Comparing descent obstruction and Brauer-Manin obstruction for open varieties

We provide a relation between Brauer-Manin obstruction and descent obstruction for torsors over open varieties under a connected linear algebraic group or a group of multiplicative type is given. Such a relation is further refined for torsors under a torus. As an appliaction, we prove that the semi-simple part of a connected linear algebraic group will satisfy strong approximation with Brauer-Manin obstruction if G iteself satisfies strong approximation with Brauer-Manin obstruction.The equivalence between descent obstruction and etale Brauer-Manin obstruction for smooth projective varieties is extended to smooth quasi-projective varieties, which provides the perspective to study integral points

A theoretical study of magnetosphere-ionosphere coupling processes

Thesis (Ph.D.) University of Alaska Fairbanks, 1991Magnetosphere and ionosphere are coupled electrodynamically by waves, field-aligned currents and parallel electric fields. Several fundamental coupling processes are addressed in my thesis. It is shown that the Alfven wave is the dominant mode in transmitting field-aligned currents. Therefore, dynamic M-I coupling can be modeled by the Alfven wave bouncing between the ionosphere and the magnetospheric boundaries. The open magnetopause, separating the solar wind and the magnetosphere, behaves like a near perfect reflector to the Alfven wave because of the large solar wind inertia. At the plasma sheet, however, the reflection coefficient may extend over a wide range, depending on the location in the plasma sheet. As the Alfven wave propagates back and forth between the magnetosphere and ionosphere, the field-aligned current density increases dramatically at certain locations, especially near the head of the westward traveling surge, causing potential drops to develop along magnetic field lines. It is found that the existence of parallel potential drops can distort the global convection pattern and limit the upward field-aligned current. The magnetic reconnection at the dayside magnetopause is responsible for enhancing the convection in the magnetosphere, which subsequently propagates toward the ionosphere by the Alfven wave. The patchy and intermittent reconnection at the dayside magnetopause can be initiated by the 3-D tearing instability, leading to the isolated magnetic islands and X-line segments. The nonlinear evolution of tearing in terms of the magnetic island coalescence is also studied

Doctor of Philosophy

dissertationHydrogen sintering and phase transformation (HSPT) is a novel low-cost process for powder metallurgy (PM) titanium alloys. The microstructure obtained from the HPST process has very fine α grains, as well as other common features of a PM product, such a

Episodic jet power extracted from a spinning black hole surrounded by a neutrino-dominated accretion flow in gamma-ray bursts

It was suggested that the relativistic jets in gamma-ray bursts (GRBs) are powered via the Blandford-Znajek (BZ) mechanism or the annihilation of neutrinos and anti-neutrinos from a neutrino cooling-dominated accretion flow (NDAF). The advection and diffusion of the large-scale magnetic field of a NDAF is calculated, and the external magnetic field is found to be dragged inward efficiently by the accretion flow for a typical magnetic Prandtl number P_m=1. The maximal BZ jet power can be ~10^53-10^54 erg/sec for an extreme Kerr black hole, if an external magnetic field with 10^14 Gauss is advected by the NDAF. This is roughly consistent with the field strength of the disk formed after a tidal disrupted magnetar. The accretion flow near the black hole horizon is arrested by the magnetic field if the accretion rate is below than a critical value for a given external field. The arrested accretion flow fails to drag the field inward and the field strength decays, and then the accretion re-starts, which leads to oscillating accretion. The typical timescale of such episodic accretion is in an order of one second. This can qualitatively explain the observed oscillation in the soft extend emission of short-type GRBs.Comment: 8 pages, to appear in ApJ, references update