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Методами точек помутнения, поляризационной микроскопии и рентгеноструктурного анализа изучены фазовые переходы систем ПЭ – о-ксилол, ПЭ – н-гексан, ПЭ – хлороформ, ПЭ – о-дихлорбензол, ПЭГ – 1,4-диоксан и ПЭГ – толуол, а также структура выделенных их них полимерных образований в магнитном поле и в его отсутствие. Построены фазовые диаграммы систем. Установлено, что магнитное поле приводит к повышению температур кристаллизации растворов и расплавов ПЭ и ПЭГ. Обнаружено, что в растворах ПЭГ в магнитном поле образуются сферолиты существенно меньших размеров, чем в отсутствие магнитного поля. Определены степени кристалличности образцов ПЭ и ПЭГ, выделенных из растворов и расплавов. Показано, что магнитное поле увеличивает степень кристалличности ПЭГ, но не влияет на степень кристалличности ПЭ. / Phase transitions of the PE – xylol, PE – hexane, PE – chloroform, PE – dichlorobenzene, PEG – 1,4-dioxane and PEG – toluene systems, and also the structure of the polymers separated from these systems have been studied using the cloud-point method, polarizing microscopy and the X-ray diffraction under magnetic field and in its absence. Phase diagrams of these systems are constructed. It is shown that the magnetic field leads to the increase in polymer crystallization temperatures from solutions and melts. It is revealed that the sizes of spherulites formed in PEG solutions under magnetic field are significantly smaller, than that in the magnetic field absence. The crystallinity degree of the PE and PEG samples separated from solutions and melts was determined. It was shown that the magnetic field increases the crystallinity degree of PEG, but doesn't influence on the PE crystallinity degree.

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Significant stray magnetic field exists around the coils when charging the electric vehicles (EVs) with inductive power transfer (IPT), owning to the large air gap between the transmitter and receiver. The methods for field attenuation usually introduce extra losses and reduce the efficiency. This study focuses on the synergetic attenuation of stray magnetic field which is optimized simultaneously with the efficiency. The optimization is realized with Pareto front. In this dissertation, three methods are discussed for the field attenuation. The first method is to tune the physical parameters of the winding, such as the inner radii, outer radii, distribution of the turns, and types of the litz wires. The second method is to add metal shields around the IPT coils, in which litz wires are used as shields to reduce the shielding losses. The third method is to control the phases of winding currents, which avoids increasing the size and weight of the IPT coils. To attenuate the stray magnetic field by tuning the physical parameters, the conventional method is to sweep all the physical parameters in finite-element simulation. This takes thousands of simulations to derive the Pareto front, and it's especially time-consuming for three-dimensional simulations. This dissertation demonstrates a faster method to derive the Pareto front. The windings are replaced by the lumped loops. As long as the number of turns for each loop is known, the efficiency and magnetic field are calculated directly from the permeance matrices and current-to-field matrices. The sweep of physical parameters in finite-element simulation is replaced by the sweep of the turns numbers for the lumped loops in calculation. Only tens of simulations are required in the entire procedure, which are used to derive the matrices. An exemplary set of coils was built and tested. The efficiency from the matrix calculation is the same as the experimental measurement. The difference for stray magnetic field is less than 12.5%. Metal shields attenuate the stray magnetic field effectively, but generates significant losses owning to the uneven distribution of shield currents. This dissertation uses litz wires to replace the conventional plate shield or ring shield. Skin effect is eliminated so the shield currents are uniformly distributed and the losses are reduced. The litz shields are categorized to two types: shorted litz shield and driven litz shield. Circuit models are derived to analyze their behaviors. The concept of lumped-loop model is applied to derive the Pareto front of efficiency versus stray magnetic field for the coils with litz shield. In an exemplary IPT system, coils without metal shield and with metal shields are optimized for the same efficiency. Both the simulation and experimental measurement verify that the shorted litz shield has the best performance. The stray magnetic field is attenuated by 65% compared to the coils without shield. This dissertation also introduces the method to attenuate the stray magnetic field by controlling the phases of winding currents. The magnetic field around the coils is decomposed to the component in the axial direction and the component in the radial direction. The axial component decreases with smaller phase difference between windings' currents, while the radial component exhibits the opposite property. Because the axial component is dominant around the IPT coils, decreasing the phase difference is preferred. The dual-side-controlled converter is applied for the circuit realization. Bridges with active switches are used for both the inverter on the transmitter side and the rectifier on the receiver side. The effectiveness of this method was verified both in simulation and experiment. Compared to the conventional series-series IPT with 90° phase difference between winding currents, stray magnetic field was attenuated by up to 30% and 40% when the phase differences of winding currents are 50° and 40°, respectively. Furthermore, an analytical method is investigated to calculate the proximity-effect resistance of the planar coils with ferrite plate. The objective of this method is to work together with the fast optimization which uses the lumped-loop model. The existence of the ferrite plate complicates the calculation of the magnetic field across each turn which is critical to derive the proximity-effect resistance. In this dissertation, the ferrite plate is replaced by the mirrored turns according to the method of image. The magnetic fields are then obtained from Ampere's Law and Biot-Savart Law. Up to 200 kHz, the difference of the proximity-effect resistance is less than 15% between calculation and measurement. / Ph. D. / Inductive power transfer for the battery charging of electric vehicles uses loosely coupled coils to replace the cables and plugs. The power is transferred from transmitter to receiver across tens of centimeters. Significant stray magnetic field exists around the coils owning to the large gap, which should be attenuated for the safety consideration of human beings. Three methods are discussed for the field attenuation. The first method is to tune the physical parameters of the winding, such as the inner radii, outer radii, distribution of the turns, and types of the litz wires. The second method is to add metal shields around the IPT coils, in which litz wires are used as shields to reduce the shielding losses. The third method is to control the phases of winding currents, which avoids the increase of the size and weight of the IPT coils. However, the field attenuation usually comes with reduced efficiency of the system. The work in this dissertation is focused on the synergetic attenuation of stray magnetic field in inductive power transfer for electric vehicles. The optimization is realized with Pareto front. The coils are optimized for low stray magnetic field and high efficiency simultaneously.

