General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

For a particle that is constrained on an ($N-1$)-dimensional ($N\geq2$) curved surface, the Cartesian components of its momentum in $N$-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of a Dirac fermion on a two-dimensional sphere and we show that there is the generalized total angular momentum whose three cartesian components form the $su(2)$ algebra, obtained before by consideration of dynamics of the particle, and we demonstrate that there is no curvature-induced geometric potential for the fermion.Comment: 8 pages, no figure. Presentation improve

Overheating threshold and its effect on time–temperature-transformation diagrams of zirconium based bulk metallic glasses

A pronounced effect of overheating is observed on the crystallization behavior for the three zirconium-based bulk metallic glasses: Zr41.2Ti13.8Cu12.5Ni10Be22.5, Zr57Cu15.4Ni12.6Al10Nb5, and Zr52.5Cu17.9Ni14.6Al10Ti5. A threshold overheating temperature is found for each of the three alloys, above which there is a drastic increase in the undercooling level and the crystallization times. Time–temperature-transformation (TTT) diagrams were measured for the three alloys by overheating above their respective threshold temperatures. The TTT curves for Zr41.2Ti13.8Cu12.5Ni10Be22.5 and Zr57Cu15.4Ni12.6Al10Nb5 are very similar in shape and scale with their respective glass transition temperatures, suggesting that system-specific properties do not play a crucial role in defining crystallization kinetics in these alloys. The critical cooling rates to vitrify the alloys as determined from the TTT curves are about 2 K/s for Zr41.2Ti13.8Cu12.5Ni10Be22.5 and 10 K/s for Zr57Cu15.4Ni12.6Al10Nb5. The measurements were conducted in a high-vacuum electrostatic levitator

Overheating threshold and its effect on time–temperature-transformation diagrams of zirconium based bulk metallic glasses

A pronounced effect of overheating is observed on the crystallization behavior for the three zirconium-based bulk metallic glasses: Zr41.2Ti13.8Cu12.5Ni10Be22.5, Zr57Cu15.4Ni12.6Al10Nb5, and Zr52.5Cu17.9Ni14.6Al10Ti5. A threshold overheating temperature is found for each of the three alloys, above which there is a drastic increase in the undercooling level and the crystallization times. Time–temperature-transformation (TTT) diagrams were measured for the three alloys by overheating above their respective threshold temperatures. The TTT curves for Zr41.2Ti13.8Cu12.5Ni10Be22.5 and Zr57Cu15.4Ni12.6Al10Nb5 are very similar in shape and scale with their respective glass transition temperatures, suggesting that system-specific properties do not play a crucial role in defining crystallization kinetics in these alloys. The critical cooling rates to vitrify the alloys as determined from the TTT curves are about 2 K/s for Zr41.2Ti13.8Cu12.5Ni10Be22.5 and 10 K/s for Zr57Cu15.4Ni12.6Al10Nb5. The measurements were conducted in a high-vacuum electrostatic levitator

A large accretion disk of extreme eccentricity in the TDE ASASSN-14li

In the canonical model for tidal disruption events (TDEs), the stellar debris circularizes quickly to form an accretion disk of size about twice the orbital pericenter of the star. Most TDEs and candidates discovered in the optical/UV have broad optical emission lines with complex and diverse profiles of puzzling origin. Liu et al. recently developed a relativistic elliptical disk model of constant eccentricity in radius for the broad optical emission lines of TDEs and well reproduced the double-peaked line profiles of the TDE candidate PTF09djl with a large and extremely eccentric accretion disk. In this paper, we show that the optical emission lines of the TDE ASASSN-14li with radically different profiles are well modelled with the relativistic elliptical disk model, too. The accretion disk of ASASSN-14li has an eccentricity 0.97 and semimajor axis of 847 times the Schwarzschild radius (r_S) of the black hole (BH). It forms as the consequence of tidal disruption of a star passing by a massive BH with orbital pericenter 25r_S. The optical emission lines of ASASSN-14li are powered by an extended X-ray source of flat radial distribution overlapping the bulk of the accretion disk and the single-peaked asymmetric line profiles are mainly due to the orbital motion of the emitting matter within the disk plane of inclination about 26\degr and of pericenter orientation closely toward the observer. Our results suggest that modelling the complex line profiles is powerful in probing the structures of accretion disks and coronal X-ray sources in TDEs.Comment: 10 pages, 8 figures, accepted for publication in the MNRA

Stabilization of a Coupled Second Order ODE-wave System

This paper considers the stabilization of a coupled second order ODE-wave system, where the ODE dynamics contain the solution of the wave equation at an intermediate point. We design a stabilizing feedback controller by choosing a suitable target system and backstepping transformation. The backstepping transformation is defined in terms of several kernel functions, for which we establish existence, uniqueness and smoothness properties. We also prove exponential stability for the resulting closed-loop system. Finally, the effectiveness of the proposed feedback controller is verified via a numerical example