Thermodynamics of Schwarzschild-de Sitter black hole: thermal stability of Nariai black hole

We study thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization, and does not favor the Bousso-Hawking normalization.Comment: 13 pages, 4 figures, version to appear in PR

Spectral Theory of Discrete Processes

We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet algorithms; even spectral theory for fractal measures. In each case, there is an associated class of harmonic functions which we study. And in addition, we study three questions in depth: In specific applications, and for a specific stochastic process, how do we realize the transfer operator $T$ as an operator in a suitable Hilbert space? And how to spectral analyze $T$ once the right Hilbert space $\mathcal{H}$ has been selected? Finally we characterize the stochastic processes that are governed by a single transfer operator. In our applications, the particular stochastic process will live on an infinite path-space which is realized in turn on a state space $S$. In the case of random walk on graphs $G$, $S$ will be the set of vertices of $G$. The Hilbert space $\mathcal{H}$ on which the transfer operator $T$ acts will then be an $L^{2}$ space on $S$, or a Hilbert space defined from an energy-quadratic form. This circle of problems is both interesting and non-trivial as it turns out that $T$ may often be an unbounded linear operator in $\mathcal{H}$; but even if it is bounded, it is a non-normal operator, so its spectral theory is not amenable to an analysis with the use of von Neumann's spectral theorem. While we offer a number of applications, we believe that our spectral analysis will have intrinsic interest for the theory of operators in Hilbert space.Comment: 34 pages with figures removed, for the full version with all the figures please go to http://www.siue.edu/~msong/Research/spectrum.pd

Mobility and Saturation Velocity in Graphene on SiO2

We examine mobility and saturation velocity in graphene on SiO2 above room temperature (300-500 K) and at high fields (~1 V/um). Data are analyzed with practical models including gated carriers, thermal generation, "puddle" charge, and Joule heating. Both mobility and saturation velocity decrease with rising temperature above 300 K, and with rising carrier density above 2x10^12 cm^-2. Saturation velocity is >3x10^7 cm/s at low carrier density, and remains greater than in Si up to 1.2x10^13 cm^-2. Transport appears primarily limited by the SiO2 substrate, but results suggest intrinsic graphene saturation velocity could be more than twice that observed here

Reddening Behaviors of Galaxies in the SDSS Photometric System

We analyze the behaviors of reddening vectors in the SDSS photometric system for galaxies of different morphologies, ages, and redshifts. As seen in other photometric systems, the dependence of reddening on the spectral energy distribution (SED) and the nonlinearity of reddening are likewise non-negligible for the SDSS system if extinction is significant (~> 1 mag). These behaviors are most significant for the g filter, which has the largest bandwidth-to-central wavelength ratio among SDSS filters. The SDSS colors involving adjacent filters show greater SED-dependence and nonlinearity. A procedure for calculating the correct amount of extinction from an observed color excess is provided. The relative extinctions between (i.e., the extinction law for) SDSS filters given by Schlegel et al., which were calculated with an older version of filter response functions, would underestimate the amount of extinction in most cases by ~5 to 10 % (maximum ~20 %). We recommend A/A_{5500} values of 1.574, 1.191, 0.876, 0.671 & 0.486 for the u, g, r, i, & z filters, respectively, as a representative extinction law for the SDSS galaxies with a small extinction (i.e., for cases where the nonlinearity and SED-dependence of the reddening is not important). The dependence of reddening on redshift at low extinction is the largest for colors involving the g filter as well, which is due to the Balmer break.Comment: Published in PASP, 119, 1449 (Dec. 2007

Slowly rotating black holes in the Horava-Lifshitz gravity

We investigate slowly rotating black holes in the Ho\v{r}ava-Lifshitz (HL) gravity. For $\Lambda_W=0$ and $\lambda=1$, we find a slowly rotating black hole of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. We discuss their thermodynamic properties by computing mass, temperature, angular momentum, and angular velocity on the horizon.Comment: 12 pages, no figures, version to appear in EPJ

Holographic interacting dark energy in the braneworld cosmology

We investigate a model of brane cosmology to find a unified description of the radiation-matter-dark energy universe. It is of the interacting holographic dark energy with a bulk-holographic matter $\chi$. This is a five-dimensional cold dark matter, which plays a role of radiation on the brane. Using the effective equations of state $\omega^{\rm eff}_{\rm \Lambda}$ instead of the native equations of state $\omega_{\rm \Lambda}$, we show that this model cannot accommodate any transition from the dark energy with $\omega^{\rm eff}_{\rm \Lambda}\ge-1$ to the phantom regime $\omega^{\rm eff}_{\rm \Lambda}<-1$. Furthermore, the case of interaction between cold dark matter and five dimensional cold dark matter is considered for completeness. Here we find that the redshift of matter-radiation equality $z_{\rm eq}$ is the same order as $z^{\rm ob}_{\rm eq}=2.4\times10^{4} \Omega_{\rm m}h^2$. Finally, we obtain a general decay rate $\Gamma$ which is suitable for describing all interactions including the interaction between holographic dark energy and cold dark matter.Comment: 17 pages, 4 figure