Feynman path integrals introduced heuristically in the 1940s are a powerful tool used in many areas of physics, but also an intriguing mathematical challenge. In this work we used techniques of infinite dimensional integration (i.e. the infinite dimensional oscillatory integrals) in two different, but strictly connected, directions. On the one hand we construct a functional integral representation for solutions of a general high-order heat-type equations exploiting a recent generalization of infinite dimensional Fresnel integrals; in this framework we prove a a Girsanov-type formula, which is related, in the case of Schrödinger equation, to the Feynman path integral representation for the solution in presence of a magnetic field; eventually a new phase space path integral solution for higher-order heat-type equations is also presented. On the other hand for the three dimensional Schrödinger equation with magnetic field we provide a rigorous mathematical Feynman path integral formula still in the context of infinite dimensional oscillatory integrals; moreover, the requirement of independence of the integral on the approximation procedure forces the introduction of a counterterm, which has to be added to the classical action functional (this is done by the example of a linear vector potential). Thanks to that, it is possible to give a natural explanation for the appearance of the Stratonovich integral in the path integral formula for both the Schrödinger and the heat equation with magnetic field.

Es werden die exzitonischen Eigenschaften von Halbleiter-Quantengräben im Magnetfeld theoretisch untersucht. Unter Benutzung der Enveloppen-Näherung wird der Hamilton-Operator des Exzitons aufgestellt. Ein allgemeines Theorem für die diamagnetische Verschiebung (DMV) des exzitonischen Grundzustands wird abgeleitet. Im ersten Teil werden Effekte der Unordnung berücksichtigt. Die numerische Ergebnisse zeigen, daß die DMV ein Maß für die Lokalisierung der Wellenfunktion ist. Einzelne Exzitonzustände, wie sie für optische Nahfeldexperimente relevant sind, zeigen eine breite Verteilung der DMV-Werte, wobei der Mittelwert mit der Energie anwächst (abnehmende Lokalisierung). Die Absorptions- und Photolumineszenz-Spektren im Fernfeld werden mit dem Magnetfeld breiter. Unter Ausnutzung der strukturellen Information über die lokale chemische Zusammensetzung einer gegebenen Probe werden die statistischen Eigenschaften der Unordnung in einem realen Quantengraben analysiert. Das ermöglicht die numerische Erzeugung neuer Unordnungspotentiale, die dann für die Simulation der optischen Eigenschaften wie DMV-Statistik und Photolumineszenzspektren genutzt werden. Der Vergleich mit den experimentellen Daten für verschiedene Temperaturen zeigt eine sehr gute Übereinstimmung. Der zweite Teil dieser Dissertation beschäftigt sich mit Quantenpunkten und Quantenringen, die in einem Quantengraben eingebettet sind, und konzentriert sich auf den exzitonischen Aharonov-Bohm Effekt. Der persistente Strom und die Magnetisierung werden berechnet. Für zirkuläre Symmetrie wird der enge Zusammenhang zwischen der oszillatorischen Komponente der Exziton-Energie und dem persistenten Strom aufgezeigt. Für nichtzirkuläre Ringe sind die Oszillationen ebenfalls beobachtbar, jedoch mit kleinerer Amplitude. Eine Untersuchung der Exzitonenkinetik zeigt die wichtige Rolle nichtradiativer Prozesse auf und setzt Grenzen für die Beobachtbarkeit der Oszillationen und für die Auslöschung der Photolumineszenz. / Excitonic properties of semiconductor quantum wells (QWs) with applied magnetic field are investigated theoretically. Using the envelope function approximation, the exciton Hamiltonian is constructed. A general theorem for the diamagnetic shift (DMS) of the lowest exciton energy is derived. In a first part, disorder is taken into account. The numerical results show that the DMS is a measure of wave function localization. Individual exciton states as relevant for optical near-field experiments show a broad distribution of DMS values while its average value increases with energy (decreasing localization). Far-field absorption and photoluminescence spectra become wider with increasing magnetic field. Using structural information on the local chemical composition of a given sample, the statistical properties of the disorder in a real QW have been analyzed. This allowed to generate new disorder potentials as input for the simulation of DMS statistics and photoluminescence spectra. Their comparison with experimental data at different temperatures shows very good agreement. The second part of the thesis deals with quantum dots and rings embedded in the QW, focusing on the exciton Aharonov-Bohm effect. Persistent current and magnetization are evaluated. For circular symmetry, a close relation between the oscillatory component of the exciton energy and the persistent current is revealed. For non-circular rings, oscillations can be observed too but with lower amplitude. A study of the exciton kinetics points to the important role of non-radiative processes, and sets limits for the experimental observability of energy oscillations and photoluminescence quenching.

