In the thesis, the error and stability analysis is made for the 2D Helmholtz equation by the method of fundamental solutions (MFS) using both Bessel and Neumann functions. The bounds of errors in bounded simply-connected domains are derived, while the bounds of condition number are derived only for disk domains. The MFS using Bessel functions is more efficient than the MFS using Neumann functions. Interestingly, for the MFS using Bessel functions, the radius R of the source points is not necessarily larger than the maximal radius r_max of the solution domain. This is against the traditional condition: r_max < R for MFS. Numerical experiments are carried out to support the analysis and conclusions made.

In this thesis, we extend the spectral collocation methods(SCM) (i.e., pseudo-spectral method) in Quarteroni and Valli [27] for the semilinear, parameter-dependentproblems(PDP) in the square with the Dirichlet boundary condition. The optimal error bounds are derived in this thesis for both H1 and L2 norms. For the solutions sufficiently smooth, the very high convergence rates can be obtained. The algorithms of the SCM are simple and easy to carry out. Only a few of basis functions are needed so that not only can the high accuracy of the PDP solutions be achieved, but also a great deal of CPU time may be saved. Moreover, for PDP the stability analysis of SCM is also made, to have the same growth rates of condition number as those for Poisson¡¦s equation. Numerical experiments are carried out to verify the theoretical analysis made.

Dynamic stall deeply affects the response of helicopter rotor blades, making its modeling accuracy very important. Two commonly used dynamic stall models were implemented in a comprehensive code, validated, and contrasted to provide improved analysis accuracy and versatility. Next, computational fluid dynamics and computational structural dynamics loose coupling methodologies are reviewed, and a general tight coupling approach was implemented and tested. The tightly coupled computational fluid dynamics and computational structural dynamics methodology is then used to assess the stability characteristics of complex rotorcraft problems. An aeroelastic analysis of rotors must include an assessment of potential instabilities and the determination of damping ratios for all modes of interest. If the governing equations of motion of a system can be formulated as linear, ordinary differential equations with constant coefficients, classical stability evaluation methodologies based on the characteristic exponents of the system can rapidly and accurately provide the system's stability characteristics. For systems described by linear, ordinary differential equations with periodic coefficients, Floquet's theory is the preferred approach. While these methods provide excellent results for simplified linear models with a moderate number of degrees of freedom, they become quickly unwieldy as the number of degrees of freedom increases. Therefore, to accurately analyze rotorcraft aeroelastic periodic systems, a fully nonlinear, coupled simulation tool is used to determine the response of the system to perturbations about an equilibrium configuration and determine the presence of instabilities and damping ratios. The stability analysis is undertaken using an algorithm based on a Partial Floquet approach that has been successfully applied with computational structural dynamics tools on rotors and wind turbines. The stability analysis approach is computationally inexpensive and consists of post processing aeroelastic data, which can be used with any aeroelastic rotorcraft code or with experimental data.

This thesis consists of the research on linkage-based fingertips for prosthetic hands. These fingertips consists of small polycentric mechanisms attached to what would be the pulp in normal anatomical fingers. These mechanisms allow the prosthetic hand to conform to the shape of objects during grasp. The goal of these prosthetic fingertips is to maximize the functionality of the hand while minimizing the number of inputs that the user has to control. The stability of the fingertip mechanisms is analyzed using the principle of virtual work. From this analysis we are able to show that the fingertip mechanism is stable for a large range of rotation of the link and for a large range of directions on which the force is applied, and that the mechanism is indifferent to the magnitude of the force applied to it (assuming that the force does not damage/deform the mechanism). To assess if the four-bar mechanisms (fingertips) improve the grasping capabilities in robotics and prosthetics, tests were performed on prosthetic hands and robot grippers with and without the fingertips. Comparisons were made using the Southampton Hand Assessment Procedure (SHAP) protocol, which tests the differences and measures the functionality of particular types of grasp, such as power, spherical, lateral, tripod, tip and extension. In the human testing, the overall Index of Functionality (IOF) of the Hosmer hook is 66.65 and 66.21 for the hook with the fingertips. The hook with the fingertips had a better IOF in the spherical and power prehensile pattern. When the IOF is calculated for the tasks that the fingertips were used, in 10 of 11 of the tasks, the IOF is higher than using the Hosmer hook. In the robotic gripper testing, the Index of Functionality was not be calculated because the time to perform the tasks depended more on the robotic control system than on the physical characteristics of the gripper.

