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Santoso, Agus Mathematics & Statistics Faculty of Science UNSW. "Evolution of climate anomalies and variability of Southern Ocean water masses on interannual to centennial time scales." Awarded by:University of New South Wales. School of Mathematics and Statistics, 2005. http://handle.unsw.edu.au/1959.4/33355.
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In this study the natural variability of Southern Ocean water masses on interannual to centennial time scales is investigated using a long-term integration of the Commonwealth Scientic and Industrial Research Organisation (CSIRO) coupled climate model. We focus our attention on analysing the variability of Antarctic IntermediateWater (AAIW), Circumpolar DeepWater (CDW), and Antarctic Bottom Water (AABW). We present an analysis of the dominant modes of temperature and salinity (T - S) variability within these water masses. Climate signals are detected and analysed as they get transmitted into the interior from the water mass formation regions. Eastward propagating wavenumber-1, -2, and -3 signals are identied using a complex empirical orthogonal function (CEOF) analysis along the core of the AAIW layer. Variability in air-sea heat uxes and ice meltwater rates are shown by heat and salt budget analyses to control variability of Antarctic Surface Water where density surfaces associated with AAIW outcrop. The dominant mode in the CDW layer is found to exhibit an interbasin-scale of variability originating from the North Atlantic, and propagating southward into the Southern Ocean. Salinity dipole anomalies appear to propagate around the Atlantic meridional overturning circulation with the strengthening and weakening of North Atlantic Deep Water formation. In the AABW layer, T - S anomalies are shown to originate from the southwestern Weddell Sea, driven by salinity variations and convective overturning in the region. It is also demonstrated that the model exhibits spatial patterns of T - S variability for the most part consistent with limited observational record in the Southern Hemisphere. However, some observations of decadal T - S changes are found to be beyond that seen in the model in its unperturbed state. We further assess sea surface temperature (SST) variability modes in the Indian Ocean on interannual time scales in the CSIRO model and in reanalysis data. The emergence of a meridional SST dipole during years of southwest Western Australian rainfall extremes is shown to be connected to a large-scale mode of Indian Ocean climate variability. The evolution of the dipole is controlled by variations in atmospheric circulation driving anomalous latent heat uxes with wind-driven ocean transport moderating the impact of evaporation and setting the conditions favourable for the next generation phase of an opposite dipole.
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Al-Hachami, Ali. "Generalised mathematical models for 3D magnetic reconnection at null points : magnetic reconnection at null points." Thesis, University of Dundee, 2011. https://discovery.dundee.ac.uk/en/studentTheses/a8cbc44e-abcc-4eb6-b4e8-2706f9ccc62f.
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Plasmas occur in many technical, laboratory and space environments, and often behave in a highly ideal manner. This means that advection of the plasma can store large amounts of energy in the magnetic field. This energy is released when a sudden change in the magnetic topology of the field occurs-facilitated by the process of `magnetic reconnection'. A great deal of research has been focussed on understanding the reconnection process and we now appreciate that the 3D process is critically di erent from early 2D models. The magnetic field in many astrophysical plasmas, for example in the solar corona, is known to have a highly complex { and clearly three-dimensional { structure. Turbulent plasma motions in high-ß regions where field lines are anchored, such as the solar interior, can store large amounts of energy in the magnetic field. This energy can only be released when magnetic reconnection occurs. Reconnection may only occur in locations where huge gradients of the magnetic field develop, and one candidate for such locations are magnetic null points, known to be abundant for example in the solar atmosphere. Reconnection leads to changes in the topology of the magnetic field, and energy being released as heat, kinetic energy and acceleration of particles. Thus reconnection is responsible for many dynamic processes, for instance solar flares and jets in the solar atmosphere.The aim of this thesis is to investigate the properties of magnetic reconnection at a 3D null point. One key focus will be to understand the dependence of the process on the symmetry of the magnetic field around the null. In particular we examine the rate of reconnection of magnetic flux at the null point, as well as how the current sheet forms and its properties. According to our present understanding, there are three main modes of magnetic reconnection that may occur at 3D nulls, spine-fan reconnection, torsional spine reconnection and torsional fan reconnection. We first consider the spine-fan reconnection mode. It is found that the basic structure of the mode of magnetic reconnection considered is una ected by varying the magnetic field symmetry, that is, the plasma flow is found to cross both the spine and fan of the null. However the peak intensity and dimensions of the current sheet are dependent on the symmetry/asymmetry of the field lines. As a result, the reconnection rate is also found to be strongly dependent on the field asymmetry. In addition, the properties of the torsional spine and torsional fan modes of magnetic reconnection at 3D nulls are investigated. New analytical models are developed which for the first time include a current layer that is fully spatially localised around the spine or fan of the null. The principal aim is to investigate the effect of varying the degree of asymmetry of the null point magnetic field on the resulting reconnection process { where previous studies always considered a non-generic radially symmetric null. Analytical solutions are derived for the steady kinematic equations at a three dimensional null point. In these models the electric current lies parallel to either the fan or spine. In order to conform the results of kinematic models, numerical simulations are performed in which the full set of resistive MHD equations are solved. It is found that the geometry of the current layers within which torsional spine and torsional fan reconnection occur is strongly dependent on the symmetry of the magnetic field. Torsional spine reconnection still occurs in a narrow tube around the spine, but with ellipticalcross-section when the fan eigenvalues are dfferent. The eccentricity of the ellipse increases as the degree of asymmetry increases, with the short axis of the ellipse being along the strong field direction. The spatiotemporal peak current, and the peak reconnection rate attained, are found not to depend strongly on the degree of asymmetry. For torsional fan reconnection, the reconnection occurs in a planar disk in the fan surface, which is again elliptical when the symmetry of the magnetic field is broken. The short axis of the ellipse is along the weak field direction, with the current being peaked in these weak field regions. The peak current and peak reconnection rate in this case are clearly dependent on the asymmetry, with the peak current increasing but the reconnection rate decreasing as the degree of asymmetry is increased.
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Klochan, Oleh V. Physics Faculty of Science UNSW. "Ballistic transport in one-dimensional p-type GaAs devices." Awarded by:University of New South Wales, 2007. http://handle.unsw.edu.au/1959.4/35186.
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In this thesis we study GaAs one dimensional hole systems with strong spin-orbit interaction effects. The primary focus is the Zeeman splitting of 1D subbands in the two orthogonal in-plane magnetic field directions. We study two types of 1D hole systems based on different (311)A grown heterostructures: a modulation doped GaAs/AlGaAs square quantum well and an undoped induced GaAs/AlGaAs triangular quantum well. The results from the modulation doped 1D wire show enhanced anisotropy of the effective Lande g-factor for the two in-plane field directions (parallel and perpendicular to the wire), compared to that in 2D hole systems. This enhancement is explained by the confinement induced reorientation of the total angular momentum ^ J from perpendicular to the 2D plane to in-plane and parallel to the wire. We use the intrinsic anisotropy of the in-plane g-factors to probe the 0:7 structure and the zero bias anomaly in 1D hole wires. We find that the behaviour of the 0:7 structure and the ZBA are correlated and depend strongly on the orientation of the in-plane field. This result proves the connection between the 0:7 and the ZBA and their relation to spin. We fabricate the first induced hole 1D wire with extremely stable gate characteristics and characterize this device. We also fabricate devices with two orthogonal induced hole wires on one chip, to study the interplay between the confinement, crystallographic anisotropy and spin-orbit coupling and their effect on the Zeeman splitting. We find that the ratios of the g-factors in the two orthogonal field directions for the two wires show opposite behaviour. We compare absolute values of the g-factors relative to the magnetic field direction. For B || [011] the g-factor is large for the wire along [011] and small for the wire along [233]. Whereas for B || [233], the g-factors are large irrespective of the wire direction. The former result can be explained by reorientation of ^ J along the wire, and the latter by an additional off-diagonal Zeeman term, which leads to the out-of-plane component of ^ J when B || [233], and as a result, to enhanced g-factors via increased exchange interactions.
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Fuentes, Fernández Jorge. "MHD evolution of magnetic null points to static equilibria." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/1897.
