltagit i insatsen berättar om hur de har fått bättre självförtroende, större nätverk och förbättrad ekonomi. Flera av deltagarna har efter insatsen fått en reguljär anställning. Vissa deltagare har dock framfört kritik för att arbetsuppgifterna känts enformiga och påhittade. Malmö hade problem att få in kvinnor i insatsen och att några inte förstod att insatsen var tillfällig. Barnen syns inte så mycket i kommunernas texter. Några kommuner prioriterar barnfamiljer medan till exempel Malmö enbart nämner barnen som blivande motiverade studenter. Kopplat till vad som framkommer i tidigare forskning skulle insatsen kunna vara bra även för barnen, de får till exempel bättre ekonomi och därmed möjlighet till fler aktiviteter. Om föräldrarna mår bättre gör barnen det också. En nackdel som kom fram var att insatsen är tillfällig då barnen känner en osäkerhet i vad som händer efter insatsen. Det framkommer skillnader i hur mammor, pappor, barn och familjer representeras i kommunernas material. För framtida forskning skulle det vara intressant att ha med barns perspektiv vid utvärdering av insatsen. Nyckelord: långvarigt försörjningsstöd, arbetslöshet, välfärdsjobb, barnperspektiv, arbetets effekter / ”Välfärdsjobb” is a relatively new kind of intervention that is used in some municipalities in Sweden. It means giving people that have been living a long time with welfare payments a fixed term employment contract. The participants get a salary and get closer to the regular labor market. Uppsala started a project called “Välfärdsjobb” autumn 2013 and that is where the interest for the subject came from. The study has a child perspective. A qualitative content analysis has been used to respond to the research questions. The data material consists of an evaluation, an interim report and different documents from the municipalities. The material was coded in relation to childhood sociology and Jahoda’s theory of latent and manifest effects of unemployment. The municipalities that have been used are Malmö, Sigtuna, Sundsvall, Uppsala, Botkyrka och Ludvika. The involved municipalities are positive to the intervention. Malmö has had it since 2005 and Sigtuna shows great economic savings. The persons participating in the intervention convey that they have gained better self-confidence, larger social networks and better economy. Several of the participants have a regular job after the intervention. The negative aspects of the intervention were that some of the participants have expressed that the work tasks felt repetitive and made up. Malmö failed to recruit women and some participants did not understand that the job was temporary. The children are not very visible in the data material. Some of the municipalities have families with children as a prioritized group, while Malmö just mentions children in terms of becoming motivated students. Looking at earlier research the intervention seems positive for children. They get a better economy and hence a wider array of activities are possible. Also, if the parents feel good, it affects the children positively. Something that could have a negative impact is that the intervention is temporary, since the children often feel worried about what will happen next. There are differences in how mothers, fathers, children and families are represented within the material from the municipalities. For future research it would be interesting to have a children’s perspective included in the evaluations of the interventions. Key words: long-time welfare payments, unemployment, workfare jobs, children’s perspective, effects of employment

Cette thèse comporte trois parties essentiellement indépendantes, dont chacune est consacrée à l'étude d'un système de particules, suivant une dynamique déterministe ou aléatoire, et à l'intérieur duquel les interactions se font uniquement aux collisions entre les particules.La Partie I propose une étude numérique et théorique des états stationnaires hors de l'équilibre du Modèle d'Échange Complet, introduit en physique pour comprendre le transport de la chaleur dans certains matériaux poreux.La Partie II est consacrée à un système de particules browniennes évoluant sur la droite réelle et interagissant à travers leur rang. Le comportement limite de ce système, en temps long et à grand nombre de particules, est décrit, puis les résultats sont appliqués à l'étude d'un modèle de marché financier dit modèle d'Atlas en champ moyen.La Partie III introduit une version multitype du système de particules étudié dans la partie précédente, qui permet d'approcher des systèmes paraboliques d'équations aux dérivées partielles non-linéaires. La limite petit bruit de ce système est appelée dynamique des particules collantes multitype et approche cette fois des systèmes hyperboliques. Une étude détaillée de cette dynamique donne des estimations de stabilité en distance de Wasserstein sur les solutions de ces systèmes. / This thesis contains three independent parts, each one of which is dedicated to the study of a particle system, following either a deterministic or a stochastic dynamics, and in which interactions only occur at collisions. Part I contains a numerical and theoretical study of nonequilibrium steady states of the Complete Exchange Model, which was introduced by physicists in order to understand heat transfer in some porous materials. Part II is dedicated to a system of Brownian particles evolving on the real line and interacting through their ranks. The long time and mean-field behaviour of this system is described, then the results are applied to the study of a model of equity market called the mean-field Atlas model. Part III introduces a multitype version of the particle system studied in the previous part, which allows to approximate parabolic systems of nonlinear partial differential equations. The small noise limit of of this system is called multitype sticky particle dynamics and now approximates hyperbolic systems. A detailed study of this dynamics provides stability estimates in Wasserstein distance for the solutions of these systems.

