L’excavation d’un tunnel profond dans des terrains poussants pose des difficultés particulières de conception et d’exécution. Ce type de terrain est caractérisé par des fortes convergences en paroi du tunnel de nature différée et souvent anisotrope. Le comportement d’un tunnel excavé en terrain poussant est très influencé par la technique d’excavation utilisée. Le cas d’étude du tunnel routier du Fréjus et de sa galerie de sécurité permet d’illustrer ce phénomène. Il s’agit de deux tunnels parallèles qui montrent une configuration très intéressante étant donné qu’ils traversent des conditions géotechniques similaires et qu’ils sont creusés avec des techniques d’excavation différentes : le tunnel routier a été creusé par méthode conventionnelle à l’explosif tandis que la galerie de sécurité a été creusée avec un tunnelier à bouclier simple. Les mesures d’auscultation réalisées pendant l’excavation des deux tunnels ont été analysées et comparées. Des modélisations numériques pour simuler la réponse des deux tunnels ont été développées avec le logiciel Flac3D. Le comportement du terrain est simulé avec un modèle visco-elasto-plastique et anisotrope. L’anisotropie liée à la schistosité du terrain est introduite dans le modèle par la présence de plans de faiblesse d’orientation donnée (ubiquitous joint model) insérés dans une matrice rocheuse caractérisée par un comportement visco-elasto-plastique isotrope. Une rétro-analyse a été réalisée sur les mesures de convergence obtenues lors du creusement du tunnel routier du Fréjus. Le comportement du terrain identifié dans le tunnel routier est ensuite extrapolé pour prédire la réponse de la galerie de sécurité. L’objectif est de reproduire l’état des contraintes observé dans les voussoirs de la galerie de sécurité et d’extrapoler les sollicitations à long terme. L’influence que la technique d’excavation, en particulier sur le comportement différé du terrain a été prise en compte dans les simulations numériques. On a mis en évidence que les déformations différées du terrain sont réduites lorsque l’excavation est réalisée au tunnelier.Par ailleurs, une synthèse critique de la méthode convergence-confinement et de ses variantes a été réalisée. Une discussion a été menée sur l’applicabilité des méthodes convergence-confinent quand elles sont utilisées pour le dimensionnement des tunnels circulaires excavés en section pleine avec l’installation d’un soutènement raide près du front d’excavation comme c’est le cas lors d’une excavation au tunnelier. Dans ce contexte, un ensemble de formules empiriques sont proposées. Elles permettent d’obtenir avec une bonne précision l’état d’équilibre entre le terrain et le soutènement et peuvent être utilisées dans la phase de pré-dimensionnement des ouvrages / During the excavation of deep tunnels, squeezing ground conditions are often encountered. The squeezing behavior of the ground is characterized by large time-dependent and usually anisotropic convergences that take place at the tunnel wall. The technique of excavation has a strong influence on the tunnel response when it is excavated under squeezing conditions. This phenomenon is illustrated throughout the case study of the Fréjus road tunnel excavated with conventional drill and blast methods and of its safety gallery excavated with a single shield tunneling boring machine. They exhibit a very interesting configuration of two tunnels excavated in parallel under the same geotechnical conditions but with different excavation techniques. Monitored geotechnical data from both tunnels are analyzed and compared. Numerical simulations of both tunnels have been carried out with Flac3D. An anisotropic creep model which includes weakness planes of given orientation embedded in a visco-elasto-plastic matrix has been used for describing the behavior of the ground. A back-analysis of convergence measurements of the Fréjus road tunnel has been carried out. The behavior of the ground identified from the Fréjus road tunnel is extrapolated to predict the response of the Fréjus safety gallery in terms of the stress state in the lining. The influence of the technique of excavation on the time-dependent parameters of the ground is taken into account in the computations and its effects are discussed. It is shown that the long term ground deformation are significantly reduced with TBM excavation as compared to traditional blast and drill method.Furthermore, the convergence-confinement methods are reviewed and their applicability is discussed when they are applied to full face circular tunnels excavated in rock masses with a stiff support system near the face. In this context, a set of empirical formula are proposed which allows to accurately predict the equilibrium state between the ground and the lining in circular tunnels excavated in full section. These formula are useful in the preliminary phase of tunnel design

