High-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime. The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time. / text

The problem of pile - soil interaction is examined in the Thesis at hand by means of both theoretical analyses and experimental investigations. Pile foundations in seismically prone areas are subjected to both direct loading, such as axial and lateral forces imposed at their heads, resulting from a phenomenon known as inertial interaction, and indirect loading along their body, such as imposed displacements due to the passage of various types of seismic waves, resulting from a phenomenon known as kinematic interaction. Along this vein, a family of analytical models of the Tajimi type are presented in the framework of linear elastodynamic theory to explore the effects of axial and lateral pile - soil interaction in homogeneous and inhomogeneous soil under static and dynamic (kinematic and inertial) loading. Apart from simplified two-dimensional models of the Baranov - Novak type, few analytical solutions are available to tackle these problems in three dimensions, the majority of which are restricted to the analysis of an elastic half space under static conditions. The proposed models are based on a continuum solution pioneered by Japanese investigators (notably Matuso & Ohara and Tajimi) in the 1960’s. In the realm of this approach the soil is modelled as a continuum, while the pile is conveniently modelled as a rod or a beam by strength-of-materials theory. Displacements and stresses are expressed through Fourier series in terms of the natural modes of the soil medium. Fundamental to the analysis presented in this study is that the influence of horizontal soil displacement on axial pile response and vertical displacement on lateral response, respectively, are negligible. However, their effect on stresses is not negligible which differentiates the proposed models from the classical Tajimi solutions in which the aforementioned displacements are set equal to zero. The above approximations are attractive, as they lead to a straightforward uncoupling of the equations of motions, even in inhomogeneous media, unlike the classical elastodynamic theory where the uncoupling is generally impossible in presence of inhomogeneity. Although approximate, the proposed models are advantageous over available analytical models and rigorous numerical schemes, as they require relative simple computations and provide excellent predictions of pile response at the frequency ranges of interest in earthquake engineering and geotechnics. In addition, they are advantageous over existing simplified analytical approaches of the Winkler type, as they are more accurate, self - standing, free of empirical constants and provide more realistic simulation of the problem. The main advantage over numerical methods (finite and boundary elements) lies in the derivation of the solution in closed form and the elucidation of complex mechanisms related to the dynamic interaction phenomenon, such as radiation damping and wave propagation in in homogeneous media. The main goal of the theoretical effort lies in the derivation of solutions in closed - form for: (i) the static stiffness and the dynamic impedances (dynamic stiffness and damping coefficients) at the pile head, (ii) translational and rotational kinematic response factors (pile head displacement or rotation over free-field response), (iii) actual, depth- dependent, Winkler moduli (spring and damping coefficients), (iv) corresponding average, depth- independent, Winkler moduli to match the pile head stiffness. In addition, simple approximate formulae for Winkler moduli to be used in engineering practice are proposed, to improve the predictions of Winkler models. Pile-to-pile