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In magnetised plasmas, magnetic reconnection is the process of magnetic field merging and recombination through which considerable amounts of magnetic energy may be converted into other forms of energy. Reconnection is a key mechanism for solar flares and coronal mass ejections in the solar atmosphere, it is believed to be an important source of heating of the solar corona, and it plays a major role in the acceleration of particles in the Earth's magnetotail. For reconnection to occur, the magnetic field must, in localised regions, be able to diffuse through the plasma. Ideal locations for diffusion to occur are electric current layers formed from rapidly changing magnetic fields in short space scales. In this thesis we consider the formation and nature of these current layers in magnetised plasmas. The study of current sheets and current layers in two, and more recently, three dimensions, has been a key field of research in the last decades. However, many of these studies do not take plasma pressure effects into consideration, and rather they consider models of current sheets where the magnetic forces sum to zero. More recently, others have started to consider models in which the plasma beta is non-zero, but they simply focus on the actual equilibrium state involving a current layer and do not consider how such an equilibrium may be achieved physically. In particular, they do not allow energy conversion between magnetic and internal energy of the plasma on their way to approaching the final equilibrium. In this thesis, we aim to describe the formation of equilibrium states involving current layers at both two and three dimensional magnetic null points, which are specific locations where the magnetic field vanishes. The different equilibria are obtained through the non-resistive dynamical evolution of perturbed hydromagnetic systems. The dynamic evolution relaxes via viscous damping, resulting in viscous heating. We have run a series of numerical experiments using LARE, a Lagrangian-remap code, that solves the full magnetohydrodynamic (MHD) equations with user controlled viscosity and resistivity. To allow strong current accumulations to be created in a static equilibrium, we set the resistivity to be zero and hence simply reach our equilibria by solving the ideal MHD equations. We first consider the relaxation of simple homogeneous straight magnetic fields embedded in a plasma, and determine the role of the coupling between magnetic and plasma forces, both analytically and numerically. Then, we study the formation of current accumulations at 2D magnetic X-points and at 3D magnetic nulls with spine-aligned and fan-aligned current. At both 2D X-points and 3D nulls with fan-aligned current, the current density becomes singular at the location of the null. It is impossible to be precisely achieve an exact singularity, and instead, we find a gradual continuous increase of the peak current over time, and small, highly localised forces acting to form the singularity. In the 2D case, we give a qualitative description of the field around the magnetic null using a singular function, which is found to vary within the different topological regions of the field. Also, the final equilibrium depends exponentially on the initial plasma pressure. In the 3D spine-aligned experiments, in contrast, the current density is mainly accumulated along and about the spine, but not at the null. In this case, we find that the plasma pressure does not play an important role in the final equilibrium. Our results show that current sheet formation (and presumably reconnection) around magnetic nulls is held back by non-zero plasma betas, although the value of the plasma pressure appears to be much less important for torsional reconnection. In future studies, we may consider a broader family of 3D nulls, comparing the results with the analytical calculations in 2D, and the relaxation of more complex scenarios such as 3D magnetic separators.
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Cook, Graeme Robert. "Magnetic flux transport simulations : applications to solar and stellar magnetic fields." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2072.
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Magnetic fields play a key role in a wide variety of phenomena found on the Sun. One such phenomena is the Coronal Mass Ejection (CME) where a large amount of material is ejected from the Sun. CME’s may directly affect the earth, therefore understanding their origin is of key importance for space weather and the near-Earth environment. In this thesis, the nature and evolution of solar magnetic fields is considered through a combination of Magnetic Flux Transport Simulations and Potential Field Source Surface Models. The Magnetic Flux Transport Simulations produce a realistic description of the evolution and distribution of the radial magnetic field at the level of the solar photosphere. This is then applied as a lower boundary condition for the Potential Field Source Surface Models which prescribe a coronal magnetic field. Using these two techniques, the location and variation of coronal null points, a key element in the Magnetic Breakout Model of CMEs, are determined. Results show that the number of coronal null points follow a cyclic variation in phase with the solar cycle. In addition, they preferentially form at lower latitudes as a result of the complex active latitude field. Although a significant number of coronal nulls may exist at any one time (≈ 17), it is shown that only half may satisfy the necessary condition for breakout. From this it is concluded that while the Magnetic Breakout Model of CMEs is an important model in understanding the origin of the CMEs, other processes must occur in order to explain the observed number of CMEs. Finally, the Magnetic Flux Transport Simulations are applied to stellar magnetic fields and in particular to the fast rotating star HD171488. From this speculative study it is shown that the Magnetic Flux Transport Simulations constructed for the Sun may be applied in very different stellar circumstances and that for HD171488 a significantly higher rate of meridional flow (1200-1400 ms⁻¹) is required to match observed magnetic field distributions.
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Gillett, David Alan. "Transient free radicals studied by laser magnetic resonance spectroscopy." Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:038bdb7e-1f8c-4112-bcea-4a0ca7ab7bcf.
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A liquid nitrogen cooled, carbon monoxide laser magnetic resonance spectrometer was used to study mid-infrared vibration-rotation transitions in the gaseous free radical NCO, in its ̅X2Π state, at very high resolution. The use of an intracavity absorption cell made possible the observation of some transitions with sub-Doppler resolution. Developments to the spectrometer extended the range of operation of the CO laser. Most importantly, a CO laser operating on overtone transitions, Δν = 2, was operated in Oxford. The Δν = 2 CO laser operates over the range 2450-3800cm-1 (4.08-2.63 μm), and the Δν = 1 CO laser over the range 1200-2100 cm-1 (8.33-4.76 μm). NCO exhibits a Renner-Teller effect in its ground electronic state, an interaction between the motion of the electrons and the bending motion of the nuclei. Vibration-rotation transitions were observed in a sequence of bands involving the excitation of the out-of-phase stretching vibration, in the region of 1900cm-1. Some of the bands involved the excited bending vibration. The Zeeman effect behaviour of the molecular energy levels, particularly in the 2Σ vibronic states, clearly showed the manifestation of the Renner-Teller effect. The Zeeman effect in the 2Σ vibronic states was considered in detail. Many of the 2Σ LMR spectra were recorded at sub-Doppler resolution. NCO is complicated to model, and unassigned LMR spectra remain. A harmonic Renner-Teller model was developed for the analysis. It was implemented by constructing an explicit matrix representation of the single electronic state N2 effective Hamiltonian, which was diagonalised exactly. A new term in this Hamiltonian, describing centrifugal distortion corrections to the Renner-Teller coupling term, was developed for the 2Σ vibronic states in order to account for anharmonic vibronic interactions.
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Stevenson, Julie E. H. "On the properties of single-separator MHS equilibria and the nature of separator reconnection." Thesis, University of St Andrews, 2015. http://hdl.handle.net/10023/6678.
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This thesis considers the properties of MHS equilibria formed through non-resistive MHD relaxation of analytical non-potential magnetic field models, which contain two null points connected by a generic separator. Four types of analytical magnetic fields are formulated, with different forms of current. The magnetic field model which has a uniform current directed along the separator, is used through the rest of this thesis to form MHS equilibria and to study reconnection. This magnetic field, which is not force-free, embedded in a high-beta plasma, relaxes non-resistively using a 3D MHD code. The relaxation causes the field about the separator to collapse leading to a twisted current layer forming along the separator. The MHS equilibrium current layer slowly becomes stronger, longer, wider and thinner with time. Its properties, and the properties of the plasma, are found to depend on the initial parameters of the magnetic field, which control the geometry of the magnetic configuration. Such a MHS equilibria is used in a high plasma-beta reconnection experiment. An anomalous resistivity ensures that only the central strong current in the separator current layer is dissipated. The reconnection occurs in two phases characterised by fast and slow reconnection, respectively. Waves, launched from the diffusion site, communicate the loss of force balance at the current layer and set up flows in the system. The energy transport in this system is dominated by Ohmic dissipation. Several methods are presented which allow a low plasma-beta value to be approached in the single-separator model. One method is chosen and this model is relaxed non-resistively to form a MHS equilibrium. A twisted current layer grows along the separator, containing stronger current than in the high plasma-beta experiments, and has a local enhancement in pressure inside it. The growth rate of this current layer is similar to that found in the high plasma-beta experiments, however, the current layer becomes thinner and narrower over time.
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Pang, Yong, and 龐勇. "Advance in two-dimensional RF pulse design and transmit SENSE." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40887856.
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Saxena, Siddharth Shanker. "Magnetic and superconducting phases of heavy fermion compounds." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323011.
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Crain, Bruce Richard. "Vector finite element methods for spurious-free solutions of unbounded dielectric and ferrite loaded waveguiding structures." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/15501.
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Sharma, Puneet. "Comparison of Delayed Contrast-Enhanced Magnetic Resonance Imaging of Myocardial Viability at 1.5 and 3 Tesla." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/6911.
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Imaging of myocardial viability using the delayed enhancement technique currently provides high image contrast between infarcted and normal tissue with the aid of a magnetization prepared fast gradient echo pulse sequence following the administration of an extracellular contrast agent. However, there exists a degree of image contrast variability and subjectivity due to contrast agent kinetics and user-specified imaging parameters. Also, the technique has not been explored at higher field strengths (3T), which offer greater inherent signal-to-noise ratio. The overall goal of this study is to compare magnetic resonance delayed contrast enhancement of myocardial infarction at 1.5T and 3T.
The analysis was conducted by first developing a comprehensive mathematical simulation of the imaging sequence, which allowed modification of various imaging parameters. Simulations were performed to optimize the sequence for flip angle and inversion time, as well as to evaluate the influence of other image parameters that affected contrast. These theoretical results were validated experimentally with phantoms.
In vivo post-contrast T1 measurements at 1.5T and 3T from normal volunteers (n=10) and patients (n=5) provided more precise input into mathematical optimization simulations. In both populations, longer T1 values were found at 3T compared to 1.5T for normal (pre-contrast: 1.24 .06s vs. 1.07 .05s; post-contrast: 0.34-0.59 vs. 0.33-0.54s, n=15) and infarcted myocardium (pre-contrast: 1.27 .06s vs. 1.04 .06s; post-contrast: 0.25-0.37s vs. 0.23-0.32s, n=5). Corresponding simulations using these T1 values revealed an infarct-to-normal tissue contrast gain at 3T of approximately 25%. In vivo image contrast between infarcted and normal tissue following contrast administration was also higher at 3T by approximately 37%.
