Trans-Magnetosonic Accretion in a Black Hole Magnetosphere

We present the critical conditions for hot trans-fast magnetohydrodynamical (MHD) flows in a stationary and axisymmetric black-hole magnetosphere. To accrete onto the black hole, the MHD flow injected from a plasma source with low velocity must pass through the fast magnetosonic point after passing through the ``inner'' or ``outer'' Alfven point. We find that a trans-fast MHD accretion solution related to the inner Alfven point is invalid when the hydrodynamical effects on the MHD flow dominate at the magnetosonic point, while the other accretion solution related to the outer Alfven point is invalid when the total angular momentum of the MHD flow is seriously large. When both regimes of the accretion solutions are valid in the black hole magnetosphere, we can expect the transition between the two regimes. The variety of these solutions would be important in many highly energetic astrophysical situations.Comment: 27 pages, 12 figures, accepted to Ap

Efficiency of Magnetized Thin Accretion Disks in the Kerr Metric

The efficiency of thin disk accretion onto black holes depends on the inner boundary condition, specifically the torque applied to the disk at the last stable orbit. This is usually assumed to vanish. I estimate the torque on a magnetized disk using a steady magnetohydrodynamic inflow model originally developed by Takahashi et al., 1990. I find that the efficiency epsilon can depart significantly from the classical thin disk value. In some cases epsilon > 1, i.e. energy is extracted from the black hole.Comment: 11 pages, 3 figures, aastex, submitted to ApJ Letter

Spins and orbits in semiconductor quantum dots

Spins in semiconductor quantum dots are among the most promising candidates for the realization of a scalable quantum bit (qubit), the basic building block of a quantum computer. With this motivation, spin and orbital properties of quantum dots in three different semiconductor systems are investigated in this thesis: depletion mode quantum dots in GaAs/AlGaAs heterostructures as well as in silicon-germanium core-shell nanowires (GeSi NW), and accumulation mode quantum dots formed in a fin field-effect transistor (FinFET). The chronological order of this thesis reflects two major shifts of focus of the semiconductor spin qubit research in recent years: a transition from lateral GaAs quantum dots towards scalable, silicon-based systems and a change from electrons towards holes as the host of the spin qubit because of better prospects for spin manipulation and spin coherence. In a lateral GaAs single electron quantum dot, a new in-plane magnetic-field-assisted spectroscopy is demonstrated, which allows one to deduce the three dimensional confinement potential landscape of the quantum dot orbitals, which gives insight into the alignment of the ellipsoidal quantum dot with respect to the crystal axes. With this full model of the confinement at hand, the dependence of the spin relaxation on the direction and strength of an in-plane magnetic field is investigated. To mitigate the spin relaxation anisotropy due to anisotropic in-plane confinement of the quantum dot, said confinement is symmetrized by tuning the gate voltages to obtain a circular quantum dot. Then, the experimentally observed spin relaxation anisotropy can be attributed to the interplay of Rashba and Dresselhaus spin-orbit interaction (SOI) present in GaAs. By using a theoretical model, the strength and the relative sign of the Rashba and Dresselhaus SOI was obtained for the first time in such a quantum dot. From the dependence of the spin relaxation on the magnetic field strength, hyperfine induced phonon mediated spin relaxation was demonstrated -- a process predicted more than 15 years ago. Here, the hyperfine interaction leads to a mixing of spin and orbital degrees of freedom and facilitates spin relaxation. Limited by this relaxation process, a spin relaxation time of 57 +/- 15 s was measured -- setting the current record for spin lifetime in a nanostructure. Inspired by the unprecedented knowledge of the confinement and the SOI in the quantum dots used, a new theory to quantify the various corrections to the g-factor was developed. Later, these theoretical predictions have been experimentally validated by measurements of the g-factor anisotropy using pulsed-gate spectroscopy. Due to short spin qubit coherence time in GaAs, which is limited by the nuclear spins, a better approach is to build a spin qubit in a semiconductor vacuum with little or no nuclear spins. Because holes have minimal overlap with the nuclei of the semiconductor due to the p-type symmetry of their wave function, this type of decoherence is strongly suppressed when changing the host of the spin qubit from electrons to holes. The longer coherence times in combination with the predicted emergence of a direct type of Rashba SOI (DRSOI) -- a particularly strong and electrically controllable SOI -- motivated the investigation of hole quantum dots in GeSi NW. In this system, anisotropic behavior of the leakage current through a double quantum dot in Pauli spin blockade was observed. This anisotropy is qualitatively explained by a phenomenological model, which involves an anisotropic g-factor and an effective spin-orbit field. While the dominant type of SOI could not be resolved conclusively, the obtained data is not inconsistent with the expectation of DRSOI. Because each wire has to be placed manually, this NW based system lacks scalability. Hole and electron quantum dots in an industry-compatible silicon FinFET structure, conversely, are promising candidates for scalable spin qubits and, therefore, hold the potential to be used in a spin-based quantum computer. Recently, DRSOI was predicted to also emerge in narrow silicon channels such as FinFETs. In this thesis, the formation of accumulation mode hole quantum dots in such a FinFET structure is reported -- an important first step towards the realization of a scalable, all-electrically controllable, DRSOI hole spin qubit

