In this dissertation we solve several combinatorial problems in different areas of mathematics: automata theory, combinatorics of partially ordered sets and extremal combinatorics. Firstly, we focus on some new automata that do not seem to have occurred much in the literature, that of solvability of mazes. For our model, a maze is a countable strongly connected digraph together with a proper colouring of its edges (without two edges leaving a vertex getting the same colour) and two special vertices: the origin and the destination. A pointer or robot starts in the origin of a maze and moves naturally between its vertices, according to a sequence of specific instructions from the set of all colours; if the robot is at a vertex for which there is no out-edge of the colour indicated by the instruction, it remains at that vertex and proceeds to execute the next instruction in the sequence. We call such a finite or infinite sequence of instructions an algorithm. In particular, one of the most interesting and very natural sets of mazes occurs when our maze is the square lattice Z2 as a graph with some of its edges removed. Obviously, we need to require that the origin and the destination vertices are in the same connected component and it is very natural to take the four instructions to be the cardinal directions. In this set-up, we make progress towards a beautiful problem posed by Leader and Spink in 2011 which asks whether there is an algorithm which solves the set of all such mazes. Next, we address a problem regarding symmetric chain decompositions of posets. We ask if there exists a symmetric chain decomposition of a 2 × 2 × ... × 2 × n cuboid (k 2’s) such that no chain has a subchain of the form (a1,...,ak,0) ≺ ... ≺ (a1,...,ak,n−1)? We show this is true precisely when k≥5 and n≥3. Thisquestion arises naturally when considering products of symmetric chain decompositions which induce orthogonal chain decompositions — the existence of the decompositions provided in this chapter unexpectedly resolves the most difficult case of previous work by Spink on almost orthogonal symmetric chain decompositions (2017) which makes progress on a conjecture of Shearer and Kleitman. Moreover, we generalize our methods to other finite graded posets. Finally, we address two different problems in extremal combinatorics related to mathematical physics. Firstly, we study metastable states in the Ising model. We propose a general model for 1-flip spin systems, and initiate the study of extremal properties of their stable states. By translating local stability conditions into Sperner- type conditions, we provide non-trivial upper bounds which are often tight for large classes of such systems. The last topic we consider is a deterministic bootstrap percolation type problem. More specifically, we prove several extremal results about fast 2-neighbour percolation on the two dimensional grid.

Neste trabalho, estudamos as Singularidades das folheações mutuamente ortogonais, numa variedade orientada M^3 de dimensão 3, cujas folhas são as curvas integrais dos campos de direções de curvatura principal associadas a uma imersão : M^3 R^4. Damos aqui continuidade às contribuições de R. Garcia referente ao estudo das singularidades genéricas das folheações principais. Apresentamos as configurações principais numa vizinhança dos pontos parcialmente umbílicos de codimensão 1, ou seja, as singularidades das folheações principais que aparecem genericamente em famílias a 1 parâmetro de hipersuperfícies imersas em R^4, e os diagramas de bifurcação pertinentes. Enfraquecendo a condição de genericidade, da maneira mais simples possível, encontramos oito tipos genéricos: D_1^ 1, D^1_ 2, D^1_ 3, D^1_, D^1_{1h,p}, D^1_{1h,n}, D^1_p e D^1_c , definidos ao longo do trabalho. Nesta tese consubstanciamos matematicamente a seguinte conclusão: As singularidades das folheações principais, que aparecem genericamente em famílias a 1 parâmetro de hipersuperfícies imersas em R^4, são os pontos parcialmente umbílicos D_1^ 1, D^1_ 2, D^1_ 3, D^1_, D^1_{1h,p}, D^1_{1h,n}, D^1_ e D^1_ , cujas definições e propriedades serão apresentados aqui. A parte central desta tese é estabelecer, analítica e geometricamente, a configuração principal destes pontos incluindo seus diagramas de bifurcação. / In this work we study the mutually ortogonal foliations, in oriented three dimensional manifolds M^3, whose leaves are the integral curves of the principal curvature direction fields associated to immersions : M^3 R^4. We focus on behavior of these foliation around singularities. Here we extend the contributions of R. Garcia concerning the study of generic singularities. To this end we establish the principal configurations in a neighborhood of partially umbilic points of codimension one. These are the singularities which appear generically in one parameter families of hypersurfaces and give their bifurcation diagrams. We express the condition of genericity by minimally weakening those given by R. Garcia and by adding instead new higher order ones. This procedure leads to the novel generic types: D^1_1, D^1_2, D^1_3, D^1_, D^1_{1h,p}, D^1_{1h,n}, D^1_p and D^1_c , studied in this work. The central part of this thesis is to establish, analitically and geometrically, the local principal configurations at these points, including their bifurcations diagrams.