In conclusion, there was good correlation between mathematical simulations of delayed enhancement and experimental results, enabling parameters to be compared and optimized offline given input T1 values. Although contrast-enhanced viability imaging at 3T suffered from artifacts due to field, RF, and inversion pulse inhomogeneity, these results suggest that 3T offers higher contrast-to-noise ratio than 1.5T for this application.
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Carcedo, Laura. "Theory and observations of the magnetic field in the solar corona." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/12948.
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Although the solar corona is one of the most studied areas in solar physics, its activity, such as flares, prominence eruptions and CMEs, is far from understood. Since the solar corona is a low-ß plasma, its structure and dynamics are driven by the magnetic field. The aim of this PhD thesis to study the magnetic field in the solar corona. Unfortunately, high quality direct measurements of the coronal magnetic field are not available and theoretical extrapolation using the observed photospheric magnetic field is required. The thesis is mainly divided in two parts. The first part deals with the comparison between theoretical models of magnetic fields and observed structures in the corona. For any theoretical model, a quantitative method to fit magnetic field lines to observed coronal loops is introduced. This method provides a quantity C that measures how closely a theoretical model can reproduce the observed coronal structures. Using linear force-free field extrapolation, the above field line fitting method is used to study the evolution of an active region. The method is also illustrated when the theoretical magnetic field depends on more than one parameter. The second part of the thesis focuses on the linear force-free field assumption using two different geometric configurations. Firstly a vertical rigid magnetic flux tube is considered. The analytical expression of the magnetic field is obtained as an expansion in terms of Bessel functions. The main properties of this system are discussed and compared with two cylindrically symmetric twist profiles. For the second system, the photosphere is assumed to be an infinite plane. Using translational geometry, the analytical expression of the linear force-free magnetic field that matches a prescribed line of sight magnetic field component is obtained. This solution is compared with the non-linear solution obtained by Roumeliotis (1993).
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MacTaggart, David. "Theoretical magnetic flux emergence." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/1692.
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Magnetic flux emergence is the subject of how magnetic fields from the solar interior can rise and expand into the atmosphere to produce active regions. It is the link that joins dynamics in the convection zone with dynamics in the atmosphere. In this thesis, we study many aspects of magnetic flux emergence through mathematical modelling and computer simulations. Our primary aim is to understand the key physical processes that lie behind emergence. The first chapter introduces flux emergence and the theoretical framework, magnetohydrodynamics (MHD), that describes it. In the second chapter, we discuss the numerical techniques used to solve the highly non-linear problems that arise from flux emergence. The third chapter summarizes the current literature. In the fourth chapter, we consider how changing the geometry and parameter values of the initial magnetic field can affect the dynamic evolution of the emerging magnetic field. For an initial toroidal magnetic field, it is found that its axis can emerge to the corona if the tube’s initial field strength is large enough. The fifth chapter describes how flux emergence models can produce large-scale solar eruptions. A 2.5D model of the breakout model, using only dynamic flux emergence, fails to produce any large scale eruptions. A 3D model of toroidal emergence with an overlying magnetic field does, however, produce multiple large-scale eruptions and the form of these is related to the breakout model. The sixth chapter is concerned with signatures of flux emergence and how to identify emerging twisted magnetic structures correctly. Here, a flux emergence model produces signatures found in observations. The signatures from the model, however, have different underlying physical mechanisms to the original interpretations of the observations. The thesis concludes with some final thoughts on current trends in theoretical magnetic flux emergence and possible future directions.
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Sturrock, Zoe. "Numerical simulations of sunspot rotation driven by magnetic flux emergence." Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/10129.
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Magnetic flux continually emerges from the Sun, rising through the solar interior, emerging at the photosphere in the form of sunspots and expanding into the atmosphere. Observations of sunspot rotations have been reported for over a century and are often accompanied by solar eruptions and flaring activity. In this thesis, we present 3D numerical simulations of the emergence of twisted flux tubes from the uppermost layers of the solar interior, examining the rotational movements of sunspots in the photospheric plane. The basic experiment introduces the mechanism and characteristics of sunspot rotation by a clear calculation of rotation angle, vorticity, magnetic helicity and energy, whereby we find an untwisting of the interior portion of the field, accompanied by an injection of twist into the atmospheric field. We extend this model by altering the initial field strength and twist of the sub-photospheric tube. This comparison reveals the rotation angle, helicity and current show a direct dependence on field strength. An increase in field strength increases the rotation angle, the length of fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. The fieldline length is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines, and hence possesses a larger rotation angle. No such direct dependence is found when varying the twist but there is a clear ordering in rotation angle, helicity, and energy, with more highly twisted tubes undergoing larger rotation angles. We believe the final angle of rotation is reached when the system achieves a constant degree of twist along the length of fieldlines. By extrapolating the size of the modelled active region, we find rotation angles and rates comparable with those observed. In addition, we explore sunspot rotation caused by sub-photospheric velocities twisting the footpoints of flux tubes.
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Bocquet, Francois-Xavier. "Investigations of current build up in topologically simple magnetic fields." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/11291.
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The solar corona is a highly conductive plasma which is dominated by the coronal magnetic field. Observations show that important solar phenomena like flares or the heating of the corona are driven by magnetic energy, probably through the process of magnetic reconnection. The release of magnetic energy by reconnection requires that non-ideal processes take place in contradiction to the high conductivity of the corona. One possibility to overcome this problem is to generate strong electrical currents in strongly localised regions. In this thesis we investigate how such localised currents can be formed by slow ideal evolution of topologically simple magnetic fields. To this purpose numerical simulations are carried out using an Eulerian and a Lagrangian MHD relaxation code. We first use a simple example (twisting of a uniform field) to investigate the advantages and disadvantages of both codes and to discover possible limitations for their application. We show that for the problems addressed in this thesis the Lagrangian code is more suited because it can resolve the localised current densities much better than the Eulerian code. We then focus in particular on magnetic fields containing a so-called Hyperbolic Flux Tube (HPT). A recently proposed analytical theory predicts that HFT's are sites where under certain conditions strong current build-up can be expected. We use our code to carry out a systematic parametric study of the dependence of current growth for a typical HFT configuration. We have also developed a completely new version of the analytical theory which is directly based on the set-up of our numerical simulations. We find that the simulations agree with the analytical prediction in a quantitative way but that the analytical theory underestimates the current growth quite substantially, probably by not taking into account the non-linear character of the full problem.
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Petit, Leon. "Screened real-space Korringa-Kohn-Rostoker description of the magnetic properties of solids." Thesis, University of Sheffield, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310727.
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Li, Fang. "An Analysis of the Linked-pulse in Steady-state Free Precession in MRI." PDXScholar, 1994. https://pdxscholar.library.pdx.edu/open_access_etds/4769.
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The steady-state free precession (SSFP) is one type of the fast scanning technique in MRI. So far most of its analysis are concentrated on the gradient echo SSFP (GR SSFP), very few paper~discuss the spin echo (SSFP (SE SSFP), and they are usually based on the simplified the hard pulse assumption. The advantage of the SE SSFP is that it can refocus the dephasing caused by the magnetic field inhomogeniety, which is the disadvantage of the GR SSFP. Also the hard pulse model can provide very limited information. The purpose of this paper is to establish the soft pulse model for both GR SSFP and SE SSFP. By using the spinor method to describe the interaction between the RF pulse, magnetic field, and the spin's magnetization, we create the steady state equations of the GR SSFP and SE SSFP, and give their analytical solutions. Because the SE SSFP's mathematical model is very complicated, we introduce a new concept, the linked-pulse, to simplify the problem, and provide the valuable results. Based on both traditional hard pulse model and our soft pulse model, we did a series of simulations, and compared both results. First of all, the soft pulse model can provide the slice profile and gradient effects, which is impossible for the hard pulse model. Second, in both models, the signal intensities are all depended on the Tl/T2 ratio, which is the characterization of the SSFP image. Third, we also observed how the pulse shape and the flip angles affect the slice profile and the signal intensity. In conclusion, the soft pulse model can give more information than hard pulse model can, such as slice profile and gradient effects, etc., provide more aspects for analyzing the SSFP image.
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Grady, Keith J. "Solar flare particle acceleration in collapsing magnetic traps." Thesis, University of St Andrews, 2012. http://hdl.handle.net/10023/2839.
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The topic of this thesis is a detailed investigation of different aspects of the particle acceleration mechanisms operating in Collapsing Magnetic Traps (CMTs), which have been suggested as one possible mechanism for particle acceleration during solar flares. The acceleration processes in CMTs are investigated using guiding centre test particle calculations. Results including terms of different orders in the guiding centre approximation are compared to help identify which of the terms are important for the acceleration of particles. For a basic 2D CMT model the effects of different initial conditions (position, kinetic energy and pitch angle) of particles are investigated in detail. The main result is that the particles that gain most energy are those with initial pitch angles close to 90° and start in weak field regions in the centre of the CMT. The dominant acceleration mechanism for these particles is betatron acceleration, but other particles also show signatures of Fermi acceleration. The basic CMT model is then extended by (a) including a magnetic field component in the invariant direction and (b) by making it asymmetric. It is found that the addition of a guide field does not change the characteristics of particle acceleration very much, but for the asymmetric models the associated energy gain is found to be much smaller than in symmetric models, because the particles can no longer remain very close to the trap centre throughout their orbit. The test particle method is then also applied to a CMT model from the literature which contains a magnetic X-line and open and closed field lines and the results are compared with the previous results and the findings in the literature. Finally, the theoretical framework of CMT models is extended to 2.5D models with shear flow and to fully 3D models, allowing the construction of more realistic CMT models in the future.
