Η εν λόγω διπλωματική εργασία αναφέρεται σε κάποια γενικά στοιχεία των μεθόδων ελέγχου του οριακού στρώματος και εστιάζεται στον έλεγχο του οριακού στρώματος με εφαρμογή της μεθόδου απορρόφησης – έγχυσης. Πιο συγκεκριμένα, στο πρώτο κεφάλαιο, με γενικό τίτλο “Οριακό Στρώμα”, αναφέρονται κάποια σύντομα ιστορικά στοιχεία και εισάγεται η έννοια του οριακού στρώματος. Στη συνέχεια, και αφού αποσαφηνιστεί η έννοια του οριακού στρώματος με τη βοήθεια εικόνων και γραφικών, εισάγονται τα χαρακτηριστικά μεγέθη αυτού. Το κεφάλαιο κλείνει με μια περιγραφή του φαινομένου της αποκόλλησης του οριακού στρώματος και των συνεπειών που η αποκόλληση αυτή επιφέρει στη ροή. Στο δεύτερο κεφάλαιο, με γενικό τίτλο “Έλεγχος του Οριακού Στρώματος”, περιγράφονται συνοπτικά οι βασικές μέθοδοι ελέγχου του οριακού στρώματος καθώς και τα πιο διαδεδομένα πεδία εφαρμογής της κάθε μιας εξ’ αυτών. Συγκεκριμένα, αναφέρονται οι μέθοδοι Κίνησης του Στερεού Ορίου (Motion of the Solid Wall), Επιτάχυνσης του Οριακού Στρώματος (Acceleration of the Boundary Layer - Blowing), Ψύξης του Τοιχώματος (Cooling of the Wall), Έγχυσης Διαφορετικού Αερίου (Injection of a Different Gas), Πρόληψης της μετάπτωσης της ροής σε τυρβώδη με κατάλληλη διαμόρφωση της γεωμετρίας του στερεού (Laminar Aerofoils) και η παράγραφος κλείνει με μια πιο εκτενή περιγραφή της μεθόδου της Απορρόφησης (Suction). Στο τρίτο κεφάλαιο, που φέρει το γενικό τίτλο “Εξισώσεις Κίνησης και Εξισώσεις Οριακού Στρώματος για Ομογενή, Ασυμπίεστα, Πραγματικά Ρευστά”, παρατίθενται οι εν λόγω εξισώσεις, ώστε να χρησιμοποιηθούν στη συνέχεια, και γίνεται μια σύντομη αναφορά στον τρόπο που, ιστορικά, αυτές παρήχθησαν. Το τέταρτο κεφάλαιο, με τίτλο “Θεωρητική Μελέτη της Μεθόδου της Απορρόφησης”, προχωράει τη μελέτη της μεθόδου απορρόφησης/έγχυσης σε επίπεδο μαθηματικών εξισώσεων. Πιο συγκεκριμένα, εισάγονται τα βασικά στοιχεία της θεωρίας και στη συνέχεια, με ένα συνδυασμό αναλυτικών και αριθμητικών διαδικασιών, πραγματοποιείται η μελέτη της απορρόφησης σε δύο συγκεκριμένα παραδείγματα. Τέλος, στο πέμπτο κεφάλαιο, με τίτλο “Εφαρμογή Απορρόφησης/Έγχυσης σε Μαγνητοϋδροδυναμική Συμπιεστή Ροή Στρωτού Οριακού Στρώματος”, μελετάται η μόνιμη, στρωτή, διδιάστατη, μαγνητοϋδροδυναμική ροή, συμπιεστού οριακού στρώματος που δημιουργείται πάνω από λεπτή, επίπεδη επιφάνεια (πλάκα), με αντίξοη βαθμίδα πίεσης και μεταφορά θερμότητας και μάζας, καθώς και τα αποτελέσματα της εφαρμογής απορρόφησης ή έγχυσης στο παραπάνω πρόβλημα. Πιο συγκεκριμένα, μετά από μια σύντομη ιστορική εισαγωγή επί του θέματος, ακολουθεί η περιγραφή του προβλήματος, καθώς και η αδιαστατοποίηση των εξισώσεων που το διέπουν. Στη συνέχεια, ακολουθεί η περιγραφή της αριθμητικής μεθόδου που χρησιμοποιείται για την επίλυση των αδιαστατοποιημένων εξισώσεων και παρατίθενται τα αποτελέσματα που προκύπτουν από τη διαδικασία αυτή της αριθμητικής επίλυσης. Το κεφάλαιο κλείνει με μια συνοπτική παράθεση των συμπερασμάτων της μελέτης του κεντρικού προβλήματος του κεφαλαίου. / This master thesis refers to some general elements of boundary layer control methods and focuses on the method of suction-injection. In particular, in Chapter I, which is simply entitled “Boundary Layer”, a short reference to some historical facts associated with this subject is being made and the general idea of boundary layer is being introduced. Following, the idea of boundary layer is being clarified with the aid of some pictures and some graphics. The chapter ends with an introduction to the phenomenon of boundary layer separation. In Chapter II, carrying the general title “Boundary Layer Control”, a short description of some of the most basic methods of boundary layer control is given and the general conditions under which each method is more effective are being briefly stated. In particular, the methods which are brought up are Motion of the Solid Wall, Acceleration of the Boundary Layer – Blowing, Cooling of the Wall, Injection of a Different Gas, Laminar Aerofoils, and the chapter ends with a more extensive description of the method of Suction. In Chapter III, entitled “Equations of Motion and Boundary Layer Equations for Homogenous, Non-Compressible, Real Fluids”, the above equations are described, with the purpose of further use in the following chapters and a short reference to the way those equations were historically introduced is being made Chapter IV, with the general title “Theoretical Study of the Method of Suction”, carries the study of the method of suction-injection to the context of mathematical equations. More specifically, basic elements of the theory are being introduced and, after that, with a combination of analytical and arithmetical techniques, two simple examples are being studied. Finally, in Chapter V entitled “Application of Suction-Injection to Magnetohydrodynamic Compressible Flow of a Laminar Boundary Layer”, the steady, laminar, two dimensional, magnetohydrodynamic flow of the compressible boundary layer which is formed over a thin flat plate, with an adverse pressure gradient and mass and heat transfer is being studied along with the results of suction-injection in the above problem. In particular, after a short historical introduction follows the description of the problem and the normalization of the equations which describe it. Then follows the description of the arithmetical method and the program being used, and the results of this procedure are stated in the next paragraph. The chapter closes with a brief description of the facts which result from the general study of the main problem of this chapter.