Management of data imprecision has become increasingly important, especially with the advance of technology enabling applications to collect and store huge amount data from multiple sources. Data collected in such applications involve a large number of variables and various types of data imperfections. These data, when used in knowledge discovery applications, require the following: 1) computationally efficient algorithms that works faster with limited resources, 2) an effective methodology for modeling data imperfections and 3) procedures for enabling knowledge discovery and quantifying and propagating partial or incomplete knowledge throughout the decision-making process. Bayesian Networks (BNs) provide a convenient framework for modeling these applications probabilistically enabling a compact representation of the joint probability distribution involving large numbers of variables. BNs also form the foundation for a number of computationally efficient algorithms for making inferences. The underlying probabilistic approach however is not sufficiently capable of handling the wider range of data imperfections that may appear in many new applications (e.g., medical data). Dempster-Shafer theory on the other hand provides a strong framework for modeling a broader range of data imperfections. However, it must overcome the challenge of a potentially enormous computational burden. In this dissertation, we introduce the joint Dirichlet BoE, a certain mass assignment in the DS theoretic framework, that simplifies the computational complexity while enabling one to model many common types of data imperfections. We first use this Dirichlet BoE model to enhance the performance of the EM algorithm used in learning BN parameters from data with missing values. To form a framework of reasoning with the Dirichlet BoE, the DS theoretic notions of conditionals, independence and conditional independence are revisited. These notions are then used to develop the DS-BN, a BN-like graphical model in the DS theoretic framework, that enables a compact representation of the joint Dirichlet BoE. We also show how one may use the DS-BN in different types of reasoning tasks. A local message passing scheme is developed for efficient propagation of evidence in the DS-BN. We also extend the use of the joint Dirichlet BoE to Markov models and hidden Markov models to address the uncertainty arising due to inadequate training data. Finally, we present the results of various experiments carried out on synthetically generated data sets as well as data sets from medical applications.

No description available.

Swedish forests are mostly used for timber harvesting and 96 % of this harvesting is made by clear cutting while only 4 % is effected through other methods such as single tree harvesting. All species are not affected by forestry to same magnitude. Some specifically generalists are not affected at all. Hence, this study, had its aim to find out vascular plant species that persist, disappear or colonize other species as a result of anthropogenic disturbances in different production forests, so as to determine not only if canopy openness affects the species distribution but also the magnitude of the effects. I examined 10 different forest localities during May and June 2008. Three of these localities were made up of clear cut forest plots, 3 with partially cut down forest plots and 4 with undisturbed production forest plots. Species composition and diversity were then compared between these plots. A total of 34 different species were found. Statistical Analysis was made on how well the species in the partially cut down forest plots fitted into the undisturbed forest group as well as comparing this results with results of how counterpart species in the clear cut forest plots fitted into the undisturbed forest groups. These results showed that there was no significant difference, ANOVA values of P = 0.839, 0.602 and 0.564 respectively among the species composition between the forest, partially cut down and clear cut forest groups between the forest, partially cut down and clear cut forest plots. However, among the 54 species found in all study plots, 11 were common between the forest and partially logged sites whereas only Carex sp in the clear cut forest was common to those in the forest plots implying that canopy openness did not affect the total species number but had an effect in species composition. Clear cutting seems to kill off everything but trees and generalists. Hence, resiliency of vegetation should be increased by management practices that ensure the maintenance of prior species.

