Identification of material properties for elastic materials is important in mechanics, material sciences, mechanical engineering and biomedical engineering. Although the principle and techniques have been long established, the application in living biology still faces challenges. The biological materials are in general nonlinear, anisotropic, heterogeneous, and subject-specific. The difficulty is compounded sometimes by the requirement of non-destructiveness in medical applications. Recently, the pointwise identification method (PWIM) was proposed to address some of the needs of soft tissue characterization. PWIM is a non-invasive identification method, designed for thin materials; it can sharply characterize arbitrary heterogeneous property distributions. The primary goal of this thesis is to extend the pointwise identification method , originally developed for membranes which by default is of convex shape in pressurized states, to thin structures of arbitrary geometry. This work consists of four parts. The first part investigates the insensitivity of stress solution to material parameters in thin shell structures. This is an important first step, because PWIM hinges on the static determinacy property of the equilibrium problem of membranes. Before introducing the shell element into PWIM, it is necessary to test to what extent the assumption of static determinacy remains reasonable. It is shown that saccular structure which bending stress is small compared to in-plane stress, can still be treated as a statically determined structure. The second part focuses on developing finite element formulations of forward and inverse shell methods for a hyperelastic material model specifically proposed for cerebral aneuryms tissues. This is a preparatory step for the core development. The third part is the development of pointwise identification method for thin shell structures. Methods for stress solution, strain acquisition, and parameter regression will be discussed in detail. The entire process is demonstrated using an example of a geometrically realistic model of aneurysm. The fourth part is testing the applicability on geometrically realistic cerebral aneurysms. Six models were selected in the study; the emphasis is placed on cerebral aneurysm with concave or saddle surface region for which the use of shell theory is a must. The identification results of all six human cerebral aneurysms successfully demonstrate that the shell PWIM can be applied to realistic cerebral aneurysms. Four types of heterogeneous property distributions are considered in the study. It is found that the method can accurately back out the property distributions in all cases. Fiber directions can also be accurately estimated. The robustness of the method at the presentence of numerical noise is also investigated. It is shown that the shell PWIM still works when small perturbations exist in displacements.

Schema mappings have been extensively studied in the context of data exchange and data integration, where they have turned out to be the right level of abstraction for formalizing data interoperability tasks. Up to now and for the most part, schema mappings have been studied as static objects, in the sense that each time the focus has been on a single schema mapping of interest or, in the case of composition, on a pair of schema mappings of interest. In this paper, we adopt a dynamic viewpoint and embark on a study of sequences of schema mappings and of the limiting behavior of such sequences. To this effect, we first introduce a natural notion of distance on sets of finite target instances that expresses how "Close" two sets of target instances are as regards the certain answers of conjunctive queries on these sets. Using this notion of distance, we investigate pointwise limits and uniform limits of sequences of schema mappings, as well as the companion notions of pointwise Cauchy and uniformly Cauchy sequences of schema mappings. We obtain a number of results about the limits of sequences of GAV schema mappings and the limits of sequences of LAV schema mappings that reveal striking differences between these two classes of schema mappings. We also consider the completion of the metric space of sets of target instances and obtain concrete representations of limits of sequences of schema mappings in terms of generalized schema mappings, that is, schema mappings with infinite target instances as solutions to (finite) source instances.