Our study is focused on the behavior of grain boundaries in uranium dioxide system under irradiation conditions. The research can be seen as two parts: the study of interaction of the grain boundary and the damage cascade, and the calculation of Kapitza resistance of grain boundaries. The connection between these two parts lies in that damage cascades bring in changes in the structure and other properties of grain boundaries, and inevitably the Kapitza resistance of the grain boundary changes as well. For the first part, we studied interactions of grain boundaries and damage cascades in uranium dioxide system by simulating two types of bombardments: one direct bombardment into a grain boundary leading to ballistic-collision-mediated interface mixing; the other bombardment is in the close vicinity of a grain boundary causing interface biased defect migration. We found that more defects are trapped by the grain boundary followed by the first type of bombardment, resulting in enhanced grain boundary energy. By comparing with the second type of bombardment, we are able to reveal the mechanisms of the interaction between defects and grain boundaries. For the second part, we employed the non-equilibrium molecular dynamics method to calculate the Kapitza resistance of different coincident site lattice boundaries with or without defects loaded, and later we found that a universal positive correlation between the Kapitza resistance and the grain boundary energy can be well established, regardless of the cause of boundary energy changes. Our study provides a deeper understanding of the Kapitza resistance of the grain boundary and its evolutions under irradiation, which benefits multi-scale modeling of uranium dioxide thermal properties under extreme radiation conditions as well as experimental studies of fuel material thermal properties.