Probabilistic graphical modeling is a framework which can be used to succinctly<br>represent multivariate probability distributions of time series in terms of each time<br>series’s dependence on others. In general, it is computationally prohibitive to sta-<br>tistically infer an arbitrary model from data. However, if we constrain the model to<br>have a tree topology, the corresponding learning algorithms become tractable. The<br>expressive power of tree-structured distributions are low, since only n − 1 dependen-<br>cies are explicitly encoded for an n node tree. One way to improve the expressive<br>power of tree models is to combine many of them in a mixture model. This work<br>presents and uses simulations to validate extensions of the standard mixtures of trees<br>model for i.i.d data to the setting of time series data. We also consider the setting<br>where the tree mixture itself forms a hidden Markov chain, which could be better<br>suited for approximating time-varying seasonal data in the real world. Both of these<br>are evaluated on artificial data sets.<br><br>

The electron transport through a molecular wire under the influence of an external laser field is studied using a reduced density matrix formalism. The full system is partitioned into the relevant part, i.e. the wire, electron reservoirs and a phonon bath. An earlier second-order perturbation theory approach of Meier and Tannor for bosonic environments which employs a numerical decomposition of the spectral density is used to describe the coupling to the phonon bath and is extended to deal with the electron transfer between the reservoirs and the molecular wire. Furthermore, from the resulting time-nonlocal (TNL) scheme a time-local (TL) approach can be determined. Both are employed to propagate the reduced density operator in time for an arbitrary time-dependent system Hamiltonian which incorporates the laser field non-perturbatively. Within the TL formulation, one can extract a current operator for the open quantum system. This enables a more general formulation of the problem which is necessary to employ an optimal control algorithm for open quantum systems in order to compute optimal control fields for time-distributed target states, e.g. current patterns. Thus, we take a fundamental step towards optimal control in molecular electronics. Numerical examples of the population dynamics, laser controlled current, TNL vs. TL and optimal control fields are presented to demonstrate the diverse applicability of the derived formalism.

Modern unsteady (multi-)field visualizations require an effective reduction of the data to be displayed. From a huge amount of information the most informative parts have to be extracted. Instead of the fuzzy application dependent notion of feature, a new approach based on information theoretic concepts is introduced in this paper to detect important regions. This is accomplished by extending the concept of local statistical complexity from finite state cellular automata to discretized (multi-)fields. Thus, informative parts of the data can be highlighted in an application-independent, purely mathematical sense. The new measure can be applied to unsteady multifields on regular grids in any application domain. The ability to detect and visualize important parts is demonstrated using diffusion, flow, and weather simulations.

The thesis describes time dependent fluorescence shift method and fluorescence correlation spectroscopy method (FCS) with its extensions FLCS, Z-scan FCS and dual-focus FCS applied on specific problems in DNA and lipid research. Compaction mechanism of a DNA molecule smaller than a resolution of a confocal microscope was elucidated. The process was revealed to be "all or non" for a polycation spermine as a condenser in contrast with the gradual compaction caused by a cationic surfactant. Biophysical properties of a phospholipid bilayer influenced by presence of oxidized phospholipids with truncated sn-2 chain were explored. The dynamics of hydrated functional groups in the headgroup region was proved to get faster while the hydration of the headgroup region increased. These effects are in relation with the reorientation of the short sn-2 chains observed in molecular dynamics simulations. Presence of oxidized species may also influence the lateral diffusion of the lipids - a slight increase of the diffusion coefficient was observed. Decrease of hydration and mobility in the headgroup region was found as an influence of heavy water on the phospholipid membrane. These finding are in line with molecular dynamics simulations which show longer lifetimes of hydrogen bonds between water and lipid molecules in...

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.