Finite size effects in superconducting nanocomposites

The present Master’s thesis presents theoretical description of the extraodinary behavior of the confined Indium nanoparticles. Superconducting properties of nanoparticles and nanocomposites are extensively reviewed. Special attention has been paid to phase fluctuation, shell and disordered effects. The experimental data has been obtained and provided by Dmitry Shamshur from Ioffe Physical Technical Institute. The investigated material represents a highly ordered system of silicate spheres filled with indium metal, where the In nanoparticles are interconnected between each other. Bulk indium is a superconductor with crititcal superconducting temperature Tc0 = 3:41 K. But indium nanoparticles exhibit different behavior, the critical temperature rise by approximately 20% up to 4.15 K. As well as transition of the indium particles to type-II superconductivity with high critical magnetic fields. Such diversity is explained by finite size effects which originate from nanosize of the samples.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Simulation and material calibration of ultra high strength steel (UHSS) S960 welded joint under static tensile test utilizing finite element method (FEM)

The aim of this work was to calibrate the material properties including strength and strain values for different material zones of ultra-high strength steel (UHSS) welded joints under monotonic static loading. The UHSS is heat sensitive and softens by heat due to welding, the affected zone is heat affected zone (HAZ). In this regard, cylindrical specimens were cut out from welded joints of Strenx® 960 MC and Strenx® Tube 960 MH, were examined by tensile test. The hardness values of specimens’ cross section were measured. Using correlations between hardness and strength, initial material properties were obtained. The same size specimen with different zones of material same as real specimen were created and defined in finite element method (FEM) software with commercial brand Abaqus 6.14-1. The loading and boundary conditions were defined considering tensile test values. Using initial material properties made of hardness-strength correlations (true stress-strain values) as Abaqus main input, FEM is utilized to simulate the tensile test process. By comparing FEM Abaqus results with measured results of tensile test, initial material properties will be revised and reused as software input to be fully calibrated in such a way that FEM results and tensile test results deviate minimum. Two type of different S960 were used including 960 MC plates, and structural hollow section 960 MH X-joint. The joint is welded by BöhlerTM X96 filler material. In welded joints, typically the following zones appear: Weld (WEL), Heat affected zone (HAZ) coarse grained (HCG) and fine grained (HFG), annealed zone, and base material (BaM). Results showed that: The HAZ zone is softened due to heat input while welding. For all the specimens, the softened zone’s strength is decreased and makes it a weakest zone where fracture happens while loading. Stress concentration of a notched specimen can represent the properties of notched zone. The load-displacement diagram from FEM modeling matches with the experiments by the calibrated material properties by compromising two correlations of hardness and strength.

Studies of rotor dynamics using a multibody simulation approach

The non-idealities in a rotor-bearing system may cause undesirable subcritical superharmonic resonances that occur when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from the non-idealities of the bearings. This study introduces a novel simulation approach that can be used to study the superharmonic vibrations of rotor-bearing systems. The superharmonic vibrations of complex rotor-bearing systems can be studied in an accurate manner by combining a detailed rotor and bearing model in a multibody simulation approach. The research looks at the theoretical background of multibody formulations that can be used in the dynamic analysis of flexible rotors. The multibody formulations currently in use are suitable for linear deformation analysis only. However, nonlinear formulation may arise in high-speed rotor dynamics applications due to the cenrrifugal stiffening effect. For this reason, finite element formulations that can describe nonlinear deformation are also introduced in this work. The description of the elastic forces in the absolute nodal coordinate formulation is studied and improved. A ball bearing model that includes localized and distributed defects is developed in this study. This bearing model could be used in rotor dynamics or multibody code as an interface elements between the rotor and the supporting structure. The model includes descriptions of the nonlinear Hertzian contact deformation and the elastohydrodynamic fluid film. The simulation approaches and models developed here are applied in the analysis of two example rotor-bearing systems. The first example is an electric motor supported by two ball bearings and the second is a roller test rig that consists of the tube roll of a paper machine supported by a hard-bearing-type balanceing machine. The simulation results are compared to the results available in literature as well as to those obtained by measuring the existing structure. In both practical examples, the comparison shows that the simulation model is capable of predicting the realistic responses of a rotor system. The simulation approaches developed in this work can be used in the analysis of the superharmonic vibrations of general rotor-bearing systems.