interaction is investigated on the basis of the superposition method for axially loaded piles. Closed-form expressions for attenuation functions are derived to be used individually or in conjunction with more elaborate methods providing more accurate predictions for static and dynamic interaction factors to assess the vertical stiffness of pile groups. New dimensionless frequency ratios controlling pile response are introduced. Finally, new solutions are added in the context of analytical Winkler models for investigating the behaviour of piles under kinematic loading due to vertically-propagating S waves. Emphasis is given on the influence of boundary conditions of the pile. With reference to kinematic pile bending, insight into the physics of the problem is gained through a rigorous superposition scheme involving an infinitely-long pile excited kinematically, and a pile of finite length excited by a concentrated force and a moment at the tip. Contrary to the classical elastodynamic theory where pile response is governed by six dimensionless ratios, in the realm of Winkler theory three only ratios suffice to fully describe the interaction problem, from which the mechanical slenderness and the effective dimensionless frequency are introduced for the first time. The selection of an appropriate value for the Winkler modulus in the accuracy of the kinematic Winkler model is demonstrated. The theoretical results are compared to new experimental data obtained from a series of tests on piles carried out on scaled models performed on the shaking table at University of Bristol Laboratory (BLADE) within the framework of the Seismic Engineering Research Infrastructures (SERIES) program, sponsored by FP7, and contribute in the investigation of pile - soil interaction. / Στην παρούσα διατριβή εξετάζεται το πρόβλημα της αλληλεπίδρασης πασσάλου - εδάφους μέσω συνδυασμένης θεωρητικής ανάλυσης και πειραματικής διερεύνησης. Οι πάσσαλοι, ως μέσο θεμελίωσης σε σεισμογόνες περιοχές, υπόκεινται σε άμεση φόρτιση στην κεφαλή, μέσω δυνάμεων και ροπών, ως αποτέλεσμα του φαινομένου της αδρανειακής αλληλεπίδρασης, αλλά και σε έμμεση φόρτιση σε όλο τους το μήκος, μέσω επιβαλλόμενων εδαφικών μετακινήσεων, ως αποτέλεσμα του φαινομένου της κινηματικής αλληλεπίδρασης. Στην κατεύθυνση αυτή παρουσιάζεται η ανάπτυξη οικογένειας αναλυτικών προσομοιωμάτων τύπου Tajimi, στο πλαίσιο της γραμμικής ελαστοδυναμικής θεωρίας, για τη διερεύνηση της αξονικής και πλευρικής αλληλεπίδρασης πασσάλου - εδάφους σε ομοιογενείς και ανομοιογενείς εδαφικούς σχηματισμούς, υπό στατική και δυναμική φόρτιση κινηματικής και αδρανειακής μορφής. Εκτός από απλοποιημένα διδιάστατα προσομοιώματα τύπου Baranov - Novak, ελάχιστες αναλυτικές λύσεις είναι διαθέσιμες σε τρεις διαστάσεις, οι περισσότερες των οποίων περιορίζονται στην ανάλυση ελαστικού ημίχωρου υπό στατικές συνθήκες. Τα προτεινόμενα προσομοιώματα βασίζονται σε μια πρωτοποριακή λύση συνεχούς μέσου (κατά Matsuo & Ohara και Tajimi) η οποία αναπτύχθηκε στη δεκαετία του 1960, αλλά δεν επεκτάθηκε ουσιαστικά μέχρι την παρούσα εργασία. Στο πλαίσιο αυτής της προσέγγισης το έδαφος προσομοιώνεται ως συνεχές μέσο και ο πάσσαλος ως ράβδος ή δοκός σύμφωνα με τη τεχνική θεωρία της κάμψης (παραδοχή επιπεδότητας των διατομών), ενώ οι μετακινήσεις και οι τάσεις εκφράζονται μέσω αναπτυγμάτων Fourier σε όρους των φυσικών ιδιομορφών του εδαφικού μέσου. Θεμελιώδης παραδοχή της προτεινόμενης ανάλυσης είναι ότι η επιρροή της οριζόντιας εδαφικής μετακίνησης στην αξονική απόκριση του πασσάλου, αλλά και η επιρροή της κατακόρυφης μετακίνησης στην πλευρική απόκριση θεωρούνται αμελητέες, ωστόσο η επίδρασή τους στις τάσεις είναι μη μηδενική, πράγμα που τις διαφοροποιεί από τις κλασσικές λύσεις τύπου Tajimi στις οποίες οι ανωτέρω μετακινήσεις