Interaction of a vortex induced by a rotating cylinder with a plane

In this article,we study theoretically and numerically the interaction of a vortex induced by a rotating cylinder with a perpendicular plane. We show the existence of weak solutions to the swirling vortex models by using the Hopf extension method, and by an elegant contradiction argument, respectively. We demonstrate numerically that the model could produce phenomena of swirling vortex including boundary layer pumping and two-celled vortex that are observed in potential line vortex interacting with a plane and in a tornado

The observed spiral structure of the Milky Way

The spiral structure of the Milky Way is not yet well determined. The keys to understanding this structure are to increase the number of reliable spiral tracers and to determine their distances as accurately as possible. HII regions, giant molecular clouds (GMCs), and 6.7-GHz methanol masers are closely related to high mass star formation, and hence they are excellent spiral tracers. We update the catalogs of Galactic HII regions, GMCs, and 6.7-GHz methanol masers, and then outline the spiral structure of the Milky Way. We collected data for more than 2500 known HII regions, 1300 GMCs, and 900 6.7-GHz methanol masers. If the photometric or trigonometric distance was not yet available, we determined the kinematic distance using a Galaxy rotation curve with the current IAU standard, $R_0$ = 8.5 kpc and $\Theta_0$ = 220 km s$^{-1}$, and the most recent updated values of $R_0$ = 8.3 kpc and $\Theta_0$ = 239 km s$^{-1}$, after we modified the velocities of tracers with the adopted solar motions. With the weight factors based on the excitation parameters of HII regions or the masses of GMCs, we get the distributions of these spiral tracers. The distribution of tracers shows at least four segments of arms in the first Galactic quadrant, and three segments in the fourth quadrant. The Perseus Arm and the Local Arm are also delineated by many bright HII regions. The arm segments traced by massive star forming regions and GMCs are able to match the HI arms in the outer Galaxy. We found that the models of three-arm and four-arm logarithmic spirals are able to connect most spiral tracers. A model of polynomial-logarithmic spirals is also proposed, which not only delineates the tracer distribution, but also matches the observed tangential directions.Comment: 22 Pages, 16 Figures, 7 Tables, updated to match the published versio

Tunable Fano-Kondo resonance in side-coupled double quantum dot system

We study the interference between the Fano and Kondo effects in a side-coupled double-quantum- dot system where one of the quantum dots couples to conduction electron bath while the other dot only side-couples to the first dot via antiferromagnetic (AF) spin exchange coupling. We apply both the perturbative renormalization group (RG) and numerical renormalization group (NRG) approaches to study the effect of AF coupling on the Fano lineshape in the conduction leads. With particle-hole symmetry, the AF exchange coupling competes with the Kondo effect and leads to a local spin-singlet ground state for arbitrary small coupling, so called "two-stage Kondo effect". As a result, via NRG we find the spectral properties of the Fano lineshape in the tunneling density of states (TDOS) of conduction electron leads shows double dip-peak features at the energy scale around the Kondo temperature and the one much below it, corresponding to the two-stage Kondo effect; it also shows an universal scaling behavior at very low energies. We find the qualitative agreement between the NRG and the perturbative RG approach. Relevance of our work to the experiments is discussed.Comment: 7 pages, 7 figure

Purchasing Power Parity and Country Characteristics: Evidence from Time Series Analysis

This paper investigates the relationships between country characteristics and the validity of PPP. We use three alternative time series methods to test for the stationarity of real exchange rates for each of the 72 countries over the period from 1976 to 2005. Our result shows that the evidence of PPP exhibits geographic difference. It is most likely to find stationary real exchange rates for European countries, whereas it is least likely to obtain the result of supporting PPP for Asian countries. We then use a probit regression model to examine if county characteristics are related to the validity of PPP. The probit regression result reveals that the validity of PPP decreases with inflation rate and increases with nominal exchange rate volatility.Purchasing power parity, Country characteristics, Unit root tests