Cardiac Imaging in the Diagnosis of Coronary Artery Disease: The Value of Quantitative Imaging of Myocardial Perfusion and Deformation

Atherosclerosis is a chronic and progressive disease of the vasculature. Increasing coronary atherosclerosis can lead to obstructive coronary artery disease (CAD) or myocardial infarction. Computed tomography angiography (CTA) allows noninvasive assessment of coronary anatomy and quantitation of atherosclerotic burden. Myocardial blood flow (MBF) can be accurately measured in absolute terms (mL/g/min) by positron emission tomography (PET) with [15O] H O as a radiotracer. We studied the coronary microvascular dysfunction as a risk factor for future coronary calcification in healthy young men by measuring the coronary flow reserve (CFR) which is the ratio between resting and hyperemic MBF. Impaired vasodilator function was not linked with accelerated atherosclerosis 11 years later. Currently, there is a global interest in quantitative PET perfusion imaging. We established optimal thresholds of [15O] H O PET perfusion for diagnosis of CAD (hyperemic MBF of 2.3 mL/g/min and CFR of 2.5) in the first multicenter study of this type (Turku, Amsterdam and Uppsala). In myocardial bridging a segment of the coronary artery travels inside the myocardium and can be seen as intramural course (CTA) or systolic compression (invasive coronary angiography). Myocardial bridging is frequently linked with proximal atherosclerotic plaques. We used quantitative [15O] H O PET perfusion to evaluate the hemodynamic effects of myocardial bridging. Myocardial bridging was not associated with decreased absolute MBF or increased atherosclerotic burden. Speckle tracking allows quantitative echocardiographic imaging of myocardial deformation. Speckle tracking during dobutamine stress echocardiography was feasible and comparable to subjective wall motion analysis in the diagnosis of CAD. In addition, it correctly risk stratified patients with multivessel disease and extensive ischemia.

Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type

Subshifts are sets of configurations over an infinite grid defined by a set of forbidden patterns. In this thesis, we study two-dimensional subshifts offinite type (2D SFTs), where the underlying grid is Z2 and the set of for-bidden patterns is finite. We are mainly interested in the interplay between the computational power of 2D SFTs and their geometry, examined through the concept of expansive subdynamics. 2D SFTs with expansive directions form an interesting and natural class of subshifts that lie between dimensions 1 and 2. An SFT that has only one non-expansive direction is called extremely expansive. We prove that in many aspects, extremely expansive 2D SFTs display the totality of behaviours of general 2D SFTs. For example, we construct an aperiodic extremely expansive 2D SFT and we prove that the emptiness problem is undecidable even when restricted to the class of extremely expansive 2D SFTs. We also prove that every Medvedev class contains an extremely expansive 2D SFT and we provide a characterization of the sets of directions that can be the set of non-expansive directions of a 2D SFT. Finally, we prove that for every computable sequence of 2D SFTs with an expansive direction, there exists a universal object that simulates all of the elements of the sequence. We use the so called hierarchical, self-simulating or fixed-point method for constructing 2D SFTs which has been previously used by Ga´cs, Durand, Romashchenko and Shen.

Real-time simulation of multibody systems with applications for working mobile vehicles

This dissertation describes an approach for developing a real-time simulation for working mobile vehicles based on multibody modeling. The use of multibody modeling allows comprehensive description of the constrained motion of the mechanical systems involved and permits real-time solving of the equations of motion. By carefully selecting the multibody formulation method to be used, it is possible to increase the accuracy of the multibody model while at the same time solving equations of motion in real-time. In this study, a multibody procedure based on semi-recursive and augmented Lagrangian methods for real-time dynamic simulation application is studied in detail. In the semirecursive approach, a velocity transformation matrix is introduced to describe the dependent coordinates into relative (joint) coordinates, which reduces the size of the generalized coordinates. The augmented Lagrangian method is based on usage of global coordinates and, in that method, constraints are accounted using an iterative process. A multibody system can be modelled as either rigid or flexible bodies. When using flexible bodies, the system can be described using a floating frame of reference formulation. In this method, the deformation mode needed can be obtained from the finite element model. As the finite element model typically involves large number of degrees of freedom, reduced number of deformation modes can be obtained by employing model order reduction method such as Guyan reduction, Craig-Bampton method and Krylov subspace as shown in this study The constrained motion of the working mobile vehicles is actuated by the force from the hydraulic actuator. In this study, the hydraulic system is modeled using lumped fluid theory, in which the hydraulic circuit is divided into volumes. In this approach, the pressure wave propagation in the hoses and pipes is neglected. The contact modeling is divided into two stages: contact detection and contact response. Contact detection determines when and where the contact occurs, and contact response provides the force acting at the collision point. The friction between tire and ground is modelled using the LuGre friction model, which describes the frictional force between two surfaces. Typically, the equations of motion are solved in the full matrices format, where the sparsity of the matrices is not considered. Increasing the number of bodies and constraint equations leads to the system matrices becoming large and sparse in structure. To increase the computational efficiency, a technique for solution of sparse matrices is proposed in this dissertation and its implementation demonstrated. To assess the computing efficiency, augmented Lagrangian and semi-recursive methods are implemented employing a sparse matrix technique. From the numerical example, the results show that the proposed approach is applicable and produced appropriate results within the real-time period.

