The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Solving large sparse linear systems over the field GF(2)

Nowadays problem of solving sparse linear systems over the field GF(2) remain as a challenge. The popular approach is to improve existing methods such as the block Lanczos method (the Montgomery method) and the Wiedemann-Coppersmith method. Both these methods are considered in the thesis in details: there are their modifications and computational estimation for each process. It demonstrates the most complicated parts of these methods and gives the idea how to improve computations in software point of view. The research provides the implementation of accelerated binary matrix operations computer library which helps to make the progress steps in the Montgomery and in the Wiedemann-Coppersmith methods faster.

Remote Observation of Radioactive Permit-Required Confined Spaces – Case: Posiva Oy’s Fuel Handling Cell

Posiva Oy’s final disposal facility’s encapsulation plant will start to operate in the 2020s. Once the operation starts, the facility is designed to run more than a hundred years. The encapsulation plant will be first of its kind in the world, being part of the solution to solve a global issue of final disposal of nuclear waste. In the encapsulation plant’s fuel handling cell the spent nuclear fuel will be processed to be deposited into the Finnish bedrock, into ONKALO. In the fuel handling cell, the environment is highly radioactive forming a permit-required enclosed space. Remote observation is needed in order to monitor the fuel handling process. The purpose of this thesis is to map (Part I) and compare (Part II) remote observation methods to observe Posiva Oy’s fuel handling cell’s process, and provide a possible theoretical solution for this case. Secondary purpose for this thesis is to provide resources for other remote observation cases, as well as to inform about possible future technology to enable readiness in the design of the encapsulation plant. The approach was to theoretically analyze the mapped remote observation methods. Firstly, the methods were filtered by three environmental challenges. These are the high levels of radiation, the permit-required confined space and the hundred year timespan. Secondly, the most promising methods were selected by the experts designing the facility. Thirdly, a customized feasibility analysis was created and performed on the selected methods to rank the methods with scores. The results are the mapped methods and the feasibility analysis scores. The three highest scoring methods were radiation tolerant camera, fiberscope and audio feed. A combination of these three methods was given as a possible theoretical solution for this case. As this case is first in the world, remote observation methods for it had not been thoroughly researched. The findings in this thesis will act as initial data for the design of the fuel handling cell’s remote observation systems and can potentially effect on the overall design of the facility by providing unique and case specific information. In addition, this thesis could provide resources for other remote observation cases.

Investigation of the composition of linear alkylbenzenes with emphasis on the identification and quantitation of some trace compounds using GS/MS system in both electron impact and chemical ionization modes

Linear alkylbenzenes, LAB, formed by the Alel3 or HF catalyzed alkylation of benzene are common raw materials for surfactant manufacture. Normally they are sulphonated using S03 or oleum to give the corresponding linear alkylbenzene sulphonates In >95 % yield. As concern has grown about the environmental impact of surfactants,' questions have been raised about the trace levels of unreacted raw materials, linear alkylbenzenes and minor impurities present in them. With the advent of modem analytical instruments and techniques, namely GCIMS, the opportunity has arisen to identify the exact nature of these impurities and to determine the actual levels of them present in the commercial linear ,alkylbenzenes. The object of the proposed study was to separate, identify and quantify major and minor components (1-10%) in commercial linear alkylbenzenes. The focus of this study was on the structure elucidation and determination of impurities and on the qualitative determination of them in all analyzed linear alkylbenzene samples. A gas chromatography/mass spectrometry, (GCIMS) study was performed o~ five samples from the same manufacturer (different production dates) and then it was followed by the analyses of ten commercial linear alkylbenzenes from four different suppliers. All the major components, namely linear alkylbenzene isomers, followed the same elution pattern with the 2-phenyl isomer eluting last. The individual isomers were identified by interpretation of their electron impact and chemical ionization mass spectra. The percent isomer distribution was found to be different from sample to sample. Average molecular weights were calculated using two methods, GC and GCIMS, and compared with the results reported on the Certificate of Analyses (C.O.A.) provided by the manufacturers of commercial linear alkylbenzenes. The GC results in most cases agreed with the reported values, whereas GC/MS results were significantly lower, between 0.41 and 3.29 amu. The minor components, impurities such as branched alkylbenzenes and dialkyltetralins eluted according to their molecular weights. Their fragmentation patterns were studied using electron impact ionization mode and their molecular weight ions confirmed by a 'soft ionization technique', chemical ionization. The level of impurities present i~ the analyzed commercial linear alkylbenzenes was expressed as the percent of the total sample weight, as well as, in mg/g. The percent of impurities was observed to vary between 4.5 % and 16.8 % with the highest being in sample "I". Quantitation (mg/g) of impurities such as branched alkylbenzenes and dialkyltetralins was done using cis/trans-l,4,6,7-tetramethyltetralin as an internal standard. Samples were analyzed using .GC/MS system operating under full scan and single ion monitoring data acquisition modes. The latter data acquisition mode, which offers higher sensitivity, was used to analyze all samples under investigation for presence of linear dialkyltetralins. Dialkyltetralins were reported quantitatively, whereas branched alkylbenzenes were reported semi-qualitatively. The GC/MS method that was developed during the course of this study allowed identification of some other trace impurities present in commercial LABs. Compounds such as non-linear dialkyltetralins, dialkylindanes, diphenylalkanes and alkylnaphthalenes were identified but their detailed structure elucidation and the quantitation was beyond the scope of this study. However, further investigation of these compounds will be the subject of a future study.

