L'imagerie par résonance magnétique de diffusion (IRMD) est une technique d'imagerie qui teste les propriétés diffusives d'un échantillon en le soumettant aux impulsions d'un gradient de champ magnétique. Plus précisément, elle détecte le mouvement de l'eau dû à la diffusion et s'avère donc être un outil puissant pour obtenir des informations sur la microstructure des tissus. Le signal acquis par le scanner IRM est une mesure moyennée sur un volume physique appelé voxel, dont la taille, pour des raisons techniques, est bien plus grande que l'échelle de variations microscopiques de la structure cellulaire. Ceci implique que les composants microscopiques des tissus ne sont pas visibles à la résolution spatiale de l'IRM et que les caractéristiques géométriques se trouvent agréger dans le signal macroscopique provenant du voxel. Une importante quantité mesurée par l'IRMD dans chaque voxel est le Coefficient de Diffusion Apparent (CDA) dont la dépendance au temps de diffusion est actée par de nombreuses expériences d'imagerie effectuées in vivo. Il existe dans la littérature un nombre important de modèles macroscopiques décrivant le CDA allant du plus simple au plus complexe (modèles phénoménologiques, stochastiques, géométriques, fondés sur des EDP, etc.), chacun étant valide sous certaines hypothèses techniques bien précises. Le but de cette thèse est de construire des modèles simples, disposant d'une bonne validité applicative, en se fondant sur une modélisation de la diffusion à l'échelle microscopique à l'aide d'EDP et de techniques d'homogénéisation.Dans un article antérieur, le modèle homogénéisé FPK a été déduit de l’EDP de Bloch-Torrey sous l'hypothèse que la perméabilité de la membrane soit petite et le temps de diffusion long. Nous effectuons tout d'abord une analyse de ce modèle et établissons sa convergence vers le modèle classique de Kärger lorsque la durée des impulsions magnétiques tend vers 0. Notre analyse montre que le modèle FPK peut être vu comme une généralisation de celui de Kärger, permettant la prise en compte de durées d'impulsions magnétiques arbitraires. Nous donnons aussi une nouvelle définition, motivée par des raisons mathématiques, du temps de diffusion pour le modèle de Kärger (celle impliquant la plus grande vitesse de convergence).Le CDA du modèle FPK est indépendant du temps ce qui entre en contradiction avec nombreuses observations expérimentales. Par conséquent, notre objectif suivant est de corriger ce modèle pour de petites valeurs de ce que l'on appelle des b-valeurs afin que le CDA homogénéisé qui en résulte soit sensible à la fois à la durée des impulsions et à la fois au temps de diffusion. Pour atteindre cet objectif, nous utilisons une technique d'homogénéisation similaire à celle utilisée pour le FPK, tout en proposant un redimensionnement adapté de l'échelle de temps et de l'intensité du gradient pour la gamme de b-valeurs considérées. Nous montrons, à l'aide de simulations numériques, l'excellente qualité de l'approximation du signal IRMD par ce nouveau modèle asymptotique pour de faibles b-valeurs. Nous établissons aussi (grâce à des développements en temps court des potentiels de surface associés à l'équation de la chaleur ou grâce à une décomposition de sa solution selon les fonctions propres) des résultats analytiques d'approximation du modèle asymptotique qui fournissent des formules explicites de la dépendance temporelle du CDA. Nos résultats sont en accord avec les résultats classiques présents dans la littérature et nous améliorons certains d'entre eux grâce à la prise en compte de la durée des impulsions. Enfin nous étudions le problème inverse consistant en la détermination d'information qualitative se rapportant à la fraction volumique des cellules à partir de signaux IRMD mesurés. Si trouver la distribution de sphères semble possible à partir de la mesure du signal IRMD complet, il nous est apparu que la mesure du seul CDA ne serait pas suffisante. / Diffusion magnetic resonance imaging (dMRI) is an imaging modality that probes the diffusion characteristics of a sample via the application of magnetic field gradient pulses. More specifically, it encodes water displacement due to diffusion and is then a powerful tool to obtain information on the tissue microstructure. The signal measured by the MRI scanner is a mean-value measurement in a physical volume, called a voxel, whose size, due to technical reasons, is much larger than the scale of the microscopic variations of the cellular structure. It follows that the microscopic components of the tissues are not visible at the spatial resolution of dMRI. Rather, their geometric features are aggregated into the macroscopic signal coming from the voxels. An important quantity measured in dMRI in each voxel is the Apparent Diffusion Coefficient (ADC) and it is well-established from imaging experiments that, in the brain, in-vivo, the ADC is dependent on the diffusion time. There is a large variety (phenomenological, probabilistic, geometrical, PDE based model, etc.) of macroscopic models for ADC in the literature, ranging from simple to complicated. Indeed, each of these models is valid under a certain set of assumptions. The goal of this thesis is to derive simple (but sufficiently sound for applications) models starting from fine PDE modelling of diffusion at microscopic scale using homogenization techniques.In a previous work, the homogenized FPK model was derived starting from the Bloch-Torrey PDE equation under the assumption that membrane's permeability is small and diffusion time is large. We first analyse this model and establish a convergence result to the well known K{"a}rger model as the magnetic pulse duration goes to 0. In that sense, our analysis shows that the FPK model is a generalisation of the K{"a}rger one for the case of arbitrary duration of the magnetic pulses. We also give a mathematically justified new definition of the diffusion time for the K{"a}rger model (the one that provides the highest rate of convergence).The ADC for the FPK model is time-independent which is not compatible with some experimental observations. Our goal next is to correct this model for small so called $b$-values so that the resulting homogenised ADC is sensitive to both the pulses duration and the diffusion time. To achieve this goal, we employed a similar homogenization technique as for FPK, but we include a suitable time and gradient intensity scalings for the range of considered $b$-values. Numerical simulations show that the derived asymptotic new model provides a very accurate approximation of the dMRI signal at low $b$-values. We also obtain some analytical approximations (using short time expansion of surface potentials for the heat equation and eigenvalue decompositions) of the asymptotic model that yield explicit formulas of the time dependency of ADC. Our results are in concordance with classical ones in the literature and we improved some of them by accounting for the pulses duration.Finally we explored the inverse problem of determining qualitative information on the cells volume fractions from measured dMRI signals. While finding sphere distributions seems feasible from measurement of the whole dMRI signal, we show that ADC alone would not be sufficient to obtain this information.