Structural studies and gabbro mylonitization within the Barton Bay Deformation Zone, Geraldton, Ontario /

Structures related to ductile siMple shear parallel to the Bankf ield-Tonbill Fault, define a 5km wide zone, the Barton Bay Deformation Zone. Structures present within this zone Include; simple shear fabrics S, C and C , asymmetric Z shaped folds with rotated axes, boudinage and pinch and swell structures and a subhorlzontal extension llneation. The most highly deformed rock is a gabbro mylonite which occurs in the fault zone. The deformation of this gabbro has been traced in stages from a protomylonite to an ultramylonite In which feldspar and chlorite grainslze has been reduced from over 100 microns to as little as 5 microns. Evidence from the mylonite and the surrounding structure indicates that deformation within the Barton Bay Deformation Zone is related to a regional simple shear zone, the Bankf ield-Tombill Fault. Movement along this shear zone was in a south over north oblique strike slip fashion with a dextral sense of displacement.

Regional variations of deformation mechanisms in the Lorrain Quartzite near Whitefish Falls, Ontario, Canada /

The quartzite microfabric found in the Lorrain Formation was studied across the La Cloche syncline, along a regional north-south transect along highway 6, near Whitefish Falls, Ontario. The complete stratigraphic sequence across the syncline is preserved, and is present on each fold limb. The lithostratigraphic units with the smallest grains size and lowest mica content are located close to the core of the fold, while coarser grained mica and feldspar rich units are situated at the northern and southern most extent of the transect. Deformation mechanisms vary with lithology and with position across the fold. Pressure solution appears to be the dominant deformation mechanism in the feldspathic, micaceous and ferruginous units. In the finer grained, mica poor white medium grained and cherty sandstone units, grain boundary migration (GBM) characteristics show dominance over those of pressure solution and show high amounts of fracturing which cut migrated boundaries and therefore post date GBM. All samples across the fold display a preferred orientation of quartz c-axes. The senses of asymmetry of fabrics are found to be similar across the syncline, with the exception of the ferruginous sandstone unit. Formation of these similar fabrics synmietries can not be the result of strain related to first order folding. The mica content appears to be related to the percentage of quartz lost due to pressure solution as a result of strain; the more mica present, the less quartz was lost. Calculations based on the shape of initial grains suggest that conservatively 30% of the quartz volume has been dissolved out of the Lorrain quartzite, and potentially migrated hundreds of meters to other members of the Huronian Supergroup as there was no meso or macroscopic evidence observed in outcrop.

Structural analysis of the Paint Lake Deformation Zone, Northern Ontario /

The Paint Lake Deformation Zone (PLDZ), located within the Superior Province of Canada, demarcates a major structural and lithological break between the Onaman-Tashota Terrane to the north and the Beardmore-Geraldton Belt to the south. The PLDZ is an east-west trending lineament, approximately 50 km in length and up to 1 km in width, comprised of an early ductile component termed the Paint Lake Shear Zone and a late brittle component known as the Paint Lake Fault. Structures associated with PLDZ development including S-, C- and C'-fabrics, stretching lineations, slickensides, C-C' intersection lineations, Z-folds and kinkbands indicate that simple shear deformation dominated during a NW-SE compressional event. Movement along the PLDZ was in a dextral sense consisting of an early differential motion with southside- down and a later strike-slip motion. Although the locus of the PLDZ may in part be lithologically controlled, mylonitization which accompanied shear zone development is not dependent on the lithological type. Conglomerate, intermediate and mafic volcanic units exhibit similar mesoscopic and microscopic structures where transected by the PLDZ. Field mapping, supported by thin section analysis, defines five strain domains increasing in intensity of deformation from shear zone boundary to centre. A change in the dominant microstructural deformation mechanism from dislocation creep to diffusion creep is observed with increasing strain during mylonitization. C'-fabric development is temporally associated with this change. A decrease in the angular relationship between C- and C'-fabrics is observed upon attaining maximum strain intensity. Strain profiling of the PLDZ demonstrates the presence of an outer primary strain gradient which exhibits a simple profile and an inner secondary strain gradient which exhibits a more complex profile. Regionally metamorphosed lithologies of lower greenschist facies outside the PLDZ were subjected to retrograde metamorphism during deformation within the PLDZ.