Pigment orientation changes detected by low temperature linear dichroism spectroscopy: cold-hardening transition in phycobilisome-containing organisms

Low temperature (77K) linear dichroism spectroscopy was used to characterize pigment orientation changes accompanying the light state transition in the cyanobacterium, Synechococcus sp. pee 6301, and cold-hardening in winter rye (Secale cereale L. cv. Puma). Samples were oriented for spectroscopy using the gel squeezing method (Abdourakhmanov et aI., 1979) and brought to 77K in liquid nitrogen. The linear dichroism (LD) spectra of Synechococcus 6301 phycobilisome/thylakoid membrane fragments cross-linked in light state 1 and light state 2 with glutaraldehyde showed differences in both chlorophyll a and phycobilin orientation. A decrease in the relative amplitude of the 681nm chlorophyll a positive LD peak was observed in membrane fragments in state 2. Reorientation of the phycobilisome (PBS) during the transition to state 2 resulted in an increase in core allophycocyanin absorption parallel to the membrane, and a decrease in rod phycocyanin parallel absorption. This result supports the "spillover" and "PBS detachment" models of the light state transition in PBS-containing organisms, but not the "mobile PBS" model. A model was proposed for PBS reorientation upon transition to state 2, consisting of a tilt in the antenna complex with respect to the membrane plane. Linear dichroism spectra of PBS/thylakoid fragments from the red alga, Porphyridium cruentum, grown in green light (containing relatively more PSI) and red light (containing relatively more PSll) were compared to identify chlorophyll a absorption bands associated with each photosystem. Spectra from red light - grown samples had a larger positive LD signal on the short wavelength side of the 686nm chlorophyll a peak than those from green light - grown fragments. These results support the identification of the difference in linear dichroism seen at 681nm in Synechococcus spectra as a reorientation of PSll chromophores. Linear dichroism spectra were taken of thylakoid membranes isolated from winter rye grown at 20°C (non-hardened) and 5°C (cold-hardened). Differences were seen in the orientation of chlorophyll b relative to chlorophyll a. An increase in parallel absorption was identified at the long-wavelength chlorophyll a absorption peak, along with a decrease in parallel absorption from chlorophyll b chromophores. The same changes in relative pigment orientation were seen in the LD of isolated hardened and non-hardened light-harvesting antenna complexes (LHCII). It was concluded that orientational differences in LHCII pigments were responsible for thylakoid LD differences. Changes in pigment orientation, along with differences observed in long-wavelength absorption and in the overall magnitude of LD in hardened and non-hardened complexes, could be explained by the higher LHCII monomer:oligomer ratio in hardened rye (Huner et ai., 1987) if differences in this ratio affect differential light scattering properties, or fluctuation of chromophore orientation in the isolated LHCII sample.