μηδενίζονται. Οι ανωτέρω προσεγγίσεις κρίνονται ως ιδιαίτερα ελκυστικές καθώς οδηγούν στην άμεση απόζευξη των εξισώσεων της κίνησης, ακόμη και σε ανομοιογενή μέσα, αντίθετα με την κλασσική ελαστοδυναμική θεωρία, η απόζευξη είναι γενικώς αδύνατη παρουσία εδαφικής ανομοιογένειας. Παρά τον προσεγγιστικό τους χαρακτήρα, τα προτεινόμενα αναλυτικά προσομοιώματα πλεονεκτούν ως προς διαθέσιμα αναλυτικά προσομοιώματα και αυστηρά αριθμητικά σχήματα, καθώς απαιτούν σχετικά απλούς υπολογισμούς και παρέχουν εξαιρετικές προβλέψεις της απόκρισης του πασσάλου για το εύρος συχνοτήτων που παρουσιάζει ενδιαφέρον στη σεισμική μηχανική και τα γεωτεχνικά. Επιπρόσθετα, υπερτερούν ως προς υφιστάμενες αναλυτικές προσεγγίσεις τύπου Winkler, καθώς είναι ακριβέστερα, αυτόνομα, απαλλαγμένα από εμπειρικές σταθερές και προσφέρουν ρεαλιστικότερη προσομοίωση του προβλήματος. Το κύριο πλεονέκτημα έναντι των αριθμητικών μεθόδων (πεπερασμένα και συνοριακά στοιχεία) έγκειται στην εξαγωγή της λύσης σε κλειστή μορφή και στη διερεύνηση πολύπλοκων φαινομένων που σχετίζονται με την αλληλεπίδραση πασσάλου - εδάφους, όπως αυτό της απόσβεσης ακτινοβολίας και της διάδοσης κυμάτων στο έδαφος - ειδικά παρουσία ανομοιογένειας. Ο κύριος στόχος της θεωρητικής διερεύνησης υλοποιείται με την εξαγωγή λύσεων σε κλειστή μορφή για: (i) τη στατική και δυναμική στιφρότητα και απόσβεση στην κεφαλή του πασσάλου, (ii) τους συντελεστές κινηματικής απόκρισης σε μετάθεση και στροφή, (iii) τους πραγματικούς, συναρτήσει του βάθους, συντελεστές Winkler (συντελεστής στιφρότητας ελατηρίων και συντελεστής απόσβεσης), (iv) τους αντίστοιχους μέσους, ανεξάρτητους από το βάθος, συντελεστές Winkler. Επιπρόσθετα, παρουσιάζονται ακριβέστερες των διαθέσιμων στη βιβλιογραφία απλές προσεγγιστικές σχέσεις για τον υπολογισμό του συντελεστή Winkler με σκοπό τη βελτίωση της ακρίβειας των προσομοιωμάτων Winkler. Διερευνάται η αλληλεπίδραση πασσάλου προς πάσσαλο στην περίπτωση αξονικά φορτισμένων πασσάλων με βάση την αρχή της επαλληλίας. Εξάγονται λύσεις σε κλειστή μορφή για τις συναρτήσεις εξασθένισης ώστε να χρησιμοποιηθούν αυτόνομα ή σε συνδυασμό με πιο εκλεπτυσμένες λύσεις δίνοντας με στόχο ακριβέστερες προβλέψεις για τους συντελεστές αλληλεπίδρασης, οδηγώντας έτσι σε πιο ρεαλιστικές εκτιμήσεις της κατακόρυφης στιφρότητας ομάδας πασσάλων. Εισάγονται νέοι αδιάστατοι λόγοι συχνοτήτων που καθορίζουν την απόκριση του πασσάλου. Τέλος, παρουσιάζονται νέες λύσεις σε αναλυτικά προσομοιώματα Winkler για τη διερεύνηση της συμπεριφοράς πασσάλων υποκείμενων σε φόρτιση λόγω της κατακόρυφης διάδοσης διατμητικών κυμάτων στο έδαφος, με έμφαση στην επίδραση των οριακών συνθηκών του προβλήματος. Σε αντίθεση με την κλασσική ελαστοδυναμική θεωρία που η απόκριση του πασσάλου καθορίζεται από έξι αδιάστατους λόγους, στο πλαίσιο της θεωρίας Winkler επαρκούν μόνο τρεις για την πλήρη περιγραφή της αλληλεπίδρασης πασσάλου - εδάφους, εκ των οποίων η μηχανική λυγηρότητα και η ενεργός αδιάστατη συχνότητα παρουσιάζονται για πρώτη φορά. Καταδεικνύεται η σημασία επιλογής της κατάλληλης τιμής του συντελεστή Winkler στην ακρίβεια των εν λόγω προσομοιωμάτων. Προτείνεται σύστημα υπέρθεσης που αποτελείται από ένα απειρομήκη πάσσαλο που διεγείρεται κινηματικά και έναν πάσσαλο πεπερασμένου μήκους που υπόκειται σε αδρανειακή φόρτιση για τη διαλεύκανση της λειτουργίας του θεμελιώδους μηχανισμού που καθορίζει την κινηματική κάμψη του πασσάλου. Τα θεωρητικά αποτελέσματα συγκρίνονται με νέα πειραματικά δεδομένα από σειρά δοκιμών σε διάταξη πασσάλων υπό κλίμακα που εκτελέστηκαν στο σεισμικό προσομοιωτή του Πανεπιστήμιου του Bristol στο πλαίσιο του Ευρωπαϊκού Προγράμματος SERIES, το οποίο χρηματοδοτήθηκε από το κοινοτικό πλαίσιο FP7 που συμβάλλουν στην περαιτέρω διερεύνηση του φαινομένου της κινηματικής αλληλεπίδρασης εδάφους - πασσάλου.

