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

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

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

Au-Ag template stripped pattern for scanning probe investigations of DNA arrays produced by Dip Pen Nanolithography

We report on DNA arrays produced by Dip Pen Nanolithography (DPN) on a novel Au-Ag micro patterned template stripped surface. DNA arrays have been investigated by atomic force microscopy (AFM) and scanning tunnelling microscopy (STM) showing that the patterned template stripped substrate enables easy retrieval of the DPN-functionalized zone with a standard optical microscope permitting a multi-instrument and multi-technique local detection and analysis. Moreover the smooth surface of the Au squares (abput 5-10 angstrom roughness) allows to be sensitive to the hybridization of the oligonucleotide array with label-free target DNA. Our Au-Ag substrates, combining the retrieving capabilities of the patterned surface with the smoothness of the template stripped technique, are candidates for the investigation of DPN nanostructures and for the development of label free detection methods for DNA nanoarrays based on the use of scanning probes.Comment: Langmuir (accepted

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

Mercury Accumulation in Tree Rings: Observed Trends in Quantity and Isotopic Composition in Shenandoah National Park, Virginia

Recent studies have shown that mercury (Hg) concentrations in tree rings have the potential to archive historical Hg exposure from local, regional, and global sources. The southeastern United States has received elevated Hg deposition, yet no studies have evaluated tree ring Hg in this region. Here, we quantify Hg accumulation and isotopic composition in tree rings collected in Shenandoah National Park, Virginia. Cores were collected from three individuals of three tree species—white oak (Quercus alba), northern red oak (Quercus rubra), and pitch pine (Pinus rigida)—within the northern, central, and southern areas of the Park (n = 27 cores). The cores were analyzed for Hg content in 10‐year increments, with some cores dating back to the early 1800s. Overall, tree ring Hg concentrations (ranging from below detection to 4.4 ng/g) were similar to other studies and varied between species, with pitch pine having higher concentrations than the deciduous species. The most notable feature of the tree ring Hg time series was a peak that occurred during the 1930s through 1950s, coinciding with the use of Hg at a local industrial facility. Atmospheric modeling indicates that potential emissions from the plant likely had a stronger impact on the southern region of the Park, consistent with the latitudinal gradient in tree ring Hg concentrations. Mass‐dependent and mass‐independent fractionation of Hg isotopes suggests contributions from both regional anthropogenic and local industrial sources during this period. This study demonstrates the potential usefulness of tree ring dendrochemistry for identifying historical sources of atmospheric Hg exposure.Key PointsTree ring mercury levels in Shenandoah National Park, Virginia, were similar to those measured in other North American forestsTree ring mercury peaked during the 1930s to 1950s, coinciding with mercury use at an industrial facility near the southern end of the ParkMercury isotopes suggest a local source at this time, demonstrating the potential of dendrochemistry to identify historical sourcesPlain Language SummaryFor many years scientists have used tree rings to reconstruct past climate. Increasingly, tree rings are being used to document the historical exposure of trees to pollutants. In this study, we cored trees in Shenandoah National Park, Virginia, dated the tree rings, and then measured the amount of mercury stored within decadal core increments. We were surprised to find that mercury levels peaked in the 1930s to 1950s, even though global mercury emissions continued to rise throughout the past century, mostly as a by‐product of energy production. Our findings suggest that the trees were exposed to a local pollutant source during this earlier time period, perhaps from a nearby industrial plant that used mercury in the production of rayon. By examining the chemistry of wood within tree rings, we can get a clearer picture of when and where human activities have affected air pollution over recent centuries.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153685/1/jgrg21576_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153685/2/jgrg21576.pd

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

Overexpressed Genes/ESTs and Characterization of Distinct Amplicons on 17823 in Breast Cancer Cells

Abstract17823 is a frequent site of gene amplification in breast cancer. Several lines of evidence suggest the presence of multiple amplicons on 17823. To characterize distinct amplicons on 17823 and localize putative oncogenes, we screened genes and expressed sequence tags (ESTs) in existing physical and radiation hybrid maps for amplification and overexpression in breast cancer cell lines by semiquantitative duplex PCR, semiquantitative duplex RT-PCR, Southern blot, Northern blot analyses. We identified two distinct amplicons on 17823, one including TBX2 and another proximal region including RPS6KB1 (PS6K) and MUL. In addition to these previously reported overexpressed genes, we also identified amplification and overexpression of additional uncharacterized genes and ESTs, some of which suggest potential oncogenic activity. In conclusion, we have further defined two distinct regions of gene amplification and overexpression on 17823 with identification of new potential oncogene candidates. Based on the amplification and overexpression patterns of known and as of yet unrecognized genes on 17823, it is likely that some of these genes mapping to the discrete amplicons function as oncogenes and contribute to tumor progression in breast cancer cells

Discrete-Lattice Model for Surface Bound States and Tunneling in d-Wave Superconductors

Surface bound states in a discrete-lattice model of a $d_{x^2 - y^2}$ cuprate superconductor are shown to be, in general, coherent superpositions of an incoming excitation and more than one outgoing excitation, and a simple graphical construction based on a surface Brillouin zone is developed to describe their nature. In addition, a momentum-dependent lifetime contribution to the width of these bound states as observed in tunneling experiments is derived and elucidated in physical terms.Comment: 4 pages, 1 figure, revte