Τα τελευταία χρόνια, γίνεται πολύς λόγος για τους καρκινικούς όγκους, καθώς η νόσος αυτή προσβάλλει ολοένα και περισσότερα άτομα κάθε χρόνο. Ιδιαίτερη βαρύτητα έχει δοθεί τόσο ερευνητικά όσο και ιατρικά στην αντιμετώπιση του καρκίνου μέσω θεραπευτικών τεχνικών (χημειοθεραπείες, χειρουργικές επεμβάσεις κλπ) καθώς και στην βελτίωση των συνθηκών διαβίωσης των καρκινοπαθών. Επίσης, αρκετή έμφαση στην έρευνα σχετικά με την ανάπτυξη του καρκίνου σε βιοχημικό επίπεδο και για την βαθύτερη κατανόηση της νόσου. Η έρευνα αφορά ερευνητές πολλών διαφορετικών ειδικοτήτων μεταξύ των οποίων και των μαθηματικών. Από το 1954 με την πρόταση των Armitage και Doll σχετικά με την μαθηματική μοντελοποίηση της γένεσης των καρκινικών όγκων, αρκετοί έχουν ασχοληθεί με την μαθηματική προτυποποίηση των διαφόρων φάσεων του καρκίνου, από την δημιουργία του μέχρι και την αντίσταση του σε φαρμακευτική αγωγή. Η εργασία αυτή πραγματεύεται την μαθηματική θεμελίωση και προτυποποίηση των καρκινικών όγκων όσον αφορά την γεωμετρική τους ανάπτυξη. Με βάση το θεμελιώδες μαθηματικό μοντέλο που προτάθηκε το 1976 από τον H. P. Greenspan, μελετάται η επίπτωση επιφανειακών διαταραχών στην ανάπτυξη σφαιρικών καθώς και ελλειψοειδών όγκων. Στην πρωτότυπη εργασία, η μελέτη περιορίστηκε στην ανάλυση των διαταραχών με μεταβλητή την πολική γωνία των σφαιρικών συντεταγμένων. Στην εργασία αυτή αρχικά μελετάται η γενίκευση του μοντέλου διαταραχών και στις δυο γωνίες του σφαιρικού συστήματος συντεταγμένων (πολική θ και αζιμουθιακή φ). Στην συνέχεια επεκτείνεται η μέθοδος σε τρία μοντέλα που γενικεύουν τις παραδοχές του αρχικού μοντέλου διατηρώντας την παραδοχή της σφαιρικής γεωμετρίας και μελετάται η ευστάθεια των αντίστοιχων επιφανειακών διαταραχών. Τέλος, μελετάται και η ευστάθεια του ίδιου προβλήματος στην ελλειψοειδή γεωμετρία επειδή η ανισοτροπία του ελλειψοειδούς σχήματος καθιστά πιο ρεαλιστική την προσέγγιση του πραγματικού σχήματος του καρκινικού όγκου. / The mathematical analysis of the tumour growth attracted a lot of interest in the last two decades. However, as of today no generally accepted model for tumour growth exists. This is due partially to the incomplete understanding of the related pathology as well as the extremely complicated procedure that guides the evolution of a tumour. Moreover, the growth of a tumour does depend on the available tissue surrounding the tumour and therefore it represents a physical case that is realistically modelled by ellipsoidal geometry. The remarkable aspect of the ellipsoidal shape is that it represents the sphere of the anisotropic space. It provides the appropriate geometrical model for any direction dependent physical quantity. In the present work we analyze the stability of a spherical tumour for four continuous models of an avascular tumour and the stability study of an ellipsoidal tumour. For all five models, conditions for the stability are stated and the results are implemented numerically. For the spherical cases, it is observed that the steady state radii that secure the stability of the tumour are different for each of the four models, and that results to differences in the stable and unstable modes. As for the ellipsoidal model, it is shown that, in contrast to the highly symmetric spherical case, where stability is possible to be achieved, there are no conditions that secure the stability of an ellipsoidal tumour. Hence, as in many physical cases, the observed instability is a consequence of the lack of symmetry.