Doctor of Philosophy / We consider the problem of minimising the eigenvalues of the Laplacian with Robin boundary conditions $\frac{\partial u}{\partial \nu} + \alpha u = 0$ and generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$ with respect to the domain $\Omega \subset \mathbb R^N$ on which the problem is defined. For the Robin problem, when $\alpha > 0$ we extend the Faber-Krahn inequality of Daners [Math. Ann. 335 (2006), 767--785], which states that the ball minimises the first eigenvalue, to prove that the minimiser is unique amongst domains of class $C^2$. The method of proof uses a functional of the level sets to estimate the first eigenvalue from below, together with a rearrangement of the ball's eigenfunction onto the domain $\Omega$ and the usual isoperimetric inequality. We then prove that the second eigenvalue attains its minimum only on the disjoint union of two equal balls, and set the proof up so it works for the Robin $p$-Laplacian. For the higher eigenvalues, we show that it is in general impossible for a minimiser to exist independently of $\alpha > 0$. When $\alpha < 0$, we prove that every eigenvalue behaves like $-\alpha^2$ as $\alpha \to -\infty$, provided only that $\Omega$ is bounded with $C^1$ boundary. This generalises a result of Lou and Zhu [Pacific J. Math. 214 (2004), 323--334] for the first eigenvalue. For the Wentzell problem, we (re-)prove general operator properties, including for the less-studied case $\beta < 0$, where the problem is ill-posed in some sense. In particular, we give a new proof of the compactness of the resolvent and the structure of the spectrum, at least if $\partial \Omega$ is smooth. We prove Faber-Krahn-type inequalities in the general case $\beta, \gamma \neq 0$, based on the Robin counterpart, and for the ``best'' case $\beta, \gamma > 0$ establish a type of equivalence property between the Wentzell and Robin minimisers for all eigenvalues. This yields a minimiser of the second Wentzell eigenvalue. We also prove a Cheeger-type inequality for the first eigenvalue in this case.

Boundary-layer flows near leading edges of generally curved obstacles have been studied for a long time. Apart from having many practical applications, the theory and approaches prevailing in this area stimulate development of a variety of computational tools and form a ground for testing them. The specific aim of this work is to study two-dimensional laminar boundary layer flows near the leading edges of airfoils and other elongated bodies, and to explore geometries for which boundary layer separation can be avoided. This class of problems is relevant to optimal design of wings, aircraft and projectile noses, laminar flow control methods and adaptive wing technology. One of the findings of this work suggests that local modifications to parabolic wing noses can yield up to 11% increase in the unseparated angle of attack. Another result obtained here is the set of shortest possible generalised elliptic noses of long symmetric bodies which allow unseparated flow. Methods adopted in this work are based on the combined use of numerically solved Prandtl equations written in Gortler variables, and inviscid solutions obtained semi-analytically by the conformal mapping method. The resulting technique being reliable, fast and computationally inexpensive, can complement or test the results obtained using a comprehensive CFD approach. / Thesis (Ph.D.)--School of Mathematical Sciences, 2002.

Doctor of Philosophy (PhD) / For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models.