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This thesis consists of an introduction and a summary, followed by two papers, both of them on the topic of function spaces on fractals. Paper I: Andreas Brodin, Pointwise Convergence of Haar type Wavelets on Self-Similar Sets, Manuscript. Paper II: Andreas Brodin, Regularization of Wavelet Expansion characterizes Besov Spaces on Fractals, Manuscript. Properties of wavelets, originally constructed by A. Jonsson, are studied in both papers. The wavelets are piecewise polynomial functions on self-similar fractal sets. In Paper I, pointwise convergence of partial sums of the wavelet expansion is investigated. On a specific fractal set, the Sierpinski gasket, pointwise convergence of the partial sums is shown by calculating the kernel explicitly, when the wavelets are piecewise constant functions. For more general self-similar fractals, pointwise convergence of the partial sums and their derivatives, in case the expanded function has higher regularity, is shown using a different technique based on Markov's inequality. A. Jonsson has shown that on a class of totally disconnected self-similar sets it is possible to characterize Besov spaces by means of the magnitude of the coefficients in the wavelet expansion of a function. M. Bodin has extended his results to a class of graph directed self-similar sets introduced by Mauldin and Williams. Unfortunately, these results only holds for fractals such that the sets in the first generation of the fractal are disjoint. In Paper II we are able to characterize Besov spaces on a class of fractals not necessarily sharing this condition by making the wavelet expansion smooth. We create continuous regularizations of the partial sums of the wavelet expansion and show that properties of these regularizations can be used to characterize Besov spaces.

In this paper, we show that a pointwise λ -symmetric λ -isotonic λ -closure function is uniquely determined by the pairs of sets it separates. We then show that when the λ -closure function of the domain is λ -isotonic and the λ -closure function of the codomain is λ -isotonic and pointwise- λ -symmetric, functions which separate only those pairs of sets which are already separated are λ -continuous.

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In the context of an aviation industry whose top priority is to face the sustainability challenge, the growing civil UAV branch is not an exception. Hydrogen-powered UAVs equipped with PEM (Polymer Electrolyte Membrane) fuel cells are more and more frequently identified as the most convincing and promising technology, particularly for long-endurance mission requirements. However, the onboard carriage of a hydrogen fuel cell leads to unexplored internal flow characteristics, including the introduction of water vapour. The purpose of this master thesis is to develop a valid CFD model and methodology for the internal flow simulation of hydrogen-powered UAVs. Given the strict environmental operational requirements of PEM fuel cells, the intended application of the model is to effectively assess the evolution of the internal bay flow temperature and humidity fields. An explicit-time fourth-order Runge-Kutta projection method is tested successfully on a sample 2D case setup. The case geometry and flow conditions are inspired by the Green Raven UAV project conceived by the Department of Aeronautical and Vehicle Engineering at KTH. / I samband med en flygindustri vars högsta prioritet är att bemöta hållbarhetsutma- ningen är den växande civila UAV-sektorn inget undantag. Vätgasdrivna UAV:er utrustade med PEM (Polymer Electrolyte Membrane) bränsleceller betecknas allt oftare som den mest övertygande och lovande teknologin, särskilt för att de ska kunna utföra långvariga uppdrag. Den ombordgående transporten av en vätebränslecell leder emellertid till outforskade inre flödesfenomen, inklusive alstrad vattenånga. Syftet med detta examensarbete är att utveckla en lämplig CFD-modell och metodik för intern flödesimulering av vätgasdrivna UAV. Med tanke på de strikta miljökraven för PEM-bränsleceller är modellens avsedda tillämpning att eektivt utvärdera utvecklingen av de inre flödestemperaturerna och luftfuktighetsfälten. En tidsexplicit Runge-Kutta-projektionsmetod av fjärde ordningen testas framgångsrikt på ett 2D-exempel. Fallets geometri och flödesförhållanden är inspirerade av Green Raven UAV-projektet som utförts på Farkost och Flyg avdelningen på KTH.

This thesis is a survey of the studies of Ames,Payne and Schaefer about the partial differential equations with nonstandard auxiliary conditions / this is where the values of the solution are prescribed as a combination of initial time t=0 and at a later time t=T. The first chaper is introductory and contains some historical background of the problem,basic definitions and theorems.In Chapter 2 energy bounds and pointwise bounds for the solutions of the nonstandard hyperbolic problems have been investigated and by means of energy bound the uniqueness of solutions is examined. Similar discussions for the nonstandard parabolic problems have been presented in Chapter 3. Lastly in Chapter 4 a new continuous dependence result has been derived for the nonstandard problem.

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