Random walk on the range of random walk

We study the random walk X on the range of a simple random walk on ℤ d in dimensions d≥4. When d≥5 we establish quenched and annealed scaling limits for the process X, which show that the intersections of the original simple random walk path are essentially unimportant. For d=4 our results are less precise, but we are able to show that any scaling limit for X will require logarithmic corrections to the polynomial scaling factors seen in higher dimensions. Furthermore, we demonstrate that when d=4 similar logarithmic corrections are necessary in describing the asymptotic behavior of the return probability of X to the origin

Lifetimes, branching ratios, and transition probabilities in Co ii

The radiative lifetime of 14 levels in the z^5F, z^5D, and z^5G terms of Co ii have been measured with use of time-resolved laser fluorescence spectroscopy with a Co+-ion beam. Our lifetime values are shorter by 15–50 % than earlier results from beam-foil time-of-flight measurements. The lifetimes were converted to 41 individual transition probabilities with use of branching ratios measured on spectra recorded with the 1-m Fourier-transform spectrometer at the Kitt Peak National Observatory. On average our transition probabilities agree with those of Kurucz and Peytremann; for ΔS=1 transitions their calculated values are lower than our experimental results by a factor of ∼(1/4)

A chemical ionization mass spectrometer for continuous underway shipboard analysis of dimethylsulfide in near-surface seawater

A compact, low-cost atmospheric pressure, chemical ionization mass spectrometer ("mini-CIMS") has been developed for continuous underway shipboard measurements of dimethylsulfide (DMS) in seawater. The instrument was used to analyze DMS in air equilibrated with flowing seawater across a porous Teflon membrane equilibrator. The equilibrated gas stream was diluted with air containing an isotopically-labeled internal standard. DMS is ionized at atmospheric pressure via proton transfer from water vapor, then declustered, mass filtered via quadrupole mass spectrometry, and detected with an electron multiplier. The instrument described here is based on a low-cost residual gas analyzer (Stanford Research Systems), which has been modified for use as a chemical ionization mass spectrometer. The mini-CIMS has a gas phase detection limit of 220 ppt DMS for a 1 min averaging time, which is roughly equivalent to a seawater DMS concentration of 0.1 nM DMS at 20°C. The mini-CIMS has the sensitivity, selectivity, and time response required for underway measurements of surface ocean DMS over the full range of oceanographic conditions. The simple, robust design and relatively low cost of the instrument are intended to facilitate use in process studies and surveys, with potential for long-term deployment on research vessels, ships of opportunity, and large buoys

On the spatial Markov property of soups of unoriented and oriented loops

We describe simple properties of some soups of unoriented Markov loops and of some soups of oriented Markov loops that can be interpreted as a spatial Markov property of these loop-soups. This property of the latter soup is related to well-known features of the uniform spanning trees (such as Wilson's algorithm) while the Markov property of the former soup is related to the Gaussian Free Field and to identities used in the foundational papers of Symanzik, Nelson, and of Brydges, Fr\"ohlich and Spencer or Dynkin, or more recently by Le Jan

Europium, Samarium, and Neodymium Isotopic Fractions in Metal-Poor Stars

We have derived isotopic fractions of europium, samarium, and neodymium in two metal-poor giants with differing neutron-capture nucleosynthetic histories. These isotopic fractions were measured from new high resolution (R ~ 120,000), high signal-to-noise (S/N ~ 160-1000) spectra obtained with the 2dCoude spectrograph of McDonald Observatory's 2.7m Smith telescope. Synthetic spectra were generated using recent high-precision laboratory measurements of hyperfine and isotopic subcomponents of several transitions of these elements and matched quantitatively to the observed spectra. We interpret our isotopic fractions by the nucleosynthesis predictions of the stellar model, which reproduces s-process nucleosynthesis from the physical conditions expected in low-mass, thermally-pulsing stars on the AGB, and the classical method, which approximates s-process nucleosynthesis by a steady neutron flux impinging upon Fe-peak seed nuclei. Our Eu isotopic fraction in HD 175305 is consistent with an r-process origin by the classical method and is consistent with either an r- or an s-process origin by the stellar model. Our Sm isotopic fraction in HD 175305 suggests a predominantly r-process origin, and our Sm isotopic fraction in HD 196944 is consistent with an s-process origin. The Nd isotopic fractions, while consistent with either r-process or s-process origins, have very little ability to distinguish between any physical values for the isotopic fraction in either star. This study for the first time extends the n-capture origin of multiple rare earths in metal-poor stars from elemental abundances to the isotopic level, strengthening the r-process interpretation for HD 175305 and the s-process interpretation for HD196944.Comment: 40 pages, 16 figures. Accepted for publication in ApJ. Full versions of tables 4 and 5 are available from the first author upon reques