Ce mémoire présente l’évaluation du remodelage osseux autour des composantes acétabulaires non cimentées press-fit d’une arthroplastie de resurfaçage (RH) et d’une prothèse totale de hanche (PTH) après un minimum de 21 mois d’implantation. Nous avons mesuré par l’absorptiométrie à rayons X en double énergie (DEXA) la densité minérale osseuse (DMO) supra acétabulaire chez 60 patients (44 RH, 16 PTH). Aucune différence significative de la moyenne des DMO au niveau de la zone globale et de la zone centrale de l’acétabulum n’a été trouvée entre la hanche opérée et la hanche controlatérale, dans les deux groupes de traitement. Cependant, la DMO des zones corticospongieuses médiale et latérale est plus élevée du côté opéré par rapport au côté non opéré avec la cupule en chrome cobalt de la RH; (p=0,014 et 0,031 respectivement). Alors que pour la PTH avec une cupule en titane, la différence de la DMO au niveau de ces zones n’est pas significative; (p=0,130 et 0,733). Ces données semblent démontrer qu’avec des cupules plus rigides, il y a transfert des contraintes de charges vers la périphérie corticale. C’est la première étude à évaluer le remodelage osseux péri acétabulaire avec un RH. Cela montre que la DMO est relativement préservée et que le transfert des contraintes vers la périphérie peut être favorable au maintien de la stabilité de l’implant primaire et aux éventuelles révisions de la cupule press-fit du RH. / We undertook a retrospective study to evaluate bone remodeling around two uncemented press-fit acetabular components: (1. Hip resurfacing (HR) and 2. total hip replacement (THR)) at a minimum of 21 months after implantation. We measured by DEXA (Dual energy X ray absorptiometry) the bone mineral density (BMD) in the supra acetabular area in 60 patients (44 HR, 16 THR). We found no significant difference in the average BMD of the global zone and central zone of the acetabulum between the operated hip and the opposite non-operated hip in both treatment groups. However, the BMD of the medial and lateral cortico-cancellous areas on the side of surgery was significantly higher compared to non-operated side in HR group with the cobalt chrome cup; (p=0,014 and 0,031 respectively) As for THR with a titanium cup, we found no significant difference in BMD at these areas (p=0,130 and 0,733). These data show that with more rigid cups, there seems to be greater load transfer to the periphery of the acetabulum without significant stress shielding. This is the first study to assess peri-acetabular bone remodeling with HR. We showed that BMD is relatively preserved. Stress transfer to the periphery may be beneficial in maintaining the stability of the primary implant while conserving bone stock for possible revisions of the press-fit cup of the HR.