The subject of this thesis is the development of new ultrasound inspection techniques for detection of cracks that are smaller than the wavelength of the inspecting wave and the characterization of cracks in fluid-filled pipes as either surface-breaking or subsurface. The spectrum of the scattered field of a partially closed crack comprises harmonic components not expected to be found in the case of linear scatterers such as pores or inclusions. Paper A presents an experimental investigation into the linear reflection and generation of the 2nd harmonic component following the incidence of an ultrasonic wave onto a dry or water-confining interface formed by elasto-plastic steel-steel surfaces in contact. The results indicate that water has an unexpected effect on the reflection, at low interfacial pressures, suggesting that fluid mediated forces play a role not accounted for in current models. The level of the generation of the 2nd harmonic measured provides support for further development of the technique for detection of dry, partially closed cracks or fluid-filled, nearly open cracks. A theoretical model describing the nonlinear scattering of acoustic waves by surface-breaking cracks with faces in partial contact is presented in Paper B. Both linear and nonlinear response of the crack are shown to be the largest for a SV wave incident on the surface containing the crack at an angle just above the critical angle for longitudinal waves. A method which provides information on whether a fracture is surface-breaking or subsurface has been modelled and its optimal experimental set-up examined in Paper C. The main assumption of the model is that water carried by pressurized pipes infiltrates and fills a surface-breaking crack, while a subsurface crack is dry. The model simulates an inspection in which the modulation technique is employed and the surface hosting the crack is not accessible. A parameter, constructed with signals recorded in backscattering configuration during a modulation cycle, is examined and shown to provide a clear criterion to distinguish subsurface from surface-breaking cracks when a SV wave at 45 degree incidence is employed as a probe. Finally, in Paper D the modulation technique is experimentally tested on steel beams that host surface-breaking fatigue cracks. The method is shown to be a successful tool to distinguish a dry from a fluid-filled crack. Furthermore, it is revealed that the dynamics of the fluid needs to be accounted for in a more accurate simulation tool. / QC 20100906

Hydrogen is added to Graphene in various compositions and configurations to modify the band structure to produce a suitable band gap for microelectronic applications. Optical and vibrational spectra are calculated as a means of characterization. Calculations performed using DFT and Quantum Espresso. / UOIT

Concrete masonry is a multi-component structural system. In the case of reinforced concrete masonry, the system includes the concrete units, the mortar, the reinforcing steel and the grout fill. Placing vertical steel reinforcing bars in the cores of the concrete units enhances the flexural strength of the wall. The vertical steel, when subjected to compression at moderate strain levels, must be confined to improve its resistance to buckling and to improve the effectiveness of the grout around the reinforcing bar. Based on the well established behaviour of reinforced concrete systems, it seems reasonable to presume that the primary means of enhancing ductility is to provide lateral confining steel at closely-spaced intervals to effectively increase the ultimate compressive strain in the grout. It may be assumed that transverse reinforcement in concrete masonry provides lateral confinement to the core so that the axial compressive strength of the grout is enhanced and the ductility improved. <p>The focus of this study was to investigate the effect of vertical reinforcement and lateral confinement on the axial capacity of short partially grouted concrete masonry walls built in running bond. In order to better understand the structural behaviour of both confined and unconfined concrete masonry, it is important to have some knowledge of the load-displacement behaviour, stress-strain behaviour and failure modes of the masonry walls with different configurations of vertical and lateral reinforcement. <p>An experimental study was performed to investigate the behaviour of partially grouted concrete masonry block walls under axial loading. Three types of test specimens of partially grouted concrete block masonry walls were tested: <p>(1) specimens with a grouted core only; <p>(2) specimens with a grouted core and vertical reinforcement (i.e. no confinement); and <p>(3) specimens with a grouted core, vertical reinforcement and spiral confinement in the grouted cores. In total, thirty short wall specimens were tested to failure. <p>The structural behaviour of vertically reinforced, laterally confined walls was compared to vertically reinforced, unconfined walls, as well as to unreinforced, unconfined masonry walls. The test results indicated that vertical reinforcement of the grouted core did not have a significant positive effect on the failure modes and strength of the short masonry walls. Due to problems with adequate compaction, the lateral confinement provided by the spiral reinforcement had a slightly negative effect on the compressive strength of concrete masonry walls built in running bond. Vertical reinforcement and lateral confinement of the grouted core had some positive effect on the ductility. From a comparison of the ductility for all three types of specimens it was found that both the vertical reinforcement and lateral confinement of the core had a beneficial influence on the post-peak ductility. <p>In general, similar crack patterns and failure modes were observed in all three types of specimens. Vertical cracks that progressed through the end faces of the concrete blocks and mortar joints, suggesting that the lateral expansion of the grouted core contributed to tensile splitting stresses in walls. All walls failed in a compression-tension stress state, which featured spalling away of the block shells and vertical tensile splitting on the end faces.

