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

Using a Kernel Adatron for Object Classification with RCS Data

Rapid identification of object from radar cross section (RCS) signals is important for many space and military applications. This identification is a problem in pattern recognition which either neural networks or support vector machines should prove to be high-speed. Bayesian networks would also provide value but require significant preprocessing of the signals. In this paper, we describe the use of a support vector machine for object identification from synthesized RCS data. Our best results are from data fusion of X-band and S-band signals, where we obtained 99.4%, 95.3%, 100% and 95.6% correct identification for cylinders, frusta, spheres, and polygons, respectively. We also compare our results with a Bayesian approach and show that the SVM is three orders of magnitude faster, as measured by the number of floating point operations.Comment: This material is based upon work supported by US Army Space & Missile Command under Contract Number W9113M-07-C-0204. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re flect the views of US Army Space & Missile Comman

Normal-Superfluid Interface Scattering For Polarized Fermion Gases

We argue that, for the recent experiments with imbalanced fermion gases, a temperature difference may occur between the normal (N) and the gapped superfluid (SF) phase. Using the mean-field formalism, we study particle scattering off the N-SF interface from the deep BCS to the unitary regime. We show that the thermal conductivity across the interface drops exponentially fast with increasing $h/k_B T$, where $h$ is the chemical potential imbalance. This implies a blocking of thermal equilibration between the N and the SF phase. We also provide a possible mechanism for the creation of gap oscillations (FFLO-like states) as seen in recent studies on these systems.Comment: 4 pages, 3 figure

The elusive old population of the dwarf spheroidal galaxy Leo I

We report the discovery of a significant old population in the dwarf spheroidal (dSph) galaxy Leo I as a result of a wide-area search with the ESO New Technology Telescope. Studies of the stellar content of Local Group dwarf galaxies have shown the presence of an old stellar population in almost all of the dwarf spheroidals. The only exception was Leo I, which alone appeared to have delayed its initial star formation episode until just a few Gyr ago. The color-magnitude diagram of Leo I now reveals an extended horizontal branch, unambiguously indicating the presence of an old, metal-poor population in the outer regions of this galaxy. Yet we find little evidence for a stellar population gradient, at least outside R > 2' (0.16 kpc), since the old horizontal branch stars of Leo I are radially distributed as their more numerous intermediate-age helium-burning counterparts. The discovery of a definitely old population in the predominantly young dwarf spheroidal galaxy Leo I points to a sharply defined first epoch of star formation common to all of the Local Group dSph's as well as to the halo of the Milky Way.Comment: 4 pages, 3 postscript figures, uses apjfonts.sty, emulateapj.sty. Accepted for publication in ApJ Letter

The assessment of the near infrared identification of Carbon stars. I. The Local Group galaxies WLM, IC 10 and NGC 6822

{The selection of AGB C and M stars from NIR colours has been done in recent years using adjustable criteria that are in needs of standardization if one wants to compare, in a coherent manner, properties of various populations.} We intend to assess the NIR colour technique to identify C and M stars. We compare the NIR colours of several C stars previously identified from spectroscopy or narrow band techniques in WLM, IC 10 and NGC 6822. We demonstrate that very few M stars have $(J-K)_0 > 1.4$ but a non negligible number of C stars are bluer than this limit. Thus, counts of M and C stars based on such limit do not produce pure samples. C/M ratios determined from NIR colours must be regarded as underestimates mainly because the M numbers include many warm C stars and also K stars if no blue limit is considered.Comment: A&A accepted 18.07.200

Wind ionization structure of the short-period eclipsing LMC Wolf-Rayet binary BAT99-129: preliminary results

BAT99-129 is a rare, short-period eclipsing Wolf-Rayet binary in the Large Magellanic Cloud. We present here medium-resolution NTT/EMMI spectra that allow us to disentangle the spectra of the two components and find the orbital parameters of the binary. We also present VLT/FORS1 spectra of this binary taken during the secondary eclipse, i.e. when the companion star passes in front of the Wolf-Rayet star. With these data we are able to extract, for the first time in absolute units for a WR+O binary, the sizes of the line emitting regions.Comment: 6 pages, 5 figures, to appear in proc. of "Close Binaries in the 21st Century: New Opportunities and Challenges", 2005 - Corrected Figure

Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates

One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of chaotic systems is proportional to the hole size and independent of position. Here we give exact formulas for the subsequent terms, as sums of correlation functions; these depend on hole size and position, hence yield information on the closed system dynamics. Conversely, the theory can be readily applied to experimental design, for example to control escape rates.Comment: Originally 4 pages and 2 eps figures incorporated into the text; v2 has more numerical results and discussion: now 6 pages, 4 figure