Chapter 1: I analyze economies of scale for fire and police services by considering how per-household costs are affected by a municipality’s size. Using 2005-2008 municipal data for the Province of Ontario, I employ a partial-linear model to non-parametrically estimate per-household cost curves for each service. The results show that cost per household is a U-shaped function of municipal size for each service. For fire services, these costs are minimized at a population of about 20,000 residents, while for police services they are minimized at about 50,000 residents. Based on these results, implications are drawn for municipal amalgamation policy. Chapter 2: I review how the literature has continued to exclude the business property tax (BPT) from the marginal effective tax rate (METR) on capital investment for over 25 years. I recast the METR theory as it relates to the BPT and compute 2013 estimates of the METR for all 10 provinces in Canada with provincial BPTs included. Building on these estimates, I compute the METR inclusive of municipal BPTs for the largest municipality in each province. I find the BPT to be substantially damaging to municipal, provincial and international competitiveness. With the business property tax representing over 60% of the Canadian METR, among the various capital taxes it is by far the largest contributor to Canada’s investment barrier. Chapter 3: I estimate the responsiveness of structure investment and the tax base to commercial property taxes, taking a new step toward resolving the “benefit view” vs. “capital tax view” debate within the literature. Using a first-difference structural model to analyze 2006-2013 municipal data for the Province of Ontario, I improve upon past studies and build onto the literature in a number of ways. I find that commercial structure investment and tax base are highly sensitive to the property tax with Ontario’s assessment-weighted average tax elasticity (and tax-base elasticity) ranging from -0.80 to -0.90 at 2011 taxation levels. The results support the capital tax view of the business property tax, building onto the growing consensus that business property taxes substantially impact investment in structures and the value of the tax base.

The importance of fire safety design has been realised due to the ever increasing loss of properties and lives caused by structural failures during fires. In recognition of the importance of fire safety design, extensive research has been undertaken in the field of fire safety of buildings and structures especially over the last couple of decades. In the same period, the development of fire safety engineering principles has brought significant reduction to the cost of fire protection. However the past fire research on steel structures has been limited to heavier, hot-rolled structural steel members and thus the structural behaviour of light gauge cold-formed steel members under fire conditions is not well understood. Since cold-formed steel structures have been commonly used for numerous applications and their use has increased rapidly in the last decade, the fire safety of cold-formed steel structural members has become an important issue. The current design standards for steel structures have simply included a list of reduction factors for the yield strength and elasticity modulus of hot-rolled steels without any detailed design procedures. It is not known whether these reduction factors are applicable to the commonly used thin, high strength steels in Australia. Further, the local buckling effects dominate the structural behaviour of light gauge cold-formed steel members. Therefore an extensive research program was undertaken at the Queensland University of Technology to investigate the local buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. The first phase of this research program included 189 tensile coupon tests including three steel grades and six thicknesses to obtain the accurate yield strength and elasticity modulus values at elevated temperatures because the deterioration of the mechanical properties is the major parameter in the structural design under fire conditions. The results obtained from the tensile tests were used to predict the ultimate strength of cold-formed steel members. An appropriate stress-strain model was also developed by considering the inelastic mechanical characteristics. The second phase of this research was based on a series of more than 120 laboratory experiments and corresponding numerical analyses on cold-formed steel compression members to investigate the local bucking behaviour of the unstiffened flange elements, stiffened web elements and stiffened web and flange elements at elevated temperatures up to 800°C. The conventional effective design rules were first simply modified considering the reduced mechanical properties obtained from the tensile coupon tests and their adequacy was studied using the experimental and numerical results. It was found that the simply modified effective width design rules were adequate for low strength steel members and yet was not adequate for high strength cold-formed steel members due to the severe reduction of the ultimate strength in the post buckling strength range and the severe reduction ratio of the elasticity modulus to the yield strength at elevated temperatures. Due to the inadequacy of the current design rules, the theoretical, semi-empirical and empirical effective width design rules were developed to accurately predict the ultimate strength of cold-formed steel compression members subject to local buckling effects at elevated temperatures. The accuracy of these new design methods was verified by comparing their predictions with a variety of experimental and numerical results. This thesis presents the details of extensive experimental and numerical studies undertaken in this research program and the results including comparison with simply modified effective width design rules. It also describes the advanced finite element models of cold-formed steel compression members developed in this research including the appropriate mechanical properties, initial imperfections, residual stresses and other significant factors. Finally, it presents the details of the new design methods proposed for the cold-formed steel compression members subject to local buckling effects at elevated temperatures.