Doctor of Philosophy / We consider the problem of minimising the eigenvalues of the Laplacian with Robin boundary conditions $\frac{\partial u}{\partial \nu} + \alpha u = 0$ and generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$ with respect to the domain $\Omega \subset \mathbb R^N$ on which the problem is defined. For the Robin problem, when $\alpha > 0$ we extend the Faber-Krahn inequality of Daners [Math. Ann. 335 (2006), 767--785], which states that the ball minimises the first eigenvalue, to prove that the minimiser is unique amongst domains of class $C^2$. The method of proof uses a functional of the level sets to estimate the first eigenvalue from below, together with a rearrangement of the ball's eigenfunction onto the domain $\Omega$ and the usual isoperimetric inequality. We then prove that the second eigenvalue attains its minimum only on the disjoint union of two equal balls, and set the proof up so it works for the Robin $p$-Laplacian. For the higher eigenvalues, we show that it is in general impossible for a minimiser to exist independently of $\alpha > 0$. When $\alpha < 0$, we prove that every eigenvalue behaves like $-\alpha^2$ as $\alpha \to -\infty$, provided only that $\Omega$ is bounded with $C^1$ boundary. This generalises a result of Lou and Zhu [Pacific J. Math. 214 (2004), 323--334] for the first eigenvalue. For the Wentzell problem, we (re-)prove general operator properties, including for the less-studied case $\beta < 0$, where the problem is ill-posed in some sense. In particular, we give a new proof of the compactness of the resolvent and the structure of the spectrum, at least if $\partial \Omega$ is smooth. We prove Faber-Krahn-type inequalities in the general case $\beta, \gamma \neq 0$, based on the Robin counterpart, and for the ``best'' case $\beta, \gamma > 0$ establish a type of equivalence property between the Wentzell and Robin minimisers for all eigenvalues. This yields a minimiser of the second Wentzell eigenvalue. We also prove a Cheeger-type inequality for the first eigenvalue in this case.

[Truncated abstract] The scaled boundary method is a powerful, though undervalued, computational analysis method. The complex mathematics of the original derivation of the method has rendered it unattractive to researchers. However, the method has proven more efficient than conventional computational analysis methods for problems involving unbounded domains and for problems involving stress singularities. The advantages of the scaled boundary method in dealing with stress singularities make it uniquely suited to the analysis of fracture mechanics problems. This study will extend the capabilities of the scaled boundary method, exploring fracture mechanics applications in particular. Only benchmark elastostatic fracture mechanics problems are analysed as the focus of this work is the development of the scaled boundary method. It will be demonstrated that the intimidating mathematics of the method can be distilled into an elegant method which offers considerable advantages when used in the analysis of crack problems. This thesis will argue that the advantages of the scaled boundary method make it more valuable than is generally perceived and that coming to grips with the sometimes intimidating method is worthwhile. In this study, a significant contribution is made to the development of the scaled boundary method with a number of advances. The scaled boundary method is used to determine the higher order terms in asymptotic crack tip fields. The higher order terms play an important role in characterising the behaviour of cracked structures, but can only be evaluated analytically for a few simple cases. The higher order terms for a number of crack configurations are calculated using the scaled boundary method. Excellent agreement with results obtained from the literature is demonstrated. A penalty formulation is developed for use with a recently developed solution procedure for the scaled boundary method. The new solution procedure is based on the theory of matrix functions and the real Schur decomposition. ... A study is presented of error estimation and adaptivity procedures for use with the scaled boundary method when a reduced set of base functions is used. The error estimation procedure based on the superconvergent patch recovery technique and the error estimation procedure based on reference solutions are modified for use with the scaled boundary method when a reduced set of base functions is used. The use of a reduced set of base functions in an adaptivity procedure for the scaled boundary method is trialled. Adaptivity based solely on the set of base functions is shown to be inefficient. In contrast, the judicious use of a reduced set of base functions is shown to improve the overall efficiency of other adaptivity procedures.

Thesis (M. App. Sc.)--Carleton University, 2005. / Includes bibliographical references. Also available in electronic format on the Internet.