Evolutionary synthesis of stochastic gene network models using feature-based search spaces

A feature-based fitness function is applied in a genetic programming system to synthesize stochastic gene regulatory network models whose behaviour is defined by a time course of protein expression levels. Typically, when targeting time series data, the fitness function is based on a sum-of-errors involving the values of the fluctuating signal. While this approach is successful in many instances, its performance can deteriorate in the presence of noise. This thesis explores a fitness measure determined from a set of statistical features characterizing the time series' sequence of values, rather than the actual values themselves. Through a series of experiments involving symbolic regression with added noise and gene regulatory network models based on the stochastic 'if-calculus, it is shown to successfully target oscillating and non-oscillating signals. This practical and versatile fitness function offers an alternate approach, worthy of consideration for use in algorithms that evaluate noisy or stochastic behaviour.

Finding the Open Spaces in Closed Systems: An Exploration of Critical Pedagogy with a Social Justice Directive in an Ontario Secondary School Classroom

This study examines the first experience of students, teachers, and an administrator in implementing a teacher-designed Leadership in Social Justice Program at a large urban Ontario secondary school. The program aimed to infuse a Freirean concept of critical pedagogical praxis (Freire, 1970/1993) in a grade 12 integrated educational experience with a social justice directive. Data were collected through two questionnaires and eight in-depth interviews. The data identified three areas of awareness that described ways in which student participants were impacted most profoundly (a) developing self-awareness, (b) understanding a new educational paradigm, and (c) finding a place in the world. The study found that the program was successful in highlighting the possibility for more meaningful education and engaged many students deeply; however, its success was limited by the lead teacher’s failure to fully grasp and implement tenets of Freirean critical pedagogy that involved the role of the teacher in pedagogical processes.

Queer Encounters: exploring experiences of (gender)queers in women's public washroom spaces

This thesis is based on 13 qualitative interviews conducted with 12 individuals whom I refer to as (gender)queers in Winnipeg, Manitoba, and St. Catharines, Ontario. Drawing on queer theory and the literature of sexuality and space, I explore how (gender)queers experience women's public washrooms as gendered and heterosexualized spaces. I examine the degree to which a simultaneous heterosexing and female gendering of women's public washrooms is linked to the marginalization and sometimes violent exclusion of (gender)queers within these particular spaces. I also discuss the ways in which (gender)queers may use a variety of strategies aimed at navigating heterosexualized and gendered public washrooms. Finally, I explore alternatives to conventional washrooms spaces, including the gender-neutral washrooms, multi-stall non-gendered public washrooms, and public washrooms in queer spaces.

Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Cognitive Behavior Therapy for Obsessive-Compulsive Behavior in Children with Autism Spectrum Disorder: A Comparison of Hierarchical Linear Modelling and Visual Analysis

Behavioral researchers commonly use single subject designs to evaluate the effects of a given treatment. Several different methods of data analysis are used, each with their own set of methodological strengths and limitations. Visual inspection is commonly used as a method of analyzing data which assesses the variability, level, and trend both within and between conditions (Cooper, Heron, & Heward, 2007). In an attempt to quantify treatment outcomes, researchers developed two methods for analysing data called Percentage of Non-overlapping Data Points (PND) and Percentage of Data Points Exceeding the Median (PEM). The purpose of the present study is to compare and contrast the use of Hierarchical Linear Modelling (HLM), PND and PEM in single subject research. The present study used 39 behaviours, across 17 participants to compare treatment outcomes of a group cognitive behavioural therapy program, using PND, PEM, and HLM on three response classes of Obsessive Compulsive Behaviour in children with Autism Spectrum Disorder. Findings suggest that PEM and HLM complement each other and both add invaluable information to the overall treatment results. Future research should consider using both PEM and HLM when analysing single subject designs, specifically grouped data with variability.

Efficient Strategy-Proof Allocation Functions in Linear Production Economies

In a linear production model, we characterize the class of efficient and strategy-proof allocation functions, and the class of efficient and coalition strategy-proof allocation functions. In the former class, requiring equal treatment of equals allows us to identify a unique allocation function. This function is also the unique member of the latter class which satisfies uniform treatment of uniforms.

Simulation-Based Finite-Sample Normality Tests in Linear Regressions

In the literature on tests of normality, much concern has been expressed over the problems associated with residual-based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location-scale model; hence reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size normality tests for the disturbances of standard linear regression, which is based on using the technique of Monte Carlo tests.