Evolving small-world networks with geographical attachment preference

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyze several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as the small-world effect and a high clustering.Comment: 11 pages, 4 figure

High Dimensional Apollonian Networks

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension

Vortex in a d-wave superconductor at low temperatures

A systematic perturbation theory is developed to describe the magnetic field-induced subdominant $s$- and $d_{xy}$-wave order parameters in the mixed state of a $d_{x^2-y^2}$-wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field H_{c1}\ltsim H\ll H_{c2} from $T_c$ down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of subdominant $d_{xy}$ pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.Comment: 20 RevTEX pages, 6 EPS figures; considerably expanded versio

Conformal transformation in f(T)f(T) theories

It is well-known that $f(R)$ theories are dynamically equivalent to a particular class of scalar-tensor theories. In analogy to the $f(R)$ extension of the Einstein-Hilbert action of general relativity, $f(T)$ theories are generalizations of the action of teleparallel gravity. The field equations are always second order, remarkably simpler than $f(R)$ theories. It is interesting to investigate whether $f(T)$ theories have the similar conformal features possessed in $f(R)$ theories. It is shown, however, that $f(T)$ theories are not dynamically equivalent to teleparallel action plus a scalar field via conformal transformation, there appears an additional scalar-torsion coupling term. We discuss briefly what constraint of this coupling term may be put on $f(T)$ theories from observations of the solar system.Comment: 4 pages, Revision to be publishe

A simple proof of Perelman's collapsing theorem for 3-manifolds

We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theorem is almost self-contained, accessible to non-experts and advanced graduate students. Perelman's collapsing theorem for 3-manifolds can be viewed as an extension of implicit function theoremComment: v1: 9 Figures. In this version, we improve the exposition of our arguments in the earlier arXiv version. v2: added one more grap

Thermal Hall conductivity of marginal Fermi liquids subject to out-of plane impurities in high-TcT_c cuprates

The effect of out-of-plane impurities on the thermal Hall conductivity $\kappa_{xy}$ of in-plane marginal-Fermi-liquid (MFL) quasiparticles in high-$T_c$ cuprates is examined by following the work on electrical Hall conductivity $\sigma_{xy}$ by Varma and Abraham [Phys. Rev. Lett. 86, 4652 (2001)]. It is shown that the effective Lorentz force exerted by these impurities is a weak function of energies of the MFL quasiparticles, resulting in nearly the same temperature dependence of $\kappa_{xy}/T$ and $\sigma_{xy}$, indicative of obedience of the Wiedemann-Franz law. The inconsistency of the theoretical result with the experimental one is speculated to be the consequence of the different amounts of out-of-plane impurities in the two YBaCuO samples used for the $\kappa_{xy}$ and $\sigma_{xy}$ measurements.Comment: 5 pages, 2 eps figures; final versio

Pectic oligosaccharide structure-function relationships: prebiotics, inhibitors of Escherichia coli O157:H7 adhesion and reduction of Shiga toxin cytotoxicity in HT29 cells

Shiga toxin (Stx)-producing, food-contaminating Escherichia coli (STEC) is a major health concern. Plant-derived pectin and pectic-oligosaccharides (POS) have been considered as prebiotics and for the protection of humans from Stx. Of five structurally different citrus pectic samples, POS1, POS2 and modified citrus pectin 1 (MCP1) were bifidogenic with similar fermentabilities in human faecal cultures and arabinose-rich POS2 had the greatest prebiotic potential. Pectic oligosaccharides also enhanced lactobacilli growth during mixed batch faecal fermentation. We demonstrated that all pectic substrates were anti-adhesive for E. coli O157:H7 binding to human HT29 cells. Lower molecular weight and deesterification enhanced the anti-adhesive activity. We showed that all pectic samples reduced Stx2 cytotoxicity in HT29 cells, as measured by the reduction of human rRNA depurination detected by our novel TaqMan-based RT-qPCR assay, with POS1 performing the best. POS1 competes with Stx2 binding to the Gb3 receptor based on ELISA results, underlining the POS anti-STEC properties

Cardy-Verlinde Formula and AdS Black Holes

In a recent paper hep-th/0008140 by E. Verlinde, an interesting formula has been put forward, which relates the entropy of a conformal formal field in arbitrary dimensions to its total energy and Casimir energy. This formula has been shown to hold for the conformal field theories that have AdS duals in the cases of AdS Schwarzschild black holes and AdS Kerr black holes. In this paper we further check this formula with various black holes with AdS asymptotics. For the hyperbolic AdS black holes, the Cardy-Verlinde formula is found to hold if we choose the ``massless'' black hole as the ground state, but in this case, the Casimir energy is negative. For the AdS Reissner-Nordstr\"om black holes in arbitrary dimensions and charged black holes in D=5, D=4, and D=7 maximally supersymmetric gauged supergravities, the Cardy-Verlinde formula holds as well, but a proper internal energy which corresponds to the mass of supersymmetric backgrounds must be subtracted from the total energy. It is failed to rewrite the entropy of corresponding conformal field theories in terms of the Cardy-Verlinde formula for the AdS black holes in the Lovelock gravity.Comment: 18 pages, latex, no figures, discussions on the charged AdS black holes change

Black holes in the Brans-Dicke-Maxwell theory

The black hole solutions in the higher dimensional Brans-Dicke-Maxwell theory are investigated. We find that the presence of the nontrivial scalar field depends on the spacetime dimensions (D). When D=4, the solution corresponds to the Reissner-Nordstr\"{o}m black hole with a constant scalar field. In higher dimensions (D>4), one finds the charged black hole solutions with the nontrivial scalar field. The thermal properties of the charged black holes are discussed and the reason why the nontrivial scalar field exists are explained. Also the solutions for higher dimensional Brans-Dicke theory are given for comparison.Comment: Revtex, 5 pages, no figures, contents were rewritten and new references were adde

A minimum single-band model for low-energy excitations in superconducting Kx_xFe2_2Se2_2

We propose a minimum single-band model for the newly discovered iron-based superconducting K$_x$Fe$_2$Se$_2$. Our model is found to be numerically consistent with the five-orbital model at low energies. Based on our model and the random phase approximation, we study the spin fluctuation and the pairing symmetry of superconducting gap function. The $(\pi/2,\pi/2)$ spin excitation and the $d_{x^2-y^2}$ pairing symmetry are revealed. All of the results can well be understood in terms of the interplay between the Fermi surface topology and the local spin interaction, providing a sound picture to explain why the superconducting transition temperature is as high as to be comparable to those in pnictides and some cuprates. A common origin of superconductivity is elucidated for this compound and other high-T$_c$ materials.Comment: 5 pages, 4 figure