Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment

The distance to the Leo I dwarf spheroidal galaxy from the Red Giant Branch Tip

We present V and I photometry of a 9.4 arcmin X 9.4 arcmin field centered on the dwarf spheroidal galaxy Leo I. The I magnitude of the tip of the Red Giant Branch is robustly estimated from two different datasets (I^{TRGB}=17.97 +0.05/-0.03). From this estimate, adopting [M/H]=-1.2 from the comparison of RGB stars with Galactic templates, we obtain a distance modulus (m-M)_0=22.02 +/- 0.13, corresponding to a distance D=254 +16/-19 Kpc.Comment: 6 pages, 5 figures, Fig. 1 and 2 provided in low resolution version. Latex. Accepted for publication by MNRA

Remarks on Renormalization of Black Hole Entropy

We elaborate the renormalization process of entropy of a nonextremal and an extremal Reissner-Nordstr\"{o}m black hole by using the Pauli-Villars regularization method, in which the regulator fields obey either the Bose-Einstein or Fermi-Dirac distribution depending on their spin-statistics. The black hole entropy involves only two renormalization constants. We also discuss the entropy and temperature of the extremal black hole.Comment: 14 pages, revtex, no figure

Single-electron transport through the vortex core levels in clean superconductors

We develop a microscopic theory of single-electron transport in N-S-N hybrid structures in the presence of applied magnetic field introducing vortex lines in a superconductor layer. We show that vortex cores in a thick and clean superconducting layer are similar to mesoscopic conducting channels where the bound core states play the role of transverse modes. The transport through not very thick layers is governed by another mechanism, namely by resonance tunneling via vortex core levels. We apply our method to calculation of the thermal conductance along the magnetic field.Comment: 4 pages, 1 figur

The Red Giant Branch Tip and Bump of the Leo II dwarf spheroidal galaxy

We present V and I photometry of a 9.4' X 9.4' field centered on the dwarf spheroidal galaxy Leo II. The Tip of the Red Giant Branch is identified at I^{TRGB}=17.83 +/- 0.03 and adopting = -1.53 +/- 0.2 from the comparison of RGB stars with Galactic templates, we obtain a distance modulus (m-M)_0=21.84 +/- 0.13, corresponding to a distance D=233 +/- 15 Kpc. Two significant bumps have been detected in the Luminosity Function of the Red Giant Branch. The fainter bump (B1, at V=21.76 +/- 0.05) is the RGB bump of the dominant stellar population, while the actual nature of the brightest one (B2, at V=21.35 +/- 0.05) cannot be firmly assessed on the basis of the available data, it can be due to the Asymptotic Giant Branch Clump of the main population or it may be a secondary RGB bump. The luminosity of the main RGB bump (B1) suggests that the majority of RGB stars in Leo II belongs to a population that is ~4 gyr younger than the classical Galactic globular clusters. The stars belonging to the He-burning Red Clump are shown to be significantly more centrally concentrated than RR Lyrae and Blue Horizontal Branch stars, probing the existence of an age/metallicity radial gradient in this remote dwarf spheroidal.Comment: Accepted for publication by MNRAS. Latex, 10 pages, 8 .ps figure

Sexual reproduction is the null hypothesis for life cycles of rust fungi

Sexual reproduction, mutation, and reassortment of nuclei increase genotypic diversity in rust fungi. Sexual reproduction is inherent to rust fungi, coupled with their coevolved plant hosts in native pathosystems. Rust fungi are hypothesised to exchange nuclei by somatic hybridisation with an outcome of increased genotypic diversity, independent of sexual reproduction. We provide criteria to demonstrate whether somatic exchange has occurred, including knowledge of parental haplotypes and rejection of fertilisation in normal rust life cycles

Non-minimal coupling and quantum entropy of black hole

Formulating the statistical mechanics for a scalar field with non-minimal $\xi R \phi^2$ coupling in a black hole background we propose modification of the original 't Hooft ``brick wall'' prescription. Instead of the Dirichlet condition we suggest some scattering ansatz for the field functions at the horizon. This modifies the energy spectrum of the system and allows one to obtain the statistical entropy dependent on the non-minimal coupling. For $\xi<0$ the entropy renormalizes the classical Bekenstein-Hawking entropy in the correct way and agrees with the result previously obtained within the conical singularity approach. For a positive $\xi$, however, the results differ.Comment: 16 pages, latex, no figures; an error in calculation of the entropy corrected, the entropy now is positive for any non-minimal couplin

Entropies of the general nonextreme stationary axisymmetric black hole: statistical mechanics and thermodynamics

Starting from metric of the general nonextreme stationary axisymmetric black hole in four-dimensional spacetime, both statistical-mechanical and thermodynamical entropies are studied. First, by means of the "brick wall" model in which the Dirichlet condition is replaced by a scattering ansatz for the field functions at the horizon and with Pauli-Villars regularization scheme, an expression for the statistical-mechanical entropy arising from the nonminimally coupled scalar fields is obtained. Then, by using the conical singularity method Mann and Solodukhin's result for the Kerr-Newman black hole (Phys. Rev. D54, 3932(1996)) is extended to the general stationary black hole and the nonminimally coupled scalar field. We last shown by comparing the two results that the statistical-mechanical entropy and one-loop correction to the thermodynamical entropy are equivalent for coupling $\xi\leq 0$. After renormalization, a relation between the two entropies is given.Comment: 18 pages, Latex, nofigue. Accepted by Phys. Rev.

Elizabeth Cary and Intersections of Catholicism and Gender in Early Modern England

Historians have analyzed the life of Elizabeth Cary, Lady Falkland, primarily in the context of her highly publicized conversion to Catholicism and her equally public separation from her Protestant husband, Henry Cary. Through this scrutiny, she has become one among many English Catholic recusant heroines. Literary critics, in contrast, have celebrated Cary\u27s literary corpus both for its challenge to traditional ideals of early modern women as chaste, silent, and obedient and for its reevaluation of women\u27s roles within marriage.1 To circumscribe our understandings of Cary in such ways obscures one of her greatest contributions. Elizabeth Cary, albeit unintentionally, provided an alternative model of Catholic woman hood that sought to negotiate a new balance between religion and gender, thus challenging assumptions about women\u27s roles in English Catholic communities and about the rigid character of Catholicism in the Reformation era

Thermodynamics of Quantum Fields in Black Hole Backgrounds

We discuss the relation between the micro-canonical and the canonical ensemble for black holes, and highlight some problems associated with extreme black holes already at the classical level. Then we discuss the contribution of quantum fields and demonstrate that the partition functions for scalar and Dirac (Majorana) fields in static space-time backgrounds, can be expressed as functional integrals in the corresponding optical space, and point out that the difference between this and the functional integrals in the original metric is a Liouville-type action. The optical method gives both the correction to the black hole entropy and the bulk contribution to the entropy due to the radiation, while (if the Liouville term is ignored) the conical singularity method just gives the divergent contribution to the black hole entropy. A simple derivation of a general formula for the free energy in the high-temperature approximation is given and applied to various cases. We conclude with a discussion of the second law.Comment: 26 pages, latex, no figures. References added, minor error correcte