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Murray, Michelle J. "Solar flux emergence : a three-dimensional numerical study." Thesis, University of St Andrews, 2008. http://hdl.handle.net/10023/441.
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Flux is continually emerging on the Sun, making its way from the solar interior up into the atmosphere. Emergence occurs on small-scales in the quiet Sun where magnetic fragments emerge, interact and cancel and on large-scales in active regions where magnetic fields emerge and concentrate to form sunspots. This thesis has been concerned with the large-scale emergence process and in particular the results from previous solar flux emergence modelling endeavours. Modelling uses numerical methods to evolve a domain representing simplified layers of the Sun’s atmosphere, within which the subsurface layer contains magnetic flux. The flux is initialised such that it will rises towards the surface at the start of the simulation. Once the flux reaches the solar surface, it can only emerge into the atmosphere if a magnetic buoyancy instability occurs, after which it expands rapidly both vertically and horizontally. The aim of this thesis is to test the robustness of these general findings from simulations to date upon the seed magnetic field. More explicitly, we have used three-dimensional numerical simulations to investigate how variations in the subsurface magnetic field modify the emergence process and the resulting atmospheric field. We initially consider a simple constant twist flux tube for the seed field and vary the tube’s magnetic field strength and degree of twist. Additionally, we have examined the effects of using non-constant twist flux tubes as the seed field by choosing two different profiles for the twist that are functions of the tube’s radius. Finally, we have investigated the effects of increasing the complexity of the seed field by positioning two flux tubes below the solar surface and testing two different configurations for the tubes. In both cases, the magnetic fields of the two tubes are such that, once the tubes come into contact with each other, reconnection occurs and a combined flux system is formed. From our investigations, we conclude that the general emergence results given by previous simulations are robust. However, for constant twist tubes with low field strength and twist, the buoyancy instability fails to be launched when the tubes reach the photosphere and they remain trapped in the low atmosphere. Similarly, when the non-constant twist profile results in a low tension force throughout the tube, we find that the buoyancy instability is not initialised.
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Ma, Yamin. "Vegetation as a biotic driver for the formation of soil geochemical anomalies for mineral exploration of covered terranes." University of Western Australia. School of Earth and Geographical Sciences, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0235.
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[Tuncated abstract] Soil is a relatively low cost and robust geochemical sampling medium and is an essential part of most mineral exploration programs. In areas of covered terrain, however, soils are less reliable as a sampling medium because they do not always develop the geochemical signature of the buried mineralisation; possibly a result of limited upward transport of ore related elements into the surficial overburden. As economic demands on the resources industry grow, mineral exploration continues to expand further into areas of covered terrain where the rewards of finding a new deposit relative to the risks of finding it may be comparatively low. Thus, improving the costeffectiveness of a geochemical exploration program requires a sound understanding of the mechanisms by which soil geochemical anomalies form in transported overburden. This thesis examines the deep biotic uplift of ore related elements by deep rooting vegetation as a mechanism for the development of soil geochemical anomalies within transported overburdens, in semi-arid and arid regions. '...' Vegetation and soils were analysed at two Au prospects in Western Australia: Berkley, Coolgardie and Torquata, 210 km south-east of Kambalda, in semi-arid Western Australia to complement both the mass balance and the differential modelling. At Berkley, both the vegetation and soils located directly over the mineralisation showed high concentrations of Au. There may be indirect evidence for the operation of the deep plant uptake flux taking effect from the field evidence at Berkley. Firstly, anomalous concentrations of Au were found in the surface soils, with no detectable Au in the transported overburden. Secondly, the trace element concentrations in vegetation showed correlation to the buried lithology, which to our knowledge has not been reported elsewhere. The results from the samples at Torquata, in contrast, were less conclusive because the Au is almost exclusively associated with a surficial calcrete horizon (at <5 m soil depth). Strong correlations of Ca and Au in leaf samples however, suggest that the vegetation may be involved in the formation of calcrete and the subsequent association of Au with the calcrete. Among the vegetation components, the litter and leaf samples gave the greatest anomaly contrast at both prospects. Finally, three main drivers for the deep biotic uplift of elements were identified based on the results from the mechanistic numerical modelling exercise: i) the deep uptake flux; ii) the maximum plant concentration and; iii) the erosional flux. The relative sizes of these three factors control the rates of formation and decay, and trace element concentrations, of the soil anomaly. The main implication for the use of soils as exploration media in covered terranes is that soil geochemical anomalies may only be transient geological features, forming and dispersing as a result of the relative sizes of the accumulative and loss fluxes. The thesis culminates in the development of the first quantitative, mechanistic model of trace element accumulation in soils by deep biotic uplift.
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Williams, Benjamin Matthew. "The dynamic topology of the solar corona : mapping the Sun's three dimensional magnetic skeleton." Thesis, University of St Andrews, 2018. http://hdl.handle.net/10023/14637.
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Observations of the surface of the Sun reveal multi-scaled, mixed magnetic features that carpet the entire solar surface. Not surprisingly, the global magnetic fields extrapolated from these observations are highly complex. This thesis explores the topology of the Sun's global coronal magnetic fields. The magnetic skeleton of a magnetic field provides us with a way of examining the magnetic field and quantifying its complexity. Using specialised codes to find the magnetic skeletons which were written during the course of this work, we first examine potential field extrapolations of the global solar coronal magnetic field determined from observed synoptic magnetograms from the Heliospheric Magnetic Imager on the Solar Dynamics Observatory. The resolution of the PFSS models is found to be very important for discovering the true nature of the global magnetic skeleton. By increasing the maximum number of harmonics used in the potential field extrapolations and, therefore, the grid resolution, 60 times more null points may be found in the coronal magnetic field. These high resolution fields also have a large global separator network which connects the coronal magnetic field over large distances and involves between 40 % and 60 % of all the null points in the solar atmosphere. This global separator network exists at both solar minimum and solar maximum and has separators that reach high into the solar atmosphere (> 1R☉) even though they connect null points close to the solar surface. These potential field extrapolations are then compared with magnetohydrostatic (MHS) extrapolations of the coronal magnetic field which also provide us with information about the plasma in the corona. With a small component of electric current density in the direction perpendicular to the radial direction, these MHS fields are found to have a plasma beta and pressure typical of the corona. As this small component of electric current density grows, the heliospheric current sheet is warped significantly and the magnetic field, plasma beta and pressure become unphysical. Torsional spine reconnection is also studied local to a single null point. First using a dynamical relaxation of a spiral null point under non-resistive magnetohydrodynamics (MHD) to a MHS equilibrium is form in which a current layer has built up around the spine lines. Then the reconnection under resistive MHD in this current sheet is studied. The current about the spine lines is dissipated and the magnetic energy is mainly converted into heat directly as the field lines untwist about the spine line.
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Sander, Peter T. "On reliably inferring differential structure from three-dimensional images." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75752.
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Early image understanding seeks to derive analytic representations from image data. This thesis presents steps towards this goal for three-dimensional imagery by focusing on the inference of trace points (points belonging to surfaces), and the estimation of associated differential structure given by the principal curvature and direction fields over smooth surfaces. Computation of these fields is posed as the determination of a cross section through the bundle of curvature frames over the estimated trace. Algorithm robustness and the stability of results are essential for analysis of real images; to this end, I present a functional minimization algorithm where the principal direction cross section meets appropriate criteria for a minimum, and develop an implementation as an iterative constraint satisfaction procedure based on local surface smoothness properties. For shape description and eventual object recognition, the exact recovery of local structure everywhere is less important than the identification of singular surface points which prove stable to noise and small surface perturbations, in particular, the umbilic points of surfaces. Such points are computed naturally from the estimated local surface structure embodied in the principal direction cross section of the frame bundle. Examples of the recovery of local structure are presented for synthetic images degraded by noise and for clinical magnetic resonance images.
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Campos, Camila Dalben Madeira 1986. "Desenvolvimento de uma microbomba de membrana com atuação magnética." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/264070.
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Orientador: Eurípedes Guilherme de Oliveira NóbregaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
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Resumo: Este trabalho teve como objetivo o desenvolvimento de uma microbomba de membrana acionada eletromagneticamente, tornando possível sua utilização futura em dispositivos que reúnam de maneira eficiente diversos processos microfluídicos. Para atingir este objetivo foi necessário o desenvolvimento do atuador, composto de uma membrana flexível e uma microbobina, e do modelo, aqui desenvolvido utilizando a técnica de grafos de conexão, que permita o planejamento futuro das aplicações deste dispositivo. A membrana flexível foi fabricada utilizando-se resina fotocurável de poliuretano-acrilato ou silício corroído em banho KOH e recebeu filmes de níquel puro, depositados por processo à vácuo e eletroquímico e filmes depositados eletroquimicamente da liga CoNiMnP. Tais membranas atingiram deslocamentos próximos a 1?m frente a campos magnéticos de aproximadamente 250 G. As microbobinas, produzidas por meio de deposição eletrolítica de ouro sobre alumina, foram capazes de gerar campos magnéticos ao redor de 50 G. A microbomba com câmara de bombeamento de 10 mm, fabricada com corpo em poliuretano-acrilato e com o atuador descrito apresentou um bom fluxo de líquido nos testes com água.