This thesis studies knowledge processes which span organisational boundaries, examining how knowledge is formed and shared between two companies with divergent interests, facing the challenges of innovation processes. Cross-boundary work provides access to diverse sources of knowledge, specialties and approaches, and this enhances the innovative performance of firms. However, managing knowledge and spanning diverse boundaries has proven to be difficult. While the epistemic and social challenges have been identified to trigger conflicts and misunderstandings across boundaries, the complexity, inter-dependency and uncertainty of innovation processes have been found to multiply these challenges. Informed by the practice-based perspective, this thesis examines how the challenges of integrating knowledge in such a context are addressed and resolved. Building upon this theoretical perspective, the thesis aims to enhance understandings of knowledge processes between the large bureaucratic organisations (publishers) and small/medium-sized companies (developers) in the videogames industry. Underpinned by a social constructionist and interpretivist methodology, a qualitative study of three publisher-developer relationships was conducted. With thirty six semi-structured interviews with senior directors, managers and team leaders, the thesis examined cross- boundary practices and the conflicts experienced in this process. In order to achieve this, the study focused on the role that boundary objects, trust development and power structures played in facilitating knowledge processes. The thesis recognises the evolving and relational character of boundary objects, highlighting that a combination of static and dynamic boundary objects were effective in facilitating knowledge integration in the publisher-developer relationship. It also reveals that despite high levels of distrust between the parties involved, they managed to create and maintain a working relationship by resorting to opportunistic practices, such as knowledge hiding, deception and collusion. It is emphasised that understanding the power dynamics in the publisher-developer relationship is a pre-requisite to explaining 2 how knowledge is managed across organisational boundaries during the course of a project. Drawing upon a Foucauldian perspective, the thesis identifies the positive and enabling aspects of power dynamics in this relationship. It argues that when the parties have discrepancies, competition and high levels of distrust, power games positively influence cross-boundary practices, the use of boundary objects and knowledge processes, ultimately mobilising knowledge integration. The thesis makes four significant contributions to the knowledge management and cross-boundary work literature. First, it identifies an evolving role for boundary objects, showing how they develop during the course of a project. Second, it finds a relational and politicised dimension for boundary objects, highlighting the role of brokers to manipulate and mobilise the use and effectiveness of these objects. Third, the thesis extends the existing literature by revealing that despite high levels of distrust, parties can create a working relationship. The research shows that this is achieved through resorting to opportunistic behaviour, such as knowledge hiding, deception and collusion. As a result, this thesis adds a complementary level to Carlile's Integrated Framework, explaining that when there are high levels of differences, dependencies and novelty in the cross-boundary work, knowledge hiding, deception and collusion are the driving force to facilitate knowledge integration and maintain a functional relationship. The fourth contribution of this thesis is recognising the positive and productive aspects of power dynamics that enable and mobilise boundary objects and knowledge processes, ultimately bringing positive outcomes and creating a functional relationship between two companies with divergent interests.

abstract: The initial microstructure of oxide fuel pellets can play a key role in their performance. At low burnups, the transport of fission products has a strong dependence on oxygen content, grain size distribution, porosity and grain boundary (GB) characteristics (crystallography, geometry and topology), all of which, in turn depend on processing conditions. These microstructural features can also affect the fuel densification, thermal conductivity and microstructure evolution inside the reactor. Understanding these effects can provide insight into microstructure evolution of fuels in-pile. In this work, mechanical and ion beam serial sectioning techniques were developed to obtain Electron Backscatter Diffraction (EBSD) data, both in 2-D and 3-D, for depleted UO2+X pellets manufactured under different conditions. The EBSD maps were used to relate processing conditions to microstructural features, with emphasis on special GBs according to the Coincident Site Lattice (CSL) model, as well as correlations between pore size and location in the microstructure. Furthermore, larger grains (at least 2.5 times the average grain size) were observed in all the samples and studied. Results indicate that larger grains, in samples manufactured under different conditions, dominate the overall crystallographic texture and have a fairly strong GB texture. Moreover, it seems that the preferential misorientation axis for these GBs, regardless of the O/M, is {001}. These results might be related to GB energy and structure and, suggest that the mechanism that controls grain growth seems to be independent of both processing conditions and stoichiometry. Additionally, a sample was heat treated to relate grain growth and crystallography. The results indicate that at least two mechanisms were involved. Lengthening of GBs was observed for larger grains. Another mechanism of grain growth was observed, in this case, grains rotate to match a neighboring grain forming a larger grain. In the new grain, the misorientation between the two neighboring grains decreases to less than 5 degrees, forming a new larger grain. The results presented in this work indicate that detailed studies of the initial microstructure of the fuel, with emphasis on the crystallography of grains and GBs could help to give insights on the in-pile microstructural evolution of the fuel. / Dissertation/Thesis / Ph.D. Materials Science and Engineering 2014