Plasma sprayed Thermal Barrier Coating systems (TBCs) are commonly used for thermal protection of components in modern gas turbine application such as power generation, marine and aero engines. The material that is most commonly used in these applications is Yttria Partially Stabilized Zirconia (YPSZ) because of this ceramic’s favourable properties, such as low thermal conductivity, phase stability to high temperature, and good erosion resistance. The coating microstructures in YPSZ coatings are highly heterogeneous, consisting of defects such as pores and cracks of different sizes which determine the coating’s final thermal and mechanical properties, and the service lives of the coatings. Determination of quantitative microstructure–property correlations is of great interest as experimental procedures are time consuming and expensive. Significant attention has been given to this field, especially in last fifteen years. The usual approach for modelling was to describe various microstructural features in some way, so as to determine their influence on the overall thermal conductivity of the coating. As the analytical models over-simplified the description of the defects, various numerical models were developed which incorporated real microstructure images.This thesis work describes two modelling approaches to further investigate the relationships between microstructure and thermal conductivity of TBCs. The first modelling approach uses a combination of a statistical model and a finite element model which could be used to evaluate and verify the relationship between microstructural defects and thermal conductivity. The second modelling approach uses the same finite element model along with a coating morphology generator, and can be used to design low thermal conductivity TBCs. A tentative verification of both the approaches has been done in this work.

Concrete masonry is a multi-component structural system. In the case of reinforced concrete masonry, the system includes the concrete units, the mortar, the reinforcing steel and the grout fill. Placing vertical steel reinforcing bars in the cores of the concrete units enhances the flexural strength of the wall. The vertical steel, when subjected to compression at moderate strain levels, must be confined to improve its resistance to buckling and to improve the effectiveness of the grout around the reinforcing bar. Based on the well established behaviour of reinforced concrete systems, it seems reasonable to presume that the primary means of enhancing ductility is to provide lateral confining steel at closely-spaced intervals to effectively increase the ultimate compressive strain in the grout. It may be assumed that transverse reinforcement in concrete masonry provides lateral confinement to the core so that the axial compressive strength of the grout is enhanced and the ductility improved. <p>The focus of this study was to investigate the effect of vertical reinforcement and lateral confinement on the axial capacity of short partially grouted concrete masonry walls built in running bond. In order to better understand the structural behaviour of both confined and unconfined concrete masonry, it is important to have some knowledge of the load-displacement behaviour, stress-strain behaviour and failure modes of the masonry walls with different configurations of vertical and lateral reinforcement. <p>An experimental study was performed to investigate the behaviour of partially grouted concrete masonry block walls under axial loading. Three types of test specimens of partially grouted concrete block masonry walls were tested: <p>(1) specimens with a grouted core only; <p>(2) specimens with a grouted core and vertical reinforcement (i.e. no confinement); and <p>(3) specimens with a grouted core, vertical reinforcement and spiral confinement in the grouted cores. In total, thirty short wall specimens were tested to failure. <p>The structural behaviour of vertically reinforced, laterally confined walls was compared to vertically reinforced, unconfined walls, as well as to unreinforced, unconfined masonry walls. The test results indicated that vertical reinforcement of the grouted core did not have a significant positive effect on the failure modes and strength of the short masonry walls. Due to problems with adequate compaction, the lateral confinement provided by the spiral reinforcement had a slightly negative effect on the compressive strength of concrete masonry walls built in running bond. Vertical reinforcement and lateral confinement of the grouted core had some positive effect on the ductility. From a comparison of the ductility for all three types of specimens it was found that both the vertical reinforcement and lateral confinement of the core had a beneficial influence on the post-peak ductility. <p>In general, similar crack patterns and failure modes were observed in all three types of specimens. Vertical cracks that progressed through the end faces of the concrete blocks and mortar joints, suggesting that the lateral expansion of the grouted core contributed to tensile splitting stresses in walls. All walls failed in a compression-tension stress state, which featured spalling away of the block shells and vertical tensile splitting on the end faces.