Conformal invariance in two-dimensional turbulence

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2d) locality often promotes scale invariance to a wider class of conformal transformations which allow for nonuniform re-scaling. Conformal invariance allows a thorough classification of universality classes of critical phenomena in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example of strongly-interacting non-equilibrium system? Here, using numerical experiment, we show that some features of 2d inverse turbulent cascade display conformal invariance. We observe that the statistics of vorticity clusters is remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a new step in the unification of 2d physics within the framework of conformal symmetry.Comment: 10 pages, 5 figures, 1 tabl

Throughput Maximization in Multiprocessor Speed-Scaling

We are given a set of $n$ jobs that have to be executed on a set of $m$ speed-scalable machines that can vary their speeds dynamically using the energy model introduced in [Yao et al., FOCS'95]. Every job $j$ is characterized by its release date $r_j$, its deadline $d_j$, its processing volume $p_{i,j}$ if $j$ is executed on machine $i$ and its weight $w_j$. We are also given a budget of energy $E$ and our objective is to maximize the weighted throughput, i.e. the total weight of jobs that are completed between their respective release dates and deadlines. We propose a polynomial-time approximation algorithm where the preemption of the jobs is allowed but not their migration. Our algorithm uses a primal-dual approach on a linearized version of a convex program with linear constraints. Furthermore, we present two optimal algorithms for the non-preemptive case where the number of machines is bounded by a fixed constant. More specifically, we consider: {\em (a)} the case of identical processing volumes, i.e. $p_{i,j}=p$ for every $i$ and $j$, for which we present a polynomial-time algorithm for the unweighted version, which becomes a pseudopolynomial-time algorithm for the weighted throughput version, and {\em (b)} the case of agreeable instances, i.e. for which $r_i \le r_j$ if and only if $d_i \le d_j$, for which we present a pseudopolynomial-time algorithm. Both algorithms are based on a discretization of the problem and the use of dynamic programming

s-Processing in the Galactic Disk. I. Super-Solar Abundances of Y, Zr, La, Ce in Young Open Clusters

In a recent study, based on homogeneous barium abundance measurements in open clusters, a trend of increasing [Ba/Fe] ratios for decreasing cluster age was reported. We present here further abundance determinations, relative to four other elements hav- ing important s-process contributions, with the aim of investigating whether the growth found for [Ba/Fe] is or not indicative of a general property, shared also by the other heavy elements formed by slow neutron captures. In particular, we derived abundances for yttrium, zirconium, lanthanum and cerium, using equivalent widths measurements and the MOOG code. Our sample includes 19 open clusters of different ages, for which the spectra were obtained at the ESO VLT telescope, using the UVES spectrometer. The growth previously suggested for Ba is confirmed for all the elements analyzed in our study. This fact implies significant changes in our views of the Galactic chemical evolution for elements beyond iron. Our results necessarily require that very low-mass AGB stars (M < 1.5M\odot) produce larger amounts of s-process elements (hence acti- vate the 13 C-neutron source more effectively) than previously expected. Their role in producing neutron-rich elements in the Galactic disk has been so far underestimated and their evolution and neutron-capture nucleosynthesis should now be reconsidered.Comment: ApJ accepte

Family health narratives : midlife women’s concepts of vulnerability to illness

Perceptions of vulnerability to illness are strongly influenced by the salience given to personal experience of illness in the family. This article proposes that this salience is created through autobiographical narrative, both as individual life story and collectively shaped family history. The paper focuses on responses related to health in the family drawn from semi-structured interviews with women in a qualitative study exploring midlife women’s health. Uncertainty about the future was a major emergent theme. Most respondents were worried about a specified condition such as heart disease or breast cancer. Many women were uncertain about whether illness in the family was inherited. Some felt certain that illness in the family meant that they were more vulnerable to illness or that their relatives’ ageing would be mirrored in their own inevitable decline, while a few expressed cautious optimism about the future. In order to elucidate these responses, we focused on narratives in which family members’ appearance was discussed and compared to that of others in the family. The visualisation of both kinship and the effects of illness, led to strong similarities being seen as grounds for worry. This led to some women distancing themselves from the legacies of illness in their families. Women tended to look at the whole family as the context for their perceptions of vulnerability, developing complex patterns of resemblance or difference within their families