Abstract: This investigation was conducted to develop a new membrane micropump, magnetically actuated, able to be used in lab-on-a-chip devices. To reach this target, a new actuator was eloped, containing a microcoil and a flexible diaphragm covered with metallic film, and a bond-graph model, leading future applications planning. The diaphragm was made using photocurable polyurethane acrylate resin or silicon etched in KOH bath, covered with pure nickel films, deposited by sputtering and electroplating techniques and electroplated CoNiMnP films. Diaphragms reached 1 ?m displacement facing 250G magnetic fields. Microcoils, obtained by electroplating over alumina surfaces, produced magnetic fields close to 50G. Micropump pumping chamber diameter of 10 mm, made using polyurethane acrylate and using the described actuator produced good water flow in the tests
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
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Wood, Paul D. "Elements of solar activity : particle acceleration and filament formation." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/11309.
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This thesis studies the acceleration of particles to super-thermal energies in explosive solar events as well as the magnetic changes in connectivity that may be responsible for changes in the morphology of quiescent filaments. Firstly a review of some of the observations of solar flare dynamics is given, as well as an introduction to the competing theories attempting to explain both particle acceleration and filament formation. An explanation of the numerical FORTRAN code that is used to calculate the trajectories of particle distribution functions in prescribed electromagnetic fields is given. Examples of known fields are used to test the accuracy of the code and the simple example of the well-known Litvinenko current sheet field is investigated. The results of charged particle orbit calculations in prescribed electric and magnetic fields motivated by magnetic reconnection models are then presented. The electromagnetic fields are chosen to resemble a current sheet with a localised reconnection region. The dependence of the model on the important physical parameters is considered. An introduction to the mathematical formulation of a collapsing magnetic trap is given. The same numerical code is used to calculate single electron orbits in this more complicated time dependent electromagnetic field. Consideration of important previous work is given before describing the best attempts to model the movement of flare loops in a realistic fashion. Finally the process of flux cancellation and filament formation is studied using a range of data including ground-based Hα and SoHO MDI magnetograms. It is found that the cancellation occurs at the ends of Hα sections of the filament and is accompanied by a noticeable increase in the Hα intensity and linkage of the sections. Measurements of the amount of flux cancelled at each site show it is in agreement with an estimate of the axial flux contained in the filament.
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Bowness, Ruth. "Current sheets in the solar corona : formation, fragmentation and heating." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2081.
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In this thesis we investigate current sheets in the solar corona. The well known 1D model for the tearing mode instability is presented, before progressing to 2D where we introduce a non-uniform resistivity. The effect this has on growth rates is investigated and we find that the inclusion of the non-uniform term in η cause a decrease in the growth rate of the dominant mode. Analytical approximations and numerical simulations are then used to model current sheet formation by considering two distinct experiments. First, a magnetic field is sheared in two directions, perpendicular to each other. A twisted current layer is formed and we find that as we increase grid resolution, the maximum current increases, the width of the current layer decreases and the total current in the layer is approximately constant. This, together with the residual Lorentz force calculated, suggests that a current sheet is trying to form. The current layer then starts to fragment. By considering the parallel electric field and calculating the perpendicular vorticity, we find evidence of reconnection. The resulting temperatures easily reach the required coronal values. The second set of simulations carried out model an initially straight magnetic field which is stressed by elliptical boundary motions. A highly twisted current layer is formed and analysis of the energetics, current structures, magnetic field and the resulting temperatures is carried out. Results are similar in nature to that of the shearing experiment.
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Yeates, Anthony Robinson. "Development and application of a global magnetic field evolution model for the solar corona." Thesis, University of St Andrews, 2009. http://hdl.handle.net/10023/734.
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Magnetic fields are fundamental to the structure and dynamics of the Sun’s corona. Observations show them to be locally complex, with highly sheared and twisted fields visible in solar filaments/prominences. The free magnetic energy contained in such fields is the primary source of energy for coronal mass ejections, which are important—but still poorly understood drivers of space weather in the near-Earth environment. In this thesis, a new model is developed for the evolution of the large-scale magnetic field in the global solar corona. The model is based on observations of the radial magnetic field on the solar photosphere (visible surface). New active regions emerge, and their transport and dispersal by surface motions are simulated accurately with a surface flux transport model. The 3D coronal magnetic field is evolved in response to these photospheric motions using a magneto-frictional technique. The resulting sequence of nonlinear force-free equilibria traces the build-up of magnetic helicity and free energy over many months. The global model is applied to study two phenomena: filaments and coronal mass ejections. The magnetic field directions in a large sample of observed filaments are compared with a 6-month simulation. Depending on the twist of newly-emerging active regions, the correct chirality is simulated for up to 96% of filaments tested. On the basis of these simulations, an explanation for the observed hemispheric pattern of filament chirality is put forward, including why exceptions occur for filaments in certain locations. Twisted magnetic flux ropes develop in the simulations, often losing equilibrium and lifting off, removing helicity. The physical basis for such losses of equilibrium is demonstrated through 2D analytical models. In the 3D global simulations, the twist of emerging regions is a key parameter controlling the number of lift-offs, which may explain around a third of observed coronal mass ejections.
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Wilmot-Smith, Antonia. "The origin and dynamic interaction of solar magnetic fields." Thesis, St Andrews, 2008. http://hdl.handle.net/10023/417.
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Restante, Anna Lisa. "The investigation of quasi-separatrix layers in solar magnetic fields." Thesis, University of St Andrews, 2011. http://hdl.handle.net/10023/2106.
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The structure of the magnetic field is often an important factor in many energetic processes in the solar corona. To determine the topology of the magnetic field features such as null points, separatrix surfaces, and separators must be found. It has been found that these features may be preferred sites for the formation of current sheets associated with the accumulation of free magnetic energy. Over the last decade, it also became clear that the geometrical analogs of the separatrices, the so-called quasi separatrix layers, have similar properties. This thesis has the aim of investigating these properties and to find correlations between these quantities. Our goal is to determine the relation between the geometrical features associated with the QSLs and with current structures, sites of reconnection and topological features. With these aims we conduct three different studies. First, we investigate a non linear force free magnetic field extrapolation from observed magnetogram data taken during a solar flare eruption concentrating our attention on two snapshots, one before the event and one after. We determine the QSLs and related structures and by considering carefully how these change between the two snapshots we are able to propose a possible scenario for how the flare occurred. In our second project we consider potential source distributions. We take different potential point source models: two four sources models already presented in the literature and a random distribution of fifteen sources. From these potential models we conduct a detailed analysis of the relationship between topological features and QSLs. It is found that the maxima of the Q-factor in the photosphere are located near and above the position of the subphotospheric null points (extending part way along their spines) and that their narrow QSLs are associated with the curves defined by the photospheric endpoints of all fan field lines that start from subphotospheric sources. Our last study investigates two different flux rope emergence simulations. In particular, we take one case with and one without an overlying magnetic field. Here, we can identify the QSLs, current, and sites of reconnection and determine the relation between them. From this work we found that not all high-Q regions are associated with current and/or reconnection and vice-versa. We also investigated the geometry of the field lines associated with high-Q regions to determine which geometrical behaviour of the magnetic field they are associated with. Those that are associated with reconnection also coincide with topological features such as separators.
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Barnes, Gary James. "Computational modelling for type-II superconductivity and the investigation of high temperature superconducting electrical machines." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365887.
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Rici, Emerson Tadeu Gonçalves. "Modelos matemáticos em finanças: desenvolvimento histórico-científico e riscos associados às premissas estruturais." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/96/96133/tde-28042008-110735/.