The provision of clean drinking water typically involves treatment processes to remove contaminants. The conventional process involves coagulation with hydrolysing metal salts, typically of aluminium (‘alum’) or trivalent iron (‘ferric’). Along with the product water this also produces a waste by-product, or sludge. The fact of increasing sludge production — due to higher levels of treatment and greater volume of water supply — conflicts with modern demands for environmental best practice, leading to higher financial costs. A further issue is the significant quantity of water that is held up in the sludge, and wasted. / One means of dealing with these problems is to dewater the sludge further. This reduces the volume of waste to be disposed of. The consistency is also improved (e.g. for the purpose of landfilling). And a significant amount of water can be recovered. The efficiency, and efficacy, of this process depends on the dewaterability of the sludge.In fact, good dewaterability is vital to the operation of conventional drinking water treatment plants (WTP’s). The usual process of separating the particulates, formed from a blend of contaminants and coagulated precipitate, relies on ‘clarification’ and ‘thickening’, which are essentially settling operations of solid–liquid separation.WTP operators — and researchers — do attempt to measure sludge dewaterability, but usually rely on empirical characterisation techniques that do not tell the full story and can even mislead. Understanding of the physical and chemical nature of the sludge is also surprisingly rudimentary, considering the long history of these processes. / The present work begins by reviewing the current state of knowledge on raw water and sludge composition, with special focus on solid aluminium and iron phases and on fractal aggregate structure. Next the theory of dewatering is examined, with the adopted phenomenological theory contrasted with empirical techniques and other theories.The foundation for subsequent analyses is laid by experimental work which establishes the solid phase density of WTP sludges. Additionally, alum sludges are found to contain pseudoböhmite, while 2-line ferrihydrite and goethite are identified in ferric sludges. / A key hypothesis is that dewaterability is partly determined by the treatment conditions. To investigate this, numerous WTP sludges were studied that had been generated under diverse conditions: some plant samples were obtained, and the remainder were generated in the laboratory (results were consistent). Dewaterability was characterised for each sludge in concentration ranges relevant to settling, centrifugation and filtration using models developed by LANDMAN and WHITE inter alia; it is expressed in terms of both equilibrium and kinetic parameters, py(φ) and R(φ) respectively.This work confirmed that dewaterability is significantly influenced by treatment conditions.The strongest correlations were observed when varying coagulation pH and coagulant dose. At high doses precipitated coagulant controls the sludge behaviour, and dewaterability is poor. Dewaterability deteriorates as pH is increased for high-dose alum sludges; other sludges are less sensitive to pH. These findings can be linked to the faster coagulation dynamics prevailing at high coagulant and alkali dose.Alum and ferric sludges in general had comparable dewaterabilities, and the characteristics of a magnesium sludge were similar too.Small effects on dewaterability were observed in response to variations in raw water organic content and shearing. Polymer flocculation and conditioning appeared mainly to affect dewaterability at low sludge concentrations. Ageing did not produce clear changes in dewaterability.Dense, compact particles are known to dewater better than ‘fluffy’ aggregates or flocs usually encountered in drinking water treatment. This explains the superior dewaterability of a sludge containing powdered activated carbon (PAC). Even greater improvements were observed following a cycle of sludge freezing and thawing for a wide range of WTP sludges. / Further aspects considered in the present work include deviations from simplifying assumptions that are usually made. Specifically: investigation of long-time dewatering behaviour, wall effects, non-isotropic stresses, and reversibility of dewatering (or ‘elasticity’).Several other results and conclusions, of both theoretical and experimental nature, are presented on topics of subsidiary or peripheral interest that are nonetheless important for establishing a reliable basis for research in this area. / This work has proposed links between industrial drinking water coagulation conditions, sludge dewaterability from settling to filtration, and the microstructure of the aggregates making up that sludge. This information can be used when considering the operation or design of a WTP in order to optimise sludge dewaterability, within the constraints of producing drinking water of acceptable quality.

Thesis (Ph. D.)--Kyoto University, 1984. / Includes bibliographical references and indexes.

