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Local Hall probe measurements and differential magneto-optical imaging with high spatial resolution have been used to investigate the magnetic state of high temperature superconducting Bi2Sr2CaCu2O8+� (BSCCO) micro-disks and platelet single crystals. The results obtained by magneto-optical imaging demonstrate that the field at which flux quantised vortices enter the disks decays exponentially with increasing temperature and the measured data agree well with analytic models for the thermal excitation of individual pancake vortices over Bean-Livingston surface barriers. Scanning Hall probe microscopy images are used to directly map the magnetic induction profiles of individual micro-disks at different applied fields and the results can be quite successfully fitted to analytic models which assume a continuous distribution of flux in the sample. At low fields, however, the characteristic mesoscopic compression of vortex clusters in increasing magnetic fields has been observed. Even at higher fields, where single vortex resolution is lost, it is still possible to track configurational changes in the vortex patterns, since competing vortex orders impose unmistakable signatures on local magnetisation curves as a function of the applied field. These observations are in excellent agreement with molecular dynamics numerical simulations which lead to a natural definition of the lengthscale for the crossover between discrete and continuum behaviours in this system. In closely related experiments, Hall magnetometry is used to probe the out-of-plane local magnetisation of platelet BSCCO single crystals. The magnetisation is found to depend on the strength and direction of an in-plane magnetic field in the crossing vortex lattices regime. The remanent magnetisation in zero out-of-plane field is found to exhibit a pronounced anisotropy, being largest with the in-plane field parallel to the crystalline a-axis, and smallest when it is parallel to the orthogonal b-axis. This behaviour is attributed to the presence of underlying linear disorder. Finally, spectral analysis of the local magnetisation data is used to estimate a lower cutoff for the characteristic frequency of thermal fluctuations of vortex positions.

Reconnection of wingtip vortices behind aircrafts is thought to be a cause of wake turbulence, detrimental to air traffic control. We observe the reconnection process for three initial vortex tube set-ups; anti-parallel, orthogonal and anti-parallel with axial flow. From these we are able to identify each of the different reconnection processes observed and discussed for the magnetic reconnection case but not necessarily the vortex reconnection case; of both 2D and 3D reconnection. We use a finite different method to solve the Navier-Stokes equation for a large array of points. We analyse the results of the first two scenarios for a range of Reynolds numbers to observe how the viscous term of Navier-Stokes affects the reconnection process. We were able to show that for an increase in $Re$ we would see an increase in the reconnection rate due to the formation of thinner and stronger vortex sheets which are necessary for a faster reconnection. For higher values of $Re$ we observed a Kelvin-Helmholtz instability within the vortex sheets and the formation of additional vortex rings during the reconnection process. We simulate a range of axial flow values to observe how kinetic helicity and twist evolve with reconnection. We were able to identify the loss of twist in the vortex tubes due to 3D reconnection known as 'slipping'. In these and the orthogonal runs we observed the generation of null pairs and the formation of a separator between them. We utilised the plots of both vorticity isosurfaces and vorticity fieldlines to observe and analyse the reconnection process where isosurfaces have been the norm for vortex reconnection observations in previous work. The vorticity fieldlines allow us to observe the orientation of vorticity during reconnection and allow us to observe both the 'threads' and 'bridges' and their evolution together.

Abstract not available

Thesis (Ph. D.)--University of Chicago, August 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Electronic structure of a conventional superconductor in the vicinity of a single, iso- lated magnetic impurity has been probed experimentally with scanning tunneling spectroscopy by Yazdani et al.. Motivated by their experiment, we study the ef- fects of a single magnetic impurity on superconductivity by means of the mean-¯eld Bogoliubov-de Gennes theory. The Bogoliubov-de Gennes equations are solved di- rectly and numerically, utilizing parallel computation on a CFI-founded 128-CPU Beowulf-class PC cluster here at the University of Saskatchewan. As a preliminary study, we also examine the electronic structure around a magnetic vortex. The local magnetic field around a vortex breaks up Cooper pairs and suppresses superconduc- tivity locally. Quasiparticle excitations are created and bound in the vortex core area due to repeated Andreev scattering. A magnetic impurity tends to align the spins of the neighboring electrons and break up Cooper pairs, and has similar effects of lo- cally suppressing superconductivity. A striking difference, however, from the vortex problem is that around a magnetic impurity there is particle-hole asymmetry in the tunneling conductance. This is due to different probability amplitudes in the spin-up branch and the spin-down branch of quasiparticle excitations. Furthermore, for the spin potential strength larger than a certain critical value, the nature of quasiparticle excitations is changed dramatically. Within a model of classical spin, we propose an explanation of the measured tunneling conductance of the experiment. This work is significant in that it gives us insight into superconductivity and magnetism{two complementary manifestation of strong electron correlations.