Σκοπός της παρούσας Διατριβής Ειδίκευσης είναι η παρακολούθηση του κατολισθητικού φαινομένου του οικισμού Καρυάς του Δήμου Πατρέων, με μετρήσεις αποκλισιομέτρων ώστε να προσδιοριστεί ποσοτικά ο ρυθμός μετακίνησης της περιοχής μελέτης και να εξαχθούν συμπεράσματα για την μελλοντική του εξέλιξη, όπως καθορίζεται μέσω αναλύσεων ευστάθειας πρανών. Η εν λόγω περιοχή παρουσιάζει αξιόλογο ενδιαφέρον, λόγω των ιδιαίτερων και σύνθετων γεωλογικών συνθηκών, των συχνών και σημαντικών κατολισθητικών φαινομένων των τελευταίων ετών που προκάλεσαν σημαντικές καταστροφές σε τεχνικά έργα και ανθρώπινες περιουσίες. Στα πλαίσια της Διατριβής και της παράλληλης Έρευνας του Εργαστηρίου Τεχνικής Γεωλογίας στην περιοχή ενδιαφέροντος πραγματοποιήθηκε λεπτομερής γεωτεχνική έρευνα που περιελάμβανε ανόρυξη δειγματοληπτικών γεωτρήσεων σε επιλεγμένες θέσεις με ταυτόχρονη τοποθέτηση αποκλισιομέτρων, συστηματική λήψη αποκλισιομετρικών μετρήσεων, σειρά εργαστηριακών και επί τόπου δοκιμών σε κατάλληλα διαμορφωμένα δείγματα, λεπτομερή καταγραφή των τεχνικογεωλογικών συνθηκών της περιοχής με βάση κυρίως τη σύσταση, τη δομή των γεωλογικών σχηματισμών. Έγινε διάκριση των σχηματισμών της περιοχής έρευνας σε επιμέρους Γεωτεχνικές Ενότητες και σχεδιάστηκαν αντιπροσωπευτικές γεωτεχνικές – τεχνικογεωλογικές διατομές με σκοπό τη σύνθεση και ερμηνεία του γεωτεχνικού περιβάλλοντος της περιοχής. Παράλληλα πραγματοποιήθηκαν αναλύσεις ευστάθειας πρανών με χρήση εξειδικευμένου λογισμικού σε επιλεγμένες διατομές κατά μήκος των γεωτρήσεων στην κατολισθαίνουσα ζώνη Καρυάς. Σκοπός των αναλύσεων ευστάθειας πρανών ήταν να γίνει εκτίμηση πιθανών μετακινήσεων σε επιλεγμένα σημεία της περιοχής έρευνας και να παρατηρηθεί εάν το είδος ολίσθησης εξακολουθεί να είναι το ίδιο με αυτό που είχε διαπιστωθεί κατά την τελευταία εκδήλωση του κατολισθητικού φαινομένου. / The Aim of this ΜSc. Project is the exploration of the landslide phenomeno in the region of Karya, Patras, Western Greece by inclinometer measurements in order to define quantitatively the movement rate of the study area and export conclusions on its future development, as it specified via slope stability analysis. The study area is an area with complex geological conditions and is well known especially for the important and large-scale landslide phenomena which have taken place during the last years near Karya village and caused important destructions in engineering works and human fortunes. This project was done along with survey of the Laboratory of Engineering Geology, Geology Department, University of Patras. The full survey program included geological mapping focused on the engineering properties of the soil and rock formations, fifteen (15) sampling boreholes, inclinometer installation and measurement and laboratory tests. Through laboratory testing and detailed description of soil and rock samples the formations were classified in several units and several geotechnical cross-sections were constructed to make a general geological-geotechnical model of the study area. The geological and geotechnical data were used to perform Limit Equilibrium Slope Stability analysis. The survey results were used to define probable movements of the study area and to establish the slipping type.

No description available.

The purpose of this thesis is to contribute to the methodology at the intersection of relational and evaluative bibliometrics. Experimental investigations are presented that address the question of how we can most successfully produce estimates of the subject similarity between documents. The results from these investigations are then explored in the context of citation-based research evaluations in an effort to enhance existing citation normalization methods that are used to enable comparisons of subject-disparate documents with respect to their relative impact or perceived utility. This thesis also suggests and explores an approach for revealing the uncertainty and stability (or lack thereof) coupled with different kinds of citation indicators.This suggestion is motivated by the specific nature of the bibliographic data and the data collection process utilized in citation-based evaluation studies. The results of these investigations suggest that similarity-detection methods that take a global view of the problem of identifying similar documents are more successful in solving the problem than conventional methods that are more local in scope. These results are important for all applications that require subject similarity estimates between documents. Here these insights are specifically adopted in an effort to create a novel citation normalization approach that – compared to current best practice – is more in tune with the idea of controlling for subject matter when thematically different documents are assessed with respect to impact or perceived utility. The normalization approach is flexible with respect to the size of the normalization baseline and enables a fuzzy partition of the scientific literature. It is shown that this approach is more successful than currently applied normalization approaches in reducing the variability in the observed citation distribution that stems from the variability in the articles’ addressed subject matter. In addition, the suggested approach can enhance the interpretability of normalized citation counts. Finally, the proposed method for assessing the stability of citation indicators stresses that small alterations that could be artifacts from the data collection and preparation steps can have a significant influence on the picture that is painted by the citationindicator. Therefore, providing stability intervals around derived indicators prevents unfounded conclusions that otherwise could have unwanted policy implications. Together, the new normalization approach and the method for assessing the stability of citation indicators have the potential to enable fairer bibliometric evaluative exercises and more cautious interpretations of citation indicators.

Superplastic forming (SPF) is a valuable near net shape fabrication method, used to produce very complex, contoured and monolithic structures that are often lighter, stronger and safer than the assemblies they replace. However, the widespread industrial use of Superplastic (SP) alloys is hindered by a number of issues including low production rate and limited predictive capabilities of stability during deformation and failure. Failure during SPD may result from geometrical macroscopic instabilities and/or microstructural aspects. However, the available failure criteria are either based on geometrical instabilities or microstructural features and do not account for both failure modes. The present study presents a generalized multi-scale stability criterion for SP materials, accounting for both aspects of failure under various loading conditions. A combined model accounting for cavity nucleation and plasticity controlled cavity growth along with a grain growth model and a modified microstructure based constitutive equation for SP materials is incorporated into Harts stability analysis to develop the proposed stability criterion for different loading conditions. Effects of initial grain size, initial levels of cavitation, nucleation strain, strain-rate sensitivity, and grain-growth exponent on the optimum forming curves of different SP alloys are investigated, for different loading conditions.

In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics of the instability as the perturbation growth rate omega and the cut-off wave number are studied as functions of key physical parameters.