Sauromalus hispidus

Number of Pages: 4Integrative BiologyGeological Science

Quantitative estimates of discrete harmonic measures

A theorem of Bourgain states that the harmonic measure for a domain in $\R^d$ is supported on a set of Hausdorff dimension strictly less than $d$ \cite{Bourgain}. We apply Bourgain's method to the discrete case, i.e., to the distribution of the first entrance point of a random walk into a subset of $\Z ^d$, $d\geq 2$. By refining the argument, we prove that for all \b>0 there exists \rho (d,\b)N(d,\b), any $x \in \Z^d$, and any $A\subset \{1,..., n\}^d$ | \{y\in\Z^d\colon \nu_{A,x}(y) \geq n^{-\b} \}| \leq n^{\rho(d,\b)}, where $\nu_{A,x} (y)$ denotes the probability that $y$ is the first entrance point of the simple random walk starting at $x$ into $A$. Furthermore, $\rho$ must converge to $d$ as \b \to \infty.Comment: 16 pages, 2 figures. Part (B) of the theorem is ne

Sauromalus varius

Number of Pages: 4Integrative BiologyGeological Science

A Spatial Heterodyne Spectrometer for Laboratory Astrophysics; First Interferogram

A Spatial Heterodyne Spectrometer with broad spectral coverage across the VUV - UV region and with a high (> 500,000 ) spectral resolving power is being built for laboratory measurements of spectroscopic data including emission branching fractions, improved level energies, and hyperfine/isotopic parameters

Families of Vicious Walkers

We consider a generalisation of the vicious walker problem in which N random walkers in R^d are grouped into p families. Using field-theoretic renormalisation group methods we calculate the asymptotic behaviour of the probability that no pairs of walkers from different families have met up to time t. For d>2, this is constant, but for d<2 it decays as a power t^(-alpha), which we compute to O(epsilon^2) in an expansion in epsilon=2-d. The second order term depends on the ratios of the diffusivities of the different families. In two dimensions, we find a logarithmic decay (ln t)^(-alpha'), and compute alpha' exactly.Comment: 20 pages, 5 figures. v.2: minor additions and correction

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

The Hitting Times with Taboo for a Random Walk on an Integer Lattice

For a symmetric, homogeneous and irreducible random walk on d-dimensional integer lattice Z^d, having zero mean and a finite variance of jumps, we study the passage times (with possible infinite values) determined by the starting point x, the hitting state y and the taboo state z. We find the probability that these passages times are finite and analyze the tails of their cumulative distribution functions. In particular, it turns out that for the random walk on Z^d, except for a simple (nearest neighbor) random walk on Z, the order of the tail decrease is specified by dimension d only. In contrast, for a simple random walk on Z, the asymptotic properties of hitting times with taboo essentially depend on the mutual location of the points x, y and z. These problems originated in our recent study of branching random walk on Z^d with a single source of branching

A Model Ground State of Polyampholytes

The ground state of randomly charged polyampholytes is conjectured to have a structure similar to a necklace, made of weakly charged parts of the chain, compacting into globules, connected by highly charged stretched `strings'. We suggest a specific structure, within the necklace model, where all the neutral parts of the chain compact into globules: The longest neutral segment compacts into a globule; in the remaining part of the chain, the longest neutral segment (the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so on. We investigate the size distributions of the longest neutral segments in random charge sequences, using analytical and Monte Carlo methods. We show that the length of the n-th longest neutral segment in a sequence of N monomers is proportional to N/(n^2), while the mean number of neutral segments increases as sqrt(N). The polyampholyte in the ground state within our model is found to have an average linear size proportional to sqrt(N), and an average surface area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.