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

Review of the CFC/ICCO/Bioversity project on cacao germplasm evaluation (1998-2010)

The CFC/ICCO/Bioversity project was in response to an urgent need to revitalize cacao breeding and research globally for increasing resistance to pests and disease. It aimed to strengthen national cacao improvement programmes and increase international collaboration by carrying out joint evaluation, selection and breeding activities in ten cocoa-producing countries. The project implemented in two phases – Phase I (1998- 2004) and Phase II (2004-2010), has been one of the most ambitious collaborative efforts in cacao breeding. With an understanding that a similar global collaboration is needed to tackle the impacts of climate change on cacao production, this review was developed in response to a request from the cocoa industry and research partners to evaluate the effectiveness of the project, identify key lessons learned for the implementation of new multisite evaluation field trials focused on increasing the resilience of cacao to the effects of climate change. The cacao research community will be able to use these lessons learned to be better prepared for, and more effective in, the execution of future collaborative research initiatives

Escape Rates and Physically Relevant Measures for Billiards with Small Holes

We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the scatterers. For a large class of smooth initial distributions, we establish the existence of a common escape rate and normalized limiting distribution. This limiting distribution is conditionally invariant and is the natural analogue of the SRB measure of a closed system. Finally, we prove that as the size of the hole tends to zero, the limiting distribution converges to the smooth invariant measure of the billiard map.Comment: 39 pages, 4 figure

Magellanic Cloud Periphery Carbon Stars IV: The SMC

The kinematics of 150 carbon stars observed at moderate dispersion on the periphery of the Small Magellanic Cloud are compared with the motions of neutral hydrogen and early type stars in the Inter-Cloud region. The distribution of radial velocities implies a configuration of these stars as a sheet inclined at 73+/-4 degrees to the plane of the sky. The near side, to the South, is dominated by a stellar component; to the North, the far side contains fewer carbon stars, and is dominated by the neutral gas. The upper velocity envelope of the stars is closely the same as that of the gas. This configuration is shown to be consistent with the known extension of the SMC along the line of sight, and is attributed to a tidally induced disruption of the SMC that originated in a close encounter with the LMC some 0.3 to 0.4 Gyr ago. The dearth of gas on the near side of the sheet is attributed to ablation processes akin to those inferred by Weiner & Williams (1996) to collisional excitation of the leading edges of Magellanic Stream clouds. Comparison with pre LMC/SMC encounter kinematic data of Hardy, Suntzeff, & Azzopardi (1989) of carbon stars, with data of stars formed after the encounter, of Maurice et al. (1989), and Mathewson et al. (a986, 1988) leaves little doubt that forces other than gravity play a role in the dynamics of the H I.Comment: 30 pages; 7 figures, latex compiled, 1 table; to appear in AJ (June 2000

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

Ultra-Slow Discharges That Precede Lightning Initiation

We report on ultra-slowly propagating discharge events with speeds in the range 1-13 km/s, much lower than any known lightning process. The propagation speeds of these discharges are orders of magnitude slower than leader or streamer speeds, but faster than the ion drift speed. For one particular event, a lightning leader forms about 40 ms later within 50 m of the discharge, likely within the same high field region. A second slow event forms 9 ms prior to the initiation, and leads into the negative leader. Most slow events appear to not be directly involved with lightning initiation. This suggests that the classic streamer cascade model of initiation is not always a definitive process. In this work we describe these discharge events displaying unique behavior, their relation to common lightning discharges, and their implications for lightning initiation

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

Black hole entropy: statistical mechanics agrees thermodynamics

We discuss the connection between different entropies introduced for black hole. It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechanical entropy calculated according to 't Hooft and regularized by Pauli-Villars.Comment: 10 pages, latex. Some new discussion added. Version to appear in Phys Rev.