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Este trabalho tem como objetivo estudar as origens dos estudos ligados à gestão do risco e suas aplicações no mercado de capitais, incluindo o mercado brasileiro. São destacadas importantes características estatísticas desses estudos, algumas premissas probabilísticas básicas e o questionamento do uso indiscriminado dos modelos matemáticos desenvolvidos para Finanças. Apresentamos alguns tipos de distribuições estatísticas que podem ser aplicadas ao mercado de capitais. Esta pesquisa apresenta, também, características de sistemas complexos, da Teoria da Utilidade de Bernoulli, da Teoria da Utilidade Esperada (TUE) de Von Neumann e Morgenstern (1944), da Hipótese de Mercados Eficientes (HME) organizado/sistematizado por Eugene Fama (1970), da Racionalidade Limitada, estudada por Simon (1959), das Finanças Comportamentais, tratada por Kahneman e Tverski (1979) e do uso de modelos, apresentado por Merton, (1994). É feito um estudo empírico, a título de ilustração, contemplando o mercado brasileiro, representado pelo índice BOVESPA (Ibovespa), comparado com resultados obtidos por Gabaix (2003), em estudo realizado no mercado americano, a fim de verificar a distribuição de probabilidade do retorno. Esta realização empírica é realizada no intento de reforçar a importância da reflexão acerca do uso indiscriminado dos modelos e das quebras de suas premissas.The objective of this work is to study the origins of the research related to risk and its implications to capital markets, including the Brazilian market. Important statistical characteristics, several basic probabilistic premises and the questioning of indiscriminate use of mathematical models developed by accountants and analysts in finances had been highlighted. There had been shown some kinds of statistical distribution which can be applied to capital markets. This research also presents characteristics of complex systems, Utility Theory, studied by Von Neumann and Morgenstern (1944), Efficient Markets Hypothesis (EMH), organized/systematized by Eugene Fama (1970), Limited Rationality, studied by Simon (1959), Behavioral Finance, dealt by Kahneman and Tveski (1979) and model\'s use by Merton (1994). In order to illustrate the work, there had been made an empirical study, contemplating Brazilian market and comparing it to Garbaix\'s (2003) results, obtained by American market study. This was made in order to verify the market return probability distribution to reinforce the importance of reflection in indiscriminate usage of models and its premises crack.
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Pozdin, Maksym O. "Automated Extraction of Subdural Grid Electrodes from Post-Implant MRI Scans for Epilepsy Surgery." Thesis, Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/4979.
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The objective of the current research was to develop an automated algorithm with no or little user assistance for extraction of Subdural Grid Electrodes (SGE) from post-implant MRI scans for epilepsy surgery.
The algorithm utilizes the knowledge about the artifacts created by Subdural Electrodes (SE) in MRI scans. Also the algorithm does not only extract individual electrodes, but it also extracts them as a SGE structures. Information about the number and type of implanted electrodes is recorded during the surgery [1]. This information is used to reduce the search space and produce better results. Currently, the extraction of SGE from post-implant MRI scans is performed manually by a technologist [1, 2, 3]. It is a time-consuming process, requiring on average a few hours, depending on the number of implanted SE. In addition, the process does not conserve the geometry of the structures, since electrodes are identified individually. Usually SGE extraction is complicated by nearby artifacts, making manual extraction a non-trivial task that requires a good visualization of 3D space and orientation of SGE in it. Currently, most of the technologists use 2D slice viewers for extraction of SGE from 3D MRI scans.
There is no commercial software to perform the automated extraction task. The only algorithm suggested in the literature is [4]. The goal of the proposed algorithm is to improve the performance of the algorithm in [4].
As a goal, the proposed algorithm performs extraction of SGE not only for individual electrodes, but by applying geometric constraints on SGE.
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Johnston, Craig David. "Modelling chromospheric evaporation in response to coronal heating." Thesis, University of St Andrews, 2018. http://hdl.handle.net/10023/14630.
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This thesis presents a new computationally efficient method for modelling the response of the solar corona to the release of energy. During impulsive heating events, the coronal temperature increases which leads to a downward heat flux into the transition region (TR). The plasma is unable to radiate this excess conductive heating and so the gas pressure increases locally. The resulting pressure gradient drives an upflow of dense material, creating an increase in the coronal density. This density increase is often called chromospheric evaporation. A process which is highly sensitive to the TR resolution in numerical simulations. If the resolution is not adequate, then the downward heat flux jumps over the TR and deposits the heat in the chromosphere, where it is radiated away. The outcome is that with an under-resolved TR, major errors occur in simulating the coronal density evolution. We address this problem by treating the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. In this thesis, it is shown that this method permits fast and accurate numerical solutions in both one-dimensional and multi-dimensional simulations. By modelling the TR with this appropriate jump condition, we remove the influence of poor numerical resolution and obtain the correct evaporative response to coronal heating, even when using resolutions that are compatible with multi-dimensional magnetohydrodynamic simulations.
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Munschy, Marc. "Etude geophysique detaillee du point triple de rodriguez et de la zone axiale des trois dorsales associees (ocean indien)." Université Louis Pasteur (Strasbourg) (1971-2008), 1987. http://www.theses.fr/1987STR13057.
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L'etude geophysique detaillee (bathymetrie seabeam, gravimetrie, magnetisme) du point triple rodriguez et d'un segment de la zone axiale des trois dorsales oceaniques associees situe a environ 400 km du point triple, a permis de realiser des cartes bathymetriques, gravimetriques et magnetiques de ces quatre zones qui representent des surfaces d'environ 8500 km**(2)
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Katekawa, Marcel Eiki. "Analise teorico-experimental do encolhimento : estudo da secagem de banana." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/266684.
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Orientador: Maria Aparecida SilvaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica
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Resumo: O processo de secagem de sólidos induz efeitos colaterais no material seco, sendo que a redução de volume é um destes efeitos. O objetivo deste estudo é investigar as características do processo de encolhimento e propor uma estratégia para inclusão destes efeitos na simulação da secagem. Escolheu-se a banana como objeto de estudo devido a sua importância para o Brasil e à existência de alguns estudos sobre o encolhimento desta fruta. Estudou-se inicialmente o processo de encolhimento durante a secagem e os efeitos das condições de processo sobre o comportamento dimensional do material. Fatias de banana encolhem linearmente no início da secagem, mas esse comportamento não é observado para baixos teores de umidade. Como a banana possui uma estrutura potencialmente anisotrópica, o efeito do comportamento dos diferentes tecidos da fruta teve que ser levado em consideração através do estudo da transição vítrea de cada fase durante a secagem. Um dos tecidos, o mesocarpo, possui temperatura de transição vítrea de 46ºC quando seco e pode sofrer transição durante a secagem convectiva e afetar o volume final da amostra seca. Além disso, estudou-se como a umidade é compartimentalizada no interior de cada tecido pela técnica de RMN e a influência sobre o encolhimento da amostra. O mesocarpo é seco mais rapidamente, mesmo possuindo uma quantidade de umidade livre menor que o endocarpo. Finalmente, desenvolveu-se uma resolução de equações de balanço de massa e energia utilizando-se malhas não estruturadas para poder melhor adaptar o encolhimento na modelagem
Abstract: The drying process may induce collateral effects in the dry material, such as the volume reduction. The objectives of this study are to investigate the characteristics of the shrinking process and to consider a strategy for inclusion of these effects in a drying simulation. Banana was chosen as a case study due to its importance in Brazil and to the existence of some studies on the shrinking process of this fruit during drying. Initially the effects of the drying conditions on the dimensional behavior of the material were analyzed. Banana slices shrink linearly in the beginning of the drying process, though some deviation of this behavior is observed for low moisture content. As banana possesses a potentially anisotropic structure, the behavior of the different tissues from the edible fruit had to be taken into consideration through the study of the glass transition of each phase. One of the tissues, the mesocarp, has a glass transition temperature of 46ºC when totally dry and may undergo glass transition during convective drying, which affects the final volume of the dried sample. Moreover, moisture compartmentalization in the interior of each tissue was analyzed and related to the differential behavior during drying. The mesocarp is more easily dried even though it possesses a higher concentration of unbound moisture. Finally, a resolution of mass and energy balance equations using unstructured meshes in order to allow a better inclusion of the shrinkage effects in drying was developed.
Doutorado
Engenharia de Processos
Doutor em Engenharia Química
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Johnson, Kevin Robert. "In Vivo Coronary Wall Shear Stress Determination Using CT, MRI, and Computational Fluid Dynamics." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/14482.
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Wall shear stress (WSS) has long been identified as a factor in the development of atherosclerotic lesions. Autopsy studies have revealed a strong tendency for lesion development at arterial branch sites and along the inner walls of curvature areas that, in theory, should experience low WSS. Calculations of coronary artery WSS have typically been based upon average models of coronary artery geometry with average flow conditions and then compared to average lesion distributions. With all the averaging involved, a more detailed knowledge of the correlation between WSS and atherosclerotic lesion development might be obscured. Recent advancements in hemodynamic modeling now enable the calculation of WSS in individual subjects. An image-based approach for patient-specific calculation of in vivo WSS using computational fluid dynamics (CFD) would allow a more direct study of this correlation. New state-of-the-art technologies in multi-detector computed tomography (CT) and 3.0 Tesla magnetic resonance imaging (MRI) offer potential improvements for the measurement of coronary artery geometry and blood flow.
The overall objective of this research was to evaluate the quantitative accuracy of multi-detector CT and 3.0 Tesla MRI and incorporate those imaging modalities into a patient-specific CFD model of coronary artery WSS. Using a series of vessel motion phantoms, it has been shown that 64-detector CT can provide accurate measurements of coronary artery geometry for heart rates below 70 beats per minute. A flow phantom was used to validate the use of navigator-echo gated, phase contrast MRI at 3.0 Tesla to measure velocity of coronary blood flow. Patient-specific, time-resolved CFD models of coronary WSS were created for two subjects. Furthermore, it was determined that population-average velocity curves or steady state velocities can predict locations of high or low WSS with high degrees of accuracy compared to the use of patient-specific blood flow velocity measurements as CFD boundary conditions. This work is significant because it constitutes the first technique to non-invasively calculate in vivo coronary artery WSS using image-based, patient-specific modeling.
