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 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

Strengthening of the net section of steel elements under tensile loads with bonded CFRP strips

Abstract : The use of CFRP is increasingly common as a solution for the strengthening of structures, but the majority of research and applications have focused on the retrofit of concrete structures. The application of CFRP adhesively bonded to enhance the load carrying capacity of metallic elements has been widely studied in the aeronautical industry but is also a promising technique for the civil engineering area. This paper presents an experimental study to verify the effectiveness of the use of CFRP for the strengthening of the net section of steel elements under tensile loading. A series of tensile tests were conducted with different bond lengths, different number of layers and different surface preparation of steel elements in double lap joints and steel plates. The ultimate load, the failure mode and the effective bond length for CFRP strengthened specimens were determined. The results showed that using CFRP sheets for the strengthening against net area failure provides no gain on the ultimate state, provides a small gain at the elastic limit, and provides a larger gain if the designer accepts to increase the capacity from the elastic limit to the debondig limit

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

Improved photometry of SDSS crowded field images: Structure and dark matter content in the dwarf spheroidal galaxy Leo I

We explore how well crowded field point-source photometry can be accomplished with SDSS data: We present a photometric pipeline based on DoPhot, and tuned for analyzing crowded-field images from the SDSS. Using Monte Carlo simulations we show that the completeness of source extraction is above 80% to i < 21 (AB) and a stellar surface density of about 200 sq.amin. Hence, a specialized data pipeline can efficiently be used for e.g. nearby resolved galaxies in SDSS images, where the standard SDSS photometric package Photo, when applied in normal survey mode, gives poor results. We apply our pipeline to an area of about 3.55sq.deg. around the dwarf spheroidal galaxy (dSph) Leo I, and construct a high S/N star-count map of Leo I via an optimized filter in color-magnitude space (g,r,i). Although the radial surface-density profile of the dwarf deviates from the best fit empirical King model towards outer radii, we find no evidence for tidal debris out to a stellar surface-density of 4*10^(-3) of the central value. We determine the total luminosity of Leo I, and model its mass using the spherical and isotropic Jeans equation. Assuming that 'mass follows light' we constrain a lower limit of the total mass of the dSph to be (1.7+/-0.2)*10^7 Msol. Contrary, if the mass in Leo I is dominated by a constant density dark-matter (DM) halo, then the mass within the central 12' is (2+/-0.6)*10^8 Msol. This leads to a mass-to-light ratio of >>6 (Ic_sol), and possibly >75 if the DM halo dominates the mass and extends further out than 12'. In summary, our results show that Leo I is a symmetric, relaxed and bound system; this supports the idea that Leo I is a dark-matter dominated system.Comment: 13 pages, 11 figures; accepted for publication in A

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

Subdomain Location of Mutations in Cardiac Actin Correlate with Type of Functional Change

Determining the molecular mechanisms that lead to the development of heart failure will help us gain better insight into the most costly health problem in the Western world. To understand the roles that the actin protein plays in the development of heart failure, we have taken a systematic approach toward characterizing human cardiac actin mutants that have been associated with either hypertrophic or dilated cardiomyopathy. Seven known cardiac actin mutants were expressed in a baculovirus system, and their intrinsic properties were studied. In general, the changes to the properties of the actin proteins themselves were subtle. The R312H variant exhibited reduced stability, with a Tm of 53.6°C compared to 56.8°C for WT actin, accompanied with increased polymerization critical concentration and Pi release rate, and a marked increase in nucleotide release rates. Substitution of methionine for leucine at amino acid 305 showed no impact on the stability, nucleotide release rates, or DNase-I inhibition ability of the actin monomer; however, during polymerization, a 2-fold increase in Pi release was observed. Increases to both the Tm and DNase-I inhibition activity suggested interactions between E99K actin molecules under monomer-promoting conditions. Y166C actin had a higher critical concentration resulting in a lower Pi release rate due to reduced filament-forming potential. The locations of mutations on the ACTC protein correlated with the molecular effects; in general, mutations in subdomain 3 affected the stability of the ACTC protein or affect the polymerization of actin filaments, while mutations in subdomains 1 and 4 more likely affect protein-protein interactions

On the resonance eigenstates of an open quantum baker map

We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is contained inside an annulus in the complex plane, $|z_{min}|\leq |z|\leq |z_{max}|$. We consider semiclassical sequences of eigenstates, such that the moduli of their eigenvalues converge to a fixed radius $r$. We prove that, if the moduli converge to $r=|z_{max}|$, then the sequence of eigenstates converges to a fixed phase space measure $\rho_{max}$. The same holds for sequences with eigenvalue moduli converging to $|z_{min}|$, with a different limit measure $\rho_{min}$. Both these limiting measures are supported on fractal sets, which are trapped sets of the classical dynamics. For a general radius $|z_{min}|< r < |z_{max}|$, we identify families of eigenstates with precise self-similar properties.Comment: 32 pages, 2 figure