This master's thesis focuses on the utilization of an artificially created weak magnetic field for navigation in 3D space. The theoretical part of this work deals with the general properties of the magnetic field and with its description. The next section of the theoretical part contains an overview of measuring principles for magnetic field measurements. Based on various types of measuring principles, the thesis elaborates on commercially available miniature sensors for magnetic field measurement with a measuring range up to 10 mT. The work focuses mainly on the magnetoresistive principle and fluxgate sensors. Furthermore, the theoretical part contains descriptions of methods for modeling the magnetic field of simple permanent magnets and various magnet assemblies. Lastly, the theoretical part involves a patent search of devices used for locating magnets that are installed in an intramedullary nail, which is used in intramedullary stabilization used on fractures of human bones. By locating the magnet in the nail, it is possible to precisely determine the position of the mounting holes. The practical part of the thesis deals with the analysis of magnetic field behavior in the vicinity of various magnetic assemblies, which were modeled in COMSOL Multiphysics using the finite element method. The models were created with the aim of analysing the behaviour of the magnetic field in the vicinity of the magnets and at the same time to find possible analytical functions that could be used to determine the position of the magnet in space relative to the probe. The result of this work is an analysis of various assemblies, which contains graphs of different dependencies and prescription of polynomial functions that approximate these dependencies. Another part of the thesis is the design of a probe that serves to locate the magnetic target. The work describes two possible methods of localization. For the differential method, a user interface in LabVIEW was created. The probe based on this method is fully capable of locating the magnet in the 2D plane. The state space search method is described only in theory.

Until recently, numerical modulation models for the solar modulation of cosmic rays have been based primarily on finite difference approaches; however, models based on the solution of an appropriate set of stochastic differential equations have become increasingly popular. This study utilises such a spatially three-dimensional and time-stationary model, based on that of Strauss et al. (2011b). The remarkable numerical stability and powerful illustrative capabilities of this model are utilised extensively and in a distinctly comparative fashion to enable new insights into the processes of modulation. The model is refined to provide for both the Smith-Bieber (Smith and Bieber, 1991) and Jokipii-Kota (Jokipii and Kota, 1989) modifcations to the Parker heliospheric magnetic field (Parker, 1958) and the implications for modulation are investigated. During this investigation it is conclusively illustrated that the Parker field is most conducive to drift dominated modulation, while the Jokipii-Kota and Smith-Bieber modifcations are seen to induce successively larger contributions from diffusive processes. A further refinement to the model is the incorporation of a different profile for the heliospheric current sheet. This profile is defined by its latitudinal extent given by Kota and Jokipii (1983), as opposed to the profile given by Jokipii and Thomas (1981). An extensive investigation into current sheet related matters is launched, illustrating the difference between these current sheet geometries, the associated drift velocity fields and the effect on modulation. At high levels of solar activity, such that the current sheet enters deep enough into the polar regions, the profile of Kota and Jokipii (1983) is found to significantly reduce the effective inward (outward) drifts of positively (negatively) charged particles during A > 0 polarity cycles. The analogous effect is true for A < 0 polarity cycles and the overall effect is of such an extent that the A > 0 and A < 0 solutions are found to coincide at the highest levels of solar activity to form a closed loop. This is a result that has never before been achieved without having to scale down the drift coefficient to zero at solar maximum, as was done by e.g. Ndiitwani et al. (2005). Furthermore, it is found that the drift velocity fields associated with these two current sheet profiles lead to significant differences in modulation even at such low levels of solar activity where no difference in the geometries of these profiles are yet in evidence. The model is finally applied to reproduce four observed galactic proton spectra, selected from PAMELA measurements (Adriani et al., 2013) during the atypical solar minimum of 2006 to 2009; a new proton local interstellar spectrum was employed. The results are found to be in accordance with that found by other authors and in particular Vos (2011), i.e. the diffusion was required to consistently increase from 2006 to 2009 and, in addition, the rigidity dependence below ~ 3 GV was required to change over this time so that the spectra became increasingly softer. / MSc (Space Physics), North-West University, Potchefstroom Campus, 2015