The micromorphology of Paleoseismic soft sediment deformation structures in glacial deposits from three sample sites in Scotland /

The nature of this research is to investigate paleoseismic deformation of glacial soft sediments from three sampling sites throughout the Scottish Highlands; Arrat's Mills, Meikleour and Glen Roy. The paleoseismic evidence investigated in this research will provide a basis for applying criteria to soft sediment deformation structures, and the trigger mechanisms that create these structures. Micromorphology is the tool used in this to investigate paleoseismic deformation structures in thin section. Thin section analysis, (micromorphology) of glacial sediments from the three sampling sites is used to determine microscale evidence of past earthquakes that can be correlated to modem-day events and possibly lead to a better understanding of the impact of earthquakes throughout a range of sediment types. The significance of the three sampling locations is their proximity to two major active fault zones that cross Scotland. The fault zones are the Highland Boundary Fault and the Great Glen Fault, these two major faults that parallel each other and divide the country in half Sims (1975) used a set of seven criteria that identified soft sediment deformation structures created by a magnitude six earthquake in Cahfomia. Using criteria set forth by Sims (1975), the paleoseismic evidence can be correlated to the magnitude of the deformation structures found in the glacial sediments. This research determined that the microstructures at Arrat's Mill, Meikleour and Glen Roy are consistent with a seismically induced origin. It has also been demonstrated that, even without the presence of macrostructures, the use of micromorphology techniques in detecting such activity within sediments is of immense value.

The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.

Zero-sum problems in finite cyclic groups

The purpose of this thesis is to investigate some open problems in the area of combinatorial number theory referred to as zero-sum theory. A zero-sequence in a finite cyclic group G is said to have the basic property if it is equivalent under group automorphism to one which has sum precisely IGI when this sum is viewed as an integer. This thesis investigates two major problems, the first of which is referred to as the basic pair problem. This problem seeks to determine conditions for which every zero-sequence of a given length in a finite abelian group has the basic property. We resolve an open problem regarding basic pairs in cyclic groups by demonstrating that every sequence of length four in Zp has the basic property, and we conjecture on the complete solution of this problem. The second problem is a 1988 conjecture of Kleitman and Lemke, part of which claims that every sequence of length n in Zn has a subsequence with the basic property. If one considers the special case where n is an odd integer we believe this conjecture to hold true. We verify this is the case for all prime integers less than 40, and all odd integers less than 26. In addition, we resolve the Kleitman-Lemke conjecture for general n in the negative. That is, we demonstrate a sequence in any finite abelian group isomorphic to Z2p (for p ~ 11 a prime) containing no subsequence with the basic property. These results, as well as the results found along the way, contribute to many other problems in zero-sum theory.

Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Generalization of the BTK Theory to the Case of Finite Quasiparticle Lifetimes

A generalization to the BTK theory is developed based on the fact that the quasiparticle lifetime is finite as a result of the damping caused by the interactions. For this purpose, appropriate self-energy expressions and wave functions are inserted into the strong coupling version of the Bogoliubov equations and subsequently, the coherence factors are computed. By applying the suitable boundary conditions to the case of a normal-superconducting interface, the probability current densities for the Andreev reflection, the normal reflection, the transmission without branch crossing and the transmission with branch crossing are determined. Accordingly the electric current and the differential conductance curves are calculated numerically for Nb, Pb, and Pb0.9Bi0.1 alloy. The generalization of the BTK theory by including the phenomenological damping parameter is critically examined. The observed differences between our approach and the phenomenological approach are investigated by the numerical analysis.