This thesis concerns the mathematical modelling of phase transformations with a special emphasis on martensitic phase transformations and their application to the modelling of steels. In Chapter 1, we develop a framework that determines the optimal transformation strain between any two Bravais lattices and use it to give a rigorous proof of a conjecture by E.C. Bain in 1924 on the optimality of the so-called Bain strain. In Chapter 2, we review the Ball-James model and related concepts. We present some simplification of existing results. In Chapter 3, we pose a conjecture for the explicit form of the quasiconvex hull of the three tetragonal wells, known as the three-well problem. We present a new approach to finding inner and outer bounds. In Chapter 4, we focus on highly compatible, so called self-accommodating, martensitic structures and present new results on their fine properties such as estimates on their minimum complexity and bounds on the relative proportion of each martensitic variant in them. In Chapter 5, we investigate the contrary situation when self-accommodating microstructures do not exist. We determine, whether in this situation, it is still energetically favourable to nucleate martensite within austenite. By constructing different types of inclusions, we find that the optimal shape of an inclusion is flat and thin which is in agreement with experimental observation. In Chapter 6, we introduce a mechanism that identifies transformation strains with orientation relationships. This mechanism allows us to develop a simpler, strain-based approach to phase transformation models in steels. One novelty of this approach is the derivation of an explicit dependence of the orientation relationships on the ratio of tetragonality of the product phase. In Chapter 7, we establish a correspondence between common phenomenological models for steels and the Ball-James model. This correspondence is then used to develop a new theory for the (5 5 7) lath transformation in low-carbon steels. Compared to existing theories, this new approach requires a significantly smaller number of input parameters. Furthermore, it predicts a microstructure morphology which differs from what is conventionally believed.

Dans cette thèse sur travaux, l’auteur part de deux travaux précédents sur la rentabilité de la fidélisation et la détermination du potentiel client pour faire un constat : une partie de la rentabilité de la fidélisation et du potentiel pour une marque est basée sur la part captable du chiffre d’affaire fait à la concurrence ; le taux de captation.Dans ce nouveau travail il s’agit de montrer que le taux de captation est basé sur l’élasticité du taux de nourriture. A partir d’une analyse de la littérature et de plusieurs modélisations sur des données de panel scannérisées, l’auteur démontre, sur plusieurs marchés, que l’élasticité du taux de nourriture est contrainte et prévisible.C’est donc en tenant compte de cet écart limité qu’une marque peut estimer le taux de captation et donc la rentabilité de la fidélisation ainsi que le potentiel client. / In this thesis based on works the author goes from two previous studies on the profitability of loyalty and customer potential determination to make a statement : part of the profitability of loyalty and of the potential for a brand is based on the reachable share of turnover done by the competition ; the catch rate.In this new work it is shown that the catch rate is based on the elasticity of the share of category requirement. From a review of the literature and several modeling on scanning panel data the author demonstrates on several markets that elasticity of the share of category requirement is limited and predictable.Then it’s in taking into account this small difference that a brand can estimate the “catchable” rate and therefore the profitability of loyalty and potential of a customer.

Title: Fluid-structure interaction of compressible flow Author: RNDr. Jaroslava Hasnedlová Department: Department of Numerical Mathematics, Institute of Applied Mathematics Supervisors: Prof. RNDr. Miloslav Feistauer, DrSc., Dr. h. c., Prof. Dr. Dr. h. c. Rolf Rannacher Supervisors' e-mail addresses: feist@karlin.mff.cuni.cz, rannacher@iwr.uni-heidelberg.de Abstract: The presented work is split into two parts. The first part is devoted to the theory of the discontinuous Galerkin finite element (DGFE) method for the space-time discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The DGFE method is applied sep- arately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time discretization. The main result is the proof of error estimates in L2 (L2 )-norm and in DG-norm formed by the L2 (H1 )-seminorm and penalty terms. The second part of the thesis deals with the realization of fluid-structure interaction problem of the compressible viscous flow with the elastic structure. The time-dependence of the domain occupied by the fluid is treated by the ALE (Arbitrary Lagrangian-Eulerian) method, when the compress- ible Navier-Stokes equations are formulated in...