Main purpose of the diploma thesis is to design a multi-span double-girder bridge which spans the valley of a river. The bridge spans main road of 1st class. Main superstructure of a bridge is made of prestressed concrete which is built span by span. Structure was designed according to limit states in construction stages as well as during the service. Everything was designed according to the latest European normatives. It contains static calculation and drawing documentation.

The subject of the master thesis is a prestressed double girder bridge with four spans. The bridge carries the D1 motorway over the Olše river and a crossing ramp. The structure is modelled in Scia Engineer and then assessed according to the standards for ultimate and serviceability limit states.

The aim of this thesis is design of the loadbearing structure of a bridge. Out of two proposed variants was chosen prestressed girder deck of 5 spans. The bridge is built span-by-span in a formwork supported by launching girders. Calculation of load cases is made in software Midas Civil 2021 and Scia Engineer 18.1. The construction is evaluated considering the ultimate limit state and serviceability limit state. The design and evaluation were made according to valid standards.

Advanced computational methods for the analysis of building structures are used more often in engineering practice. Their use is enforced not only by the demands for aesthetics, functionality and high economy of the construction, but often directly by code provisions and requirements. Therefore, it is necessary to provide for an engineer the robust, but transparent tool, which can be used for an efficient design of structure all over it's design working life. This work deals with the creation of a computational system for time dependent analysis of concrete and composite structures. It is assumed a solid or composite concrete section with possible application of pre-tensioned and/or post-tensioned tendons. Each phase of step-by-step build composite cross-section has a general geometry. The used algorithms give us the possibility of a detailed analysis of the structure in individual construction stages, provide the designer better view on the behavior of structures with respect to concrete aging, shrinkage and creep, relaxation of prestressed tendons and provide an information on the redistribution of internal forces in the structure and in different phases of the cross-section. Stress state of the structure calculated in this way come in useful further in the design and checking of ultimate and serviceability limit states. Results of time dependent analysis are verified by manual calculations and by comparing with the results obtained by simplified methods.

The subject of this Master's thesis is the design of a road bridge on the D1 in the section Lietavská Lúčka - Višňové in the Žilina Region, Žilina District, Slovak Republic. The bridge is used to cross the valley in KM 4,313 and the road in KM 4,410. Three variants of bridging were proposed, but further in the work an assessment is made on one of the variants. The total length of the superstructure is 354.00 m, the theoretical total span of the structure is 352.00 m. The bridge has 4 spans and is constructed by free cantilever method .The locations of the supports were limited by unsuitable geological conditions at the construction site (active shear area in Quaternary sediments), especially in span No. 3 (span lenght 104.00 m) and span No. 4 (span lenght 75.00 m). The monolithic part of the bridge structure will be concreted by free cantilever method with the largest length of the cantilever 52.00 m. The outermost parts of fields No. 1 and No. 4 will be cast-in-place using fixed scaffolding.

