Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

In this paper we give an affirmative answer to an open question mentioned in [Le Bris and Lions, Comm. Partial Differential Equations 33 (2008), 1272--1317], that is, we prove the well-posedness of the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie

Thermodynamic properties and shear viscosity over entropy density ratio of nuclear fireball in a quantum-molecular dynamics model

Thermodynamic and transport properties of nuclear fireball created in the central region of heavy-ion collisions below 400 MeV/nucleon are investigated within the isospin-dependent quantum molecular dynamic (IQMD) model. These properties including the density, temperature, chemical potential, entropy density ($s$) and shear viscosity ($\eta$), are calculated by a generalized hot Thomas Fermi formulism and a parameterized function, which was developed by Danielewicz. As the collision goes on, a transient minimal $\eta/s=5/4\pi-10/4\pi$ occurs in the largest compression stage. Besides, the relationship of $\eta/s$ to temperature ($T$) in the freeze-out stage displays a local minimum which is about 9-20 times $1/4\pi$ around $T$ = 8-12 MeV, which can be argued as indicative of a liquid gas phase transition. In addition, the influences of nucleon-nucleon (NN) cross section ($\sigma_{NN}$) and symmetry energy coefficient ($C_{s}$) are also discussed, and it is found that the results are sensitive to $\sigma_{NN}$ but not to $C_{s}$.Comment: 10 pages, 13 figures; Phys. Rev. C (in press) (x-axis of Fig.1 is corrected

Engineering the Kondo and Fano effects in double quantum dots

We demonstrate delicate control over the Kondo effect and its interplay with quantum interference in an Aharonov-Bohm interferometer containing one Kondo dot and one noninteracting dot. It is shown that the Kondo resonance undergoes a dramatic evolution as the interdot tunnel coupling progressively increases. A novel triple Kondo splitting occurs from the interference between constant and Lorentzian conduction bands that cooperate in forming the Kondo singlet. The device also manifests a highly controllable Fano-Kondo effect in coherent electronic transport, and can be tuned to a regime where the coupled dots behave as decoupled dots.Comment: 5 pages, 4 figure

Simulating the X-ray Forest

Numerical simulations predict that a large number of baryons reside in intergalactic space at temperatures between 10^5-10^7 K. Highly-ionized metals, such as O VII and O VIII, are good tracers of this ``warm-hot intergalactic medium'', or WHIM. For collisionally-ionized gas, the ionization fraction of each ion peaks at some particular temperature (``peak temperatures''), so different ions can therefore trace the IGM at different temperatures. We performed a hydrodynamic simulation to study the metal distributions in the IGM. We then draw random lines-of-sight across the simulated region and synthesize resonance absorption line spectra in a similar way to simulating the Ly-alpha forest. By studying the distribution functions of H- and He-like O, Si and Fe in a collisionally-ionized IGM and comparing with semi-analytic results based on the Press-Schechter formalism, we find: (1) ions with higher peak temperatures (for instance, Fe XXVI) tend to concentrate around virialized halos, which can be well described by the Press-Schechter distribution, ions with lower peak temperatures are found both in small halos (such as groups of galaxies) and in filaments; (2) lower peak temperature ions are more abundant and should be easily observed; (3) peculiar velocities contribute a significant part to the broadening of the resonant absorption lines.Comment: 43 pages, 18 figures. Accepted for publication in the Astrophysical Journal. For high resolution figures, see http://space.mit.edu/~fangt/www/x-ra

The profile of an emission line from relativistic outflows around a black hole

Recent observations show strong evidence for the presence of Doppler-shifted emission lines in the spectrum of both black hole candidates and active galactic nuclei. These lines are likely to originate from relativistic outflows (or jets) in the vicinity of the central black hole. Consequently, the profile of such a line should be distorted by strong gravitational effects near the black hole, as well as special relativistic effects. In this paper, we present results from a detailed study on how each process affects the observed line profile. We found that the profile is sensitive to the intrinsic properties of the jets (Lorentz factor, velocity profile, and emissivity law), as well as to the spin of the black hole and the viewing angle (with respect to the axis of the jets). More specifically, in the case of approaching jets, an intrisically narrow line (blue-shifted) is seen as simply broadened at small viewing angles, but it shows a doubly peaked profile at large viewing angles for extreme Kerr black holes (due to the combination of gravitational focusing and Doppler effects); the profile is always singly peaked for Schwarzschild black holes. For receding jets, however, the line profile becomes quite complicated owing to complicated photon trajectories. To facilitate comparison with observations, we searched a large parameter space to derive representative line profiles. We show the results and discuss how to use emission lines as a potential tool for probing the inner region of a black hole jet system.Comment: 16 pages in emulateapj style, 11 figure

The radial abundance gradient of oxygen towards the Galactic anticentre

We present deep optical spectroscopy of eight HII regions located in the anticentre of the Milky Way. The spectra were obtained at the 10.4m GTC and 8.2m VLT. We determined Te([NII]) for all objects and Te([OIII]) for six of them. We also included in our analysis an additional sample of 13 inner-disc Galactic Hii regions from the literature that have excellent T_e determinations. We adopted the same methodology and atomic dataset to determine the physical conditions and ionic abundances for both samples. We also detected the CII and OII optical recombination lines in Sh 2-100, which enables determination of the abundance discrepancy factor for this object. We found that the slopes of the radial oxygen gradients defined by the HII regions from R_25 (= 11.5 kpc) to 17 kpc and those within R_25 are similar within the uncertainties, indicating the absence of flattening in the radial oxygen gradient in the outer Milky Way. In general, we found that the scatter of the O/H ratios of Hii regions is not substantially larger than the observational uncertainties. The largest possible local inhomogeneities of the oxygen abundances are of the order of 0.1 dex. We also found positive radial gradients in Te([O III]) and Te([N II]) across the Galactic disc. The shapes of these temperature gradients are similar and also consistent with the absence of flattening of the metallicity distribution in the outer Galactic disc.Comment: 20 pages, 11 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Societ