Safety and Operational Assessment of Rural Free Right-Turn Ramp Intersections

Free right-turn (FRT) ramps are alternative right-turn lane designs for intersecting highways. As of 2023, 79 FRT ramps exist at 68 rural highway intersections in Nebraska. FRT ramps may be located on three-legged or four-legged intersections and may be on the minor, the major, or both minor and major approaches of the same intersection. This research compared the 68 rural FRT intersections to 24 similar non-FRT rural intersections to identify differences in crash frequency and crash rate and tested for statistical significance using a two-sample t-test. Crash data were obtained for the ten- year period of 2010-2019, with a focus on crashes reported within a quarter mile of each intersection leg. Forty different comparisons were made between the FRT and non-FRT intersections, testing varying intersection legs, AADT, and location of the FRT ramp on the major, minor, or both approaches. The results of this analysis indicated a lack of any statistically significant difference in crash frequency or crash rate among the rural FRT ramp and rural non-FRT intersections. In addition to the safety analysis, a conflict analysis was conducted to analyze the vehicle interactions between right-turning vehicles at the FRT ramp intersections and non-FRT intersections. Miovision Scout video recording equipment was used to record the traffic conflicts over 72 hours at six FRT intersections of varying AADT and the number of intersection legs. Six non-FRT intersections were paired with the FRT intersections and the conflict experienced by right-turn movement on the same approach as its FRT counterpart was observed. The conflict analysis showed that non-FRT right- turns experienced higher conflicts per 1000 entering right-turning vehicles than the FRT ramp intersections. It was concluded that the presence of FRT ramps at rural intersections does not affect the crash frequency or crash rate experienced. It was also concluded that conflict is reduced between right-turning vehicles and other traffic present at the intersection when an FRT ramp is present, especially compared to non-FRT intersections where no exclusive right-turn lane is present on the major approach. It is recommended that future research assess additional operational benefits of FRT ramps, such as delay and travel time. Advisor: Aemal Khatta

Relativistic Dynamos in Magnetospheres of Rotating Compact Objects

The kinematic evolution of axisymmetric magnetic fields in rotating magnetospheres of relativistic compact objects is analytically studied, based on relativistic Ohm's law in stationary axisymmetric geometry. By neglecting the poloidal flows of plasma in simplified magnetospheric models, we discuss self-excited dynamos due to the frame-dragging effect (originally pointed out by Khanna & Camenzind), and we propose alternative processes to generate axisymmetric magnetic fields against ohmic dissipation. The first process (which may be called induced excitation) is caused by the help of a background uniform magnetic field in addition to the dragging of inertial frames. It is shown that excited multipolar components of poloidal and azimuthal fields are sustained as stationary modes, and outgoing Poynting flux converges toward the rotation axis. The second one is self-excited dynamo through azimuthal convection current, which is found to be effective if plasma rotation becomes highly relativistic with a sharp gradient in the angular velocity. In this case no frame-dragging effect is needed, and the coupling between charge separation and plasma rotation becomes important. We discuss briefly the results in relation to active phenomena in the relativistic magnetospheres.Comment: 16 pages, AASLaTeX macros v4.