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Hurdal, Monica Kimberly. "Mathematical and computer modelling of the human brain with reference to cortical magnification and dipole source localisation in the visual cortx." Thesis, Queensland University of Technology, 1998.
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Derry, Philip. "Quasiparticle interference in strongly correlated electronic systems." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:f487c821-dbbb-4ebe-8b05-c13807379c2c.
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We investigate the manifestation of strong electronic correlations in the quasiparticle interference (QPI), arising from the scattering of conduction electrons from defects and impurities in an otherwise translationally-invariant host. The QPI may be measured experimentally as the Fourier transform of the spatial modulations in the host surface density of states that result, which are mapped using a scanning tunnelling microscope. We calculate the QPI for a range of physically relevant models, demonstrating the effect of strong local electronic correlations arising in systems of magnetic impurities adsorbed on the surface of non-interacting host systems. In the first instance the effect of these magnetic impurities is modelled via the single Anderson impurity model, treated via numerical renormalization group (NRG) calculations. The scattering of conduction electrons, and hence the QPI, demonstrate an array of characteristic signatures of the many-body state formed by the impurity, for example due to the Kondo effect. The effect of multiple impurities on the QPI is also investigated, with a numerically-exact treatment of the system of two Anderson impurities via state-of-the-art NRG calculations. Inter-impurity interactions are found to result in additional scattering channels and additional features in the QPI. The QPI is then investigated for the layered transition metal oxide Sr2RuO4, for which strong interactions in the host conduction electrons give rise to an unconventional triplet superconducting state at Tc ∼ 1.5K. The detailed mechanism for this superconductivity is still unknown, but electron-electron or electron-phonon interactions are believed to play a central role. We simulate the QPI in Sr2RuO4, employing an effective parametrized model consisting of three conduction bands derived from the Ru 4d t2g orbitals that takes into account spin orbit coupling and the anisotropy of the Ru t2g orbitals. Signatures of such interactions in the normal state are investigated by comparing these model calculations to experimental results. We also calculate the QPI in the superconducting state, and propose how experimental measurements may provide direct evidence of the anisotropy and symmetry of the superconducting gap, and thus offer insight into the pairing mechanism and the superconducting state.
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Gregory, Scott G. "T Tauri stars : mass accretion and X-ray emission." Thesis, St Andrews, 2007. http://hdl.handle.net/10023/336.
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Dixit, Sanjay. "Simulation of tropical pacific circulation anomalies with linear atmosphere and ocean models." Thesis, 1987. http://hdl.handle.net/1957/28619.
Full textAbstract:
A simple atmosphere and ocean model of relevance to El Nino
and Southern Oscillation (ENSO) is discussed. Both the
atmosphere and ocean models are two layer, three
dimensional, linear and baroclinic, and generally follow
the Oregon State University coupled general circulation
model. However, the parameterization differs considerably
from previous work in the treatment of the atmospheric
latent heat release. This new parameterization follows the
formula used in the theory of conditional instability of
the second kind (CISK). In this the latent heat release is
proportional to the low level convergence. Utilizing the
"Comprehensive Ocean Atmosphere Data Set" (COADS), which
contains all oceanic and atmospheric surface variables over
the global ocean from 1946-1979, experimental model results
are discussed for determination of the validity of the
parameterizations. In particular, the years 1957, 1965 and
1972 in which El Nino events occurred are examined. The
parameterization is deemed to be realistic, and should
permit simulation of the El Nino upon coupling the two
models.Graduation date: 1988
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Ji, Jin-Chen. "Nonlinear dynamics of magnetic bearing systems." Thesis, 2006. http://hdl.handle.net/2440/63568.
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The aim of the work outlined in this thesis was to gain a deep insight into the effects of nonlinearities of magnetic bearings and the influence of time delays occurring in the feedback path control on their dynamic behaviour and performance. Emphasis was on stability analysis, bifurcation control, determination of stable operating conditions, prediction of bearing performance, and on aspects of nonlinear dynamic behaviour including bifurcations, coexistance of multiple solutions and complicated motions ... The present thesis comprises 12 papers which were recently published in seven international journals.Thesis (Ph.D.) - University of Adelaide, School of Mechanical Engineering, 2006
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Dolasinski, Brian D. "Exploring the feasibility of the detection of neuronal activity evoked by dendrite currents using MRI." 2010. http://liblink.bsu.edu/uhtbin/catkey/1629784.
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MRI has been applied to directly detecting neuronal activity. The direct detection of multiple dendrite sites within the brain offers an important tool in the analysis of the brain for mapping cognition. In this, multiple dendrite contributions can be applied with the same model between the parallel and anti-parallel orientations depending on a spatial depolarization and re-polarization wave. Once the strength of the dendritic contribution was calculated, the spatially dependent phase shifts were theoretically modeled. In the construction of this column the dendrites were modeled as having cylindrical symmetry, uniform current density, and the intracellular current was taken as the primary current contribution to the volume dendrite model.
The method examined the system using the known volume density of the dendrites treated with the current dipole model over a voxel. The maximum effect of the field strength, phase, and percent signal change was theoretically calculated. The maximum field was calculated as 1.07 nT, the maximum phase was calculated as 2.14 mrad, and the maximum percent signal increase was calculated as 0.217 %.Overview of the basics of MRI imaging -- Overview of neural activation and imaging of the activation -- Theory and methods -- Results.
Department of Physics and Astronomy
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Toumelin, Emmanuel. "Pore-scale petrophysical models for the simulation and combined interpretation of nuclear magnetic resonance and wide-band electromagnetic measurements of saturated rocks." Thesis, 2006. http://hdl.handle.net/2152/2614.
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Wang, Yanan. "Mathematical modelling of bone remodelling in mechanical, electro-magnetic fields at the cellular level." Phd thesis, 2010. http://hdl.handle.net/1885/151461.
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The skeleton is a metabolically active organ that undergoes continuous remodelling throughout life. At the cellular level, bone remodelling is an organised process whereby osteoclasts remove old bone and osteoblasts replace them with newly formed bone. The osteoclasts and osteoblasts work together in a coupled manner within a so-called 'basic multicellular unit' (BMU). Bone remodelling helps to repair microdamages in bone matrix, preventing the accumulation of old bone. It also plays an important role in maintaining plasma calcium homeostasis. The regulation of bone remodelling is both systemic and local. The most important systemic regulator is parathyroid hormone (PTH), which has been used as a therapy to treat osteoporosis in clinics; however, the underlying mechanism by which PTH is regulated is still not clear. As far as local regulation of bone remodelling is concerned, the discovery of the RANKIRANKL/OPG pathway is significant to the understanding of the interaction between osteoclastic cells and osteoblastic cells in BMU. A large number of therapeutic drugs and other stimuli have been found to apply their effects via RANKIRANKL/OPG. Mechanical stimulus has significant influence on bone remodelling. Disuse or lack of loading causes bone remodelling with bone resorption dominating bone formation and thus a loss of bone mass or density. Conversely, overuse or increased loading causes bone mass or density to increase. Additionally, loadings with different characteristics such as frequency, number of loading cycles in a session and rest time between loading bouts affects bone remodelling differently. However, the underlying mechanisms are not fully understood despite a great deal of experimental work in this field. Pulsed electro-magnetic fields (PEMF) devices have been widely used in clinics to treat bone fracture non-union and shorten the recovery period of fracture. Despite the clinical success, it is still not clear how PEMF stimulus interacts with cells, factors or molecules that are involved in bone remodelling. This thesis will use a computational system biology approach to address the issues proposed above. Computational system biology is a systems biology approach that integrates experimental and computational research in order to understand complex biological systems such as bone remodelling. Based on the latest experimental results and mathematical advances, a mathematical model of bone remodelling at the cellular level is developed with PTH included. Building on this platform model, mechanical stimulus and PEMF are taken into account. Thus, their effects on bone remodelling and the underlying control mechanisms at the cellular level are investigated. The work in the thesis will further current understanding of bone remodelling at the cellular level. The quantitative analysis using our model will help pharmacological and non-pharmacological therapies developments, which eventually benefit patients who suffer from bone loss diseases such as osteoporosis.
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Rhee, Brian Kanghee. "Enhancement of mass transfer coefficient in three-phase magnetically stabilized fluidized bed." Thesis, 1998. http://hdl.handle.net/1957/33757.
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Videlefsky, Daryn Michael. "Investigating emerging market economies Reverse REIT-Bond Yield Gap anomalies: a case for tactical asset allocation under the multivariate Markov regime switching model." Thesis, 2017. http://hdl.handle.net/10539/23698.