This thesis presents results from experimental and numerical investigations of the hydrodynamic forces on a rigid cylinder moving with prescribed orbits in uniform flow. The hydrodynamic forces are measured in both in-line (IL) and cross- ow (CF) directions. The measurements are processed to nd excitation and added mass coeffcients at discrete frequencies. The numerical simulations are used to illustrate the vortex shedding modes and are compared with the experimental results. The hydrodynamic coeffcients obtained from the harmonic forced motion experiments of a rigid cylinder do not always represent forces on a cross section of a exible beam. The orbits used in the forced motion experiments are therefore extracted from the measured motions of cross sections of a exible pipe under uniform and shear flows. Both periodic and observed orbits within a time window are applied as prescribed motions. Higher order displacement components are present in such orbits. IL response amplitudes from combined IL and CF response are larger than pure IL response amplitudes. The hydrodynamic coefficients obtained from the periodic experiments are often larger than those obtained from the pure IL tests. Higher order displacement components are more common in the IL direction than in the CF direction, and higher order IL displacement components will cause larger hydrodynamic forces in both directions. The hydrodynamic coefficients obtained from periodic motion tests are adequate for representing quasi-periodic observed motions. For chaotic observed motions, periodic orbits will yield hydrodynamic coefficients with larger uncertainties. Results from numerical analyses using large eddy simulation (LES) indicate that this method can be used to identify vortex shedding patterns and predict hydrodynamic forces under certain Re numbers and orbits.

Electronic structure of a conventional superconductor in the vicinity of a single, iso- lated magnetic impurity has been probed experimentally with scanning tunneling spectroscopy by Yazdani et al.. Motivated by their experiment, we study the ef- fects of a single magnetic impurity on superconductivity by means of the mean-¯eld Bogoliubov-de Gennes theory. The Bogoliubov-de Gennes equations are solved di- rectly and numerically, utilizing parallel computation on a CFI-founded 128-CPU Beowulf-class PC cluster here at the University of Saskatchewan. As a preliminary study, we also examine the electronic structure around a magnetic vortex. The local magnetic field around a vortex breaks up Cooper pairs and suppresses superconduc- tivity locally. Quasiparticle excitations are created and bound in the vortex core area due to repeated Andreev scattering. A magnetic impurity tends to align the spins of the neighboring electrons and break up Cooper pairs, and has similar effects of lo- cally suppressing superconductivity. A striking difference, however, from the vortex problem is that around a magnetic impurity there is particle-hole asymmetry in the tunneling conductance. This is due to different probability amplitudes in the spin-up branch and the spin-down branch of quasiparticle excitations. Furthermore, for the spin potential strength larger than a certain critical value, the nature of quasiparticle excitations is changed dramatically. Within a model of classical spin, we propose an explanation of the measured tunneling conductance of the experiment. This work is significant in that it gives us insight into superconductivity and magnetism{two complementary manifestation of strong electron correlations.

Liquid and gas do not separate naturally in microgravity, presenting a problem for twophase space systems. Increased integration of multiphase systems requires a separation method adaptable to a variety of systems. Researchers at Texas A&M University (TAMU) have developed a microgravity vortex separator (MVS) capable of handling both a wide range of inlet conditions and changes in these conditions. To optimize the MVS design, the effects of nozzle area, separator geometry, and inlet flow rate must be understood. Computational fluid dynamics (CFD), in the form of Adapco’s Star-CD, is used, along with laboratory testing, to accomplish this goal. Furthermore, as analysis aids for the laboratory data and CFD results, relationships for radial pressure, bubble transit time, and momentum transfer were developed. Ground testing data showed a linear relationship between rotational speed and inlet flow rate. The CFD results compared well with the ground data and indicated that the majority of the rotational flow travels at nearly the same rotational speed. Examination of the tangential velocity profile also showed that a reduction of nozzle outlet area resulted in increased tangential velocities. Using dimensional analysis, a relationship between separator radius, inlet momentum rate, fluid properties, and rotational speed was found. Applying this relationship to the ground data and CFD results showed a strong correlation between the two dimensionless groups. Linear regression provided an equation linking rotational speed to the separator parameters. This equation was tested against the ground data and shown to predict average rotational speed well for all separator models. These results were used to calculate the radial and axial transit times of gas bubbles within the separation volume. Radial transit time was found to decrease more rapidly than axial transit time as gas volume increased, indicating axial and radial transit times are closest in value for the all liquid case and increasing gas core diameter improves the operational characteristics of the separator. From a design standpoint, the all liquid case provides a minimum flow rate for successful phase separation. Maximum flow rate depends on the pressure resources of the system.