The subject of the diploma thesis is a design of a highway bridge across the Svratka river in Brno. Among three options, the arch bridge with a trapezoidal bridge deck from prestressed concrete was chosen. The load effect is calculated with the assistance of Scia Engineer software. The design and the assessment of the structure are made for the ultimate limit state and serviceability limit state. Static assessment is done by hand calculation according to CSN EN 1992-2. The thesis includes drawings and visualizations of the bridge structure.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20904号 / 理博第4356号 / 新制||理||1625(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 杉本 茂樹, 教授 川合 光, 准教授 國友 浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The exact exchange-correlation kernel is a functional derivative of the exact time-dependent exchange-correlation (XC) potential with respect to the time-dependent density, evaluated at the ground-state density. As the XC potential is not known, the exact kernel is also unavailable. Therefore, it must be modeled either using many-body perturbation theory or by satisfying the exact constraints for various prototype systems such as the paradigm uniform electron gas (UEG). The random phase approximation (RPA) neglects the kernel, therefore, fails to provide the accurate ground- and excited-state properties for various systems from a simple uniform electron gas to more complex periodic ones. There are numerous corrections to RPA available, including kernel-corrected RPA, often called the beyond-RPA (bRPA) methods. In this work, we employed various bRPA methods for a diverse set of systems together with RPA. At first, we applied RPA based methods to study the phase stability of the cesium halides. Cesium halides phase stability is one of the stringent tests for a density functional approximation to assess its accuracy for dispersion interaction. Experimentally, CsF prefers the rocksalt (B1) phase, while the other halides CsCl, CsBr, and CsI prefer the cesium chloride (B2) phase. Without dispersion interaction, PBE and PBE0 predict all halides to prefer the B1 phase. However, all RPA based methods predict the experimental observations. The bRPA methods usually improve the quantitative prediction over RPA for the ground-state equilibrium properties of cesium halides. Next, we explored binary intermetallic alloys, where we showed that RPA successfully predicts the accurate formation energies of weakly bonded alloys. However, a kernel corrected RPA is needed when dealing with strongly bonded alloys with partially filled d-band metals. We utilized the renormalized ALDA (rALDA) and rAPBE kernel as bRPA methods. Exact constraints and appropriate norms such as the uniform electron gas are very useful to construct various approximations for the exchange-correlation potentials in the ground-state, and the exchange-correlation kernel in the linear-response theory within the TDDFT. These mathematical formulations not only guide us to formulate more robust nonempirical methods, but they also have more predictive power. We showed the importance of these constraints by calculating plasmon dispersion of the uniform electron gas using the non-local, energy-optimized (NEO) kernel using only a few constraints. More predictive power comes with more constraint satisfaction. As a result, we developed a new wavevector- and frequency-dependent exchange-correlation kernel that satisfies all the constraints that it should satisfy with a real frequency. It gives accurate ground-state correlation energy and describes the charge density wave in low-density UEG. It also predicts an accurate plasmon dispersion with a finite lifetime at wavevectors less than the critical one, where the plasmon dispersion meets the electron-hole continuum. / Physics

The famous Moore's law states: Since the invention of the integrated circuit, the number of transistors that can be placed on an integrated circuit has increased exponentially, doubling approximately every two years. As a result of the downscaling of the size of the transistor, quantum effects have become increasingly important while affecting significantly the device performances. Nowadays, at the nanometer scale, inter-atomic interactions and quantum mechanical properties need to be studied extensively. Device and material simulations are important to achieve these goals because they are flexible and less expensive than experiments. They are also important for designing and characterizing new generation of electronic device such as silicon nanowire or carbon nanotube (CNT) transistors. Several modeling methods have been developed and applied to electronic structure calculations, such as: Hartree-Fock, density functional theory (DFT), empirical tight-binding, etc. For transport simulations, most of the device community focuses on studying the stationary problem for obtaining characteristics such as I-V curves. The non-equilibrium transport problem is then often addressed by solving a multitude of time-independent Schrodinger-type equation for all possible energies. On the other hand, for many other electronic applications including high-frequency electronics response (e.g. when a time-dependent potential is applied to the system), the description of the system behavior necessitate insights on the time dependent electron dynamics. To address this problem, it is then necessary to solve a time-dependent Schrodinger-type equation. In this thesis, we will focus on solving time-dependent problems with application to CNTs. We will be identifying all the numerical difficulties and propose new effective modeling and numerical schemes to address the current limitations in time-dependent quantum simulations. we will point out that two numerical errors may occur: an integration error and the anti-commutation issue error; the direct computation above being mathematically equivalent to performing the integration of the time dependent Hamiltonian using a rectangle numerical quadrature formula along the total simulation times. After careful study and many numerical experiments, we found that the Gaussian quadrature scheme provides a good trade off between computational consumption and numerically accuracy, meanwhile unitary, stability and time reversal properties are well preserved. The new Gaussian quadrature integration scheme uses (i) much fewer points in time to approximate the integral of the Hamiltonian, (ii) ordered exponential to factorize the time evolution operator, (iii) FEM discretize techniques (iv) and at last, the FEAST eigenvalue solver to diagonalize and solve each exponential.