This dissertation contains work that addresses both theoretical and numerical aspects of reduced order models (ROMs). In an under-resolved regime, the classical Galerkin reduced order model (G-ROM) fails to yield accurate approximations. Thus, we propose a new ROM, the data-driven variational multiscale ROM (DD-VMS-ROM) built by adding a closure term to the G-ROM, aiming to increase the numerical accuracy of the ROM approximation without decreasing the computational efficiency. The closure term is constructed based on the variational multiscale framework. To model the closure term, we use data-driven modeling. In other words, by using the available data, we find ROM operators that approximate the closure term. To present the closure term's effect on the ROMs, we numerically compare the DD-VMS-ROM with other standard ROMs. In numerical experiments, we show that the DD-VMS-ROM is significantly more accurate than the standard ROMs. Furthermore, to understand the closure term's physical role, we present a theoretical and numerical investigation of the closure term's role in long-time integration. We theoretically prove and numerically show that there is energy exchange from the most energetic modes to the least energetic modes in closure terms in a long time averaging. One of the promising contributions of this dissertation is providing the numerical analysis of the data-driven closure model, which has not been studied before. At both the theoretical and the numerical levels, we investigate what conditions guarantee that the small difference between the data-driven closure model and the full order model (FOM) closure term implies that the approximated solution is close to the FOM solution. In other words, we perform theoretical and numerical investigations to show that the data-driven model is verifiable. Apart from studying the ROM closure problem, we also investigate the setting in which the G-ROM converges optimality. We explore the ROM error bounds' optimality by considering the difference quotients (DQs). We theoretically prove and numerically illustrate that both the ROM projection error and the ROM error are suboptimal without the DQs, and optimal if the DQs are used. / Doctor of Philosophy / In many realistic applications, obtaining an accurate approximation to a given problem can require a tremendous number of degrees of freedom. Solving these large systems of equations can take days or even weeks on standard computational platforms. Thus, lower-dimensional models, i.e., reduced order models (ROMs), are often used instead. The ROMs are computationally efficient and accurate when the underlying system has dominant and recurrent spatial structures. Our contribution to reduced order modeling is adding a data-driven correction term, which carries important information and yields better ROM approximations. This dissertation's theoretical and numerical results show that the new ROM equipped with a closure term yields more accurate approximations than the standard ROM.

The analysis of long-time formant distribution is relatively young but promising discipline of speaker identification. It is a method of mapping the long-term behavior of formants in speech of individual speakers. Frequently encountered problems in practice are bad acoustic quality and very short duration of analyzed recordings. This work aims to present the historical development of forensic phonetics and currently used methods. In the practical part, it deals with the usability of LTF method in forensic practice, especially in recordings containing background noise. It was shown that the noise appreciably affects extracted LTF values and unfortunately the change is not systematic. Therefore, we proposed several methods to compensate the noise in recordings, in order to be able to compare recordings with and without noise. We also investigated the minimum duration of recording, which is necessary for statistical reliability of the resulting values. This boundary is not exact and for each speaker, it is substantially individual. But it is apparent that recordings (vocalic streams) shorter than 15 s often provide incomplete information, wherefore they cannot be recommended for analysis. Keywords: LTF, long-time formant distribution, speaker identification, forensic phonetics, acoustic quality of...