Full textAbstract:
Submitted in partial fulfilment of the requirements for the degree of Masters of Management in Finance and Investments In the Faculty of Commerce, Law and Management University of the Witwatersrand, Wits Business School, 2016This paper presents a first time application of a variant of the concepts underpinning the Fed Model, amalgamated with the Bond-Stock Earnings Yield Differential, by applying it to the dividend yields of REIT indices. This modification is termed the yield gap, quantitatively constructed and adapted in this paper as the Reverse REIT-Bond Yield Gap. This metric is then used as the variable of interest in a multivariate Markov regime switching model framework, along with a set of three regressors. The REIT indices trailing dividend yield and associated metrics are the FTSE/EPRA NAREIT series. All data are from Bloomberg Terminals. This paper examines 11 markets, of which the EMEs are classified as Brazil, Mexico, Turkey and South Africa, whereas the advanced market counterparts are Australia, France, Japan, the Netherlands, Singapore, the United Kingdom, and the United States. The time-frame spans the period June 2013 until November 2015 for the EMEs, whilst their advanced market counterparts time-span covers the period November 2009 until November 2015. This paper encompasses a tri-fold research objective, and aims to accomplish them in a scientifically-based, objective and coherent fashion. Specifically, the purpose is in an attempt to gauge the reasons underlying EMEs observed anomalies entailing reverse REIT-Bond yield gaps, whereby their tenyear nominal government bonds out-yield their trailing dividend yields on their associated REIT indices; what drives fluctuations in this metric; and whether or not profitable tactical asset allocation strategies can be formulated to exploit any arbitrage mispricing opportunities. The Markov models were unable to generate clear-cut, definitive reasons regarding why EMEs experience this anomaly. Objectives two and three were achieved, except for France and Mexico. The third objective was also met. The REIT-Bond Yield Gaps static conditions have high probabilities of continuing in the same direction and magnitude into the future. In retrospection, the results suggest that by positioning an investment strategy, taking cognisance of the chain of economic events that are likely to occur following static REIT-Bond Yield Gaps, then investors, portfolio rebalancing and risk management techniques, hedging, targeted, tactical and strategic asset allocation strategies could be formulated to exploit any potential arbitrage profits. The REIT-Bond Yield Gaps are considered highly contentious, yet encompasses the potential for significant reward. The Fed Model insinuates that EME REIT markets are overvalued relative to their respective government bonds, whereas their advanced market counterparts exhibit the opposite phenomenon.
XL2018
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Armstrong, James D. 1970. "Structure and energy transport of the solar convection zone." Thesis, 2004. http://hdl.handle.net/10125/12102.
Full textAbstract:
Thesis (Ph. D.)--University of Hawaii at Manoa, 2004.Includes bibliographical references (leaves 134-139).
Also available by subscription via World Wide Web
xvi, 139 leaves, bound ill. 29 cm
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Marchenko, N. B., and E. P. Nechyporuk. "Spectral-time models of data signals under the action of interferences in the tasks related to electric and magnetic values measuring." Thesis, 2012. http://er.nau.edu.ua/handle/NAU/18543.
Full textAbstract:
Spectral-time models based on the use of linear and harmonizable random processes allow to describe and study a wide range of data signals and influencing interferences during measuring of the parameters and characteristics of electric and magnetic values not only in terms of correlation theory but taking into account higher-order moments
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Hicks, Joshua M. "Analysis of secondary structures in nucleic acid binding proteins and nuclear magnetic resonance investigation of helix propagation and residual motions in proteins." Thesis, 2005. http://hdl.handle.net/1957/29424.
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Sahoo, Shaon. "Studies Of Electronic, Magnetic And Entanglement Properties Of Correlated Models In Low-Dimensional Systems." Thesis, 2012. http://etd.iisc.ernet.in/handle/2005/2480.
Full textAbstract:
This thesis consists of six chapters. The first chapter gives an introduction to the field of low-dimensional magnetic and electronic systems and relevant numerical techniques. The recent developments in molecular magnets are highlighted. The numerical techniques are reviewed along with their advantages and disadvantages from the present perspective. Study of entanglement of a system can give a great insight into the system. At the last part of this chapter a general overview is given regarding entanglement, its measures and its significance in studying many-body systems.
Chapter 2 deals with the technique that has been developed by us for the full symmetry adaptation of non-relativistic Hamiltonians. It is advantageous both computationally and physically/chemically to exploit both spin and spatial symmetries of a system. It has been a long-standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of a point group, particularly for non-Abelian point groups. A very general technique is discussed in this chapter which is a hybrid method based on valence-bond basis and the basis of the z-component of the total spin. This technique is not only applicable to a system with arbitrary site spins and belonging to any point group symmetry, it is also quite easy to implement computationally. To demonstrate the power of the method, it is applied to the molecular magnetic system, Cu6Fe8, with cubic symmetry.
In chapter 3, the extension of the previous hybrid technique to electronic systems is discussed. The power of the method is illustrated by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and is in the largest non-Abelian point group. All the eigenstates of the model are obtained using our technique.
Chapter 4 deals with the thermodynamic properties of an important class of single-chain magnets (SCMs). This class of SCMs has alternate isotropic spin-1/2 units and anisotropic high spin units with the anisotropy axes being non-collinear. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. A transfer matrix (TM) method is developed to study statistical behavior of this class of SCMs. For the first time, it is also discussed in detail that how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. This technique is applied to a real helical chain magnet, which has been studied experimentally.
In the fifth chapter a bipartite entanglement entropy of finite systems is studied using exact diagonalization techniques to examine how the entanglement changes in the presence of long-range interactions. The PariserParrPople model with long-range interactions is used for this purpose and corresponding results are com-pared with those for the Hubbard and Heisenberg models with short-range interactions. This study helps understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions in the PPP model. It is also investigated if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, an interesting observation is made on the entanglement profiles of different states, across the full energy spectrum, in comparison with the corresponding profile of the density of states.
The entanglement can be localized between two noncomplementary parts of a many-body system by performing local measurements on the rest of the system. This localized entanglement (LE) depends on the chosen basis set of measurement (BSM). In this chapter six, an optimality condition for the LE is derived, which would be helpful in finding optimal values of the LE, besides, can also be of use in studying mixed states of a general bipartite system. A canonical way of localizing entanglement is further discussed, where the BSM is not chosen arbitrarily, rather, is fully determined by the properties of a system. The LE obtained in this way, called the localized entanglement by canonical measurement (LECM), is not only easy to calculate practically, it provides a nice way to define the entanglement length. For spin-1/2 systems, the LECM is shown to be optimal in some important cases. At the end of this chapter, some numerical results are presented for j1 −j2 spin model to demonstrate how the LECM behaves.
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"Numerical studies of the magnetic properties of double layer system =: 雙層系統的磁性質之數値硏究." 2002. http://library.cuhk.edu.hk/record=b5891196.
Full textAbstract:
Tam Ka Ming.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.
Includes bibliographical references (leaves 142-145).
Text in English; abstracts in English and Chinese.
Tam Ka Ming.
Acknowledgement --- p.ii
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Models for Many Body Systems --- p.1
Chapter 1.2 --- High Temperature Superconductor --- p.5
Chapter 1.3 --- Reasons of Study Double Layers --- p.9
Chapter 1.4 --- "Incommensurate Magnetic Excitation, Order Parameters" --- p.10
Chapter 1.5 --- Thesis Organization --- p.10
Chapter 2 --- Monte Carlo Methods --- p.12
Chapter 2.1 --- General Aspects of Monte Carlo Simulation --- p.12
Chapter 2.2 --- "Markov Chain, Metropolis Algorithm, Heat-Bath Algorithm" --- p.18
Chapter 2.3 --- Quantum Monte Carlo --- p.21
Chapter 2.4 --- Variational Quantum Monte Carlo --- p.22
Chapter 2.5 --- Green Function Monte Carlo --- p.27
Chapter 2.6 --- Auxiliary Field Monte Carlo --- p.35
Chapter 2.7 --- Summary of Quantum Monte Carlo --- p.38
Chapter 3 --- Constrained Path Monte Carlo --- p.40
Chapter 3.1 --- Various Formulas Used in Constrained Path Monte Carlo --- p.40
Chapter 3.2 --- Constrained Path Monte Carlo --- p.47
Chapter 3.3 --- Constrained Path Approximation --- p.51
Chapter 3.4 --- Measurements --- p.52
Chapter 3.5 --- Method of Avoiding Numerical Instability --- p.55
Chapter 4 --- Parallelisation of CPMC Program --- p.57
Chapter 4.1 --- Architecture of Parallel Machine --- p.57
Chapter 4.2 --- Communication Methods in Parallel Program --- p.65
Chapter 4.3 --- Comparison of Parallel and Serial Program --- p.74
Chapter 4.4 --- Measure of Parallel Program --- p.85
Chapter 4.5 --- Analysis of Serial CPMC Program --- p.89
Chapter 4.6 --- Analysis of the Parallel CPMC Program --- p.93
Chapter 5 --- Results from CPMC --- p.101
Chapter 5.1 --- Hubbard Model with Next Nearest Neighbour Hopping --- p.101
Chapter 5.2 --- Spin and Charge Correlations --- p.104
Chapter 5.3 --- Vertex Contributions --- p.111
Chapter 6 --- Mean Field Calculations of bilayer --- p.119
Chapter 6.1 --- Objective --- p.119
Chapter 6.2 --- Theoretical Model --- p.121
Chapter 6.3 --- Method of Solving the Model --- p.122
Chapter 6.4 --- Finding Susceptibility by RPA --- p.131
Chapter 6.5 --- Results --- p.136
Chapter 6.6 --- Summary --- p.140
Chapter 7 --- Summary --- p.141
Bibliography --- p.142