Improved Laboratory Transition Probabilities for Ce II, Application to the Cerium Abundances of the Sun and Five r-process Rich, Metal-Poor Stars, and Rare Earth Lab Data

Recent radiative lifetime measurements accurate to +/- 5% using laser-induced fluorescence (LIF) on 43 even-parity and 15 odd-parity levels of Ce II have been combined with new branching fractions measured using a Fourier transform spectrometer (FTS) to determine transition probabilities for 921 lines of Ce II. This improved laboratory data set has been used to determine a new solar photospheric Ce abundance, log epsilon = 1.61 +/- 0.01 (sigma = 0.06 from 45 lines), a value in excellent agreement with the recommended meteoritic abundance, log epsilon = 1.61 +/- 0.02. Revised Ce abundances have also been derived for the r-process-rich metal-poor giant stars BD+17 3248, CS 22892-052, CS 31082-001, HD 115444 and HD 221170. Between 26 and 40 lines were used for determining the Ce abundance in these five stars, yielding a small statistical uncertainty of 0.01 dex similar to the Solar result. The relative abundances in the metal-poor stars of Ce and Eu, a nearly pure r-process element in the Sun, matches r-process only model predictions for Solar System material. This consistent match with small scatter over a wide range of stellar metallicities lends support to these predictions of elemental fractions. A companion paper includes an interpretation of these new precision abundance results for Ce as well as new abundance results and interpretations for Pr, Dy and Tm.Comment: 84 pages, 8 Figures, 14 Tables; To appear in the Astrophysical Journal Supplemen

Experimental investigation of a variable speed constant frequency electric generating system from a utility perspective

As efforts are accelerated to improve the overall capability and performance of wind electric systems, increased attention to variable speed configurations has developed. A number of potentially viable configurations have emerged. Various attributes of variable speed systems need to be carefully tested to evaluate their performance from the utility points of view. With this purpose, the NASA experimental variable speed constant frequency (VSCF) system has been tested. In order to determine the usefulness of these systems in utility applications, tests are required to resolve issues fundamental to electric utility systems. Legitimate questions exist regarding how variable speed generators will influence the performance of electric utility systems; therefore, tests from a utility perspective, have been performed on the VSCF system and an induction generator at an operating power level of 30 kW on a system rated at 200 kVA and 0.8 power factor

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

SLE_k: correlation functions in the coefficient problem

We apply the method of correlation functions to the coefficient problem in stochastic geometry. In particular, we give a proof for some universal patterns conjectured by M. Zinsmeister for the second moments of the Taylor coefficients for special values of kappa in the whole-plane Schramm-Loewner evolution (SLE_kappa). We propose to use multi-point correlation functions for the study of higher moments in coefficient problem. Generalizations related to the Levy-type processes are also considered. The exact multifractal spectrum of considered version of the whole-plane SLE_kappa is discussed

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

LERW as an example of off-critical SLEs

Two dimensional loop erased random walk (LERW) is a random curve, whose continuum limit is known to be a Schramm-Loewner evolution (SLE) with parameter kappa=2. In this article we study ``off-critical loop erased random walks'', loop erasures of random walks penalized by their number of steps. On one hand we are able to identify counterparts for some LERW observables in terms of symplectic fermions (c=-2), thus making further steps towards a field theoretic description of LERWs. On the other hand, we show that it is possible to understand the Loewner driving function of the continuum limit of off-critical LERWs, thus providing an example of application of SLE-like techniques to models near their critical point. Such a description is bound to be quite complicated because outside the critical point one has a finite correlation length and therefore no conformal invariance. However, the example here shows the question need not be intractable. We will present the results with emphasis on general features that can be expected to be true in other off-critical models.Comment: 45 pages, 2 figure

New Rare Earth Element Abundance Distributions for the Sun and Five r-Process-Rich Very Metal-Poor Stars

We have derived new abundances of the rare-earth elements Pr, Dy, Tm, Yb, and Lu for the solar photosphere and for five very metal-poor, neutron-capture r-process-rich giant stars. The photospheric values for all five elements are in good agreement with meteoritic abundances. For the low metallicity sample, these abundances have been combined with new Ce abundances from a companion paper, and reconsideration of a few other elements in individual stars, to produce internally-consistent Ba, rare-earth, and Hf (56<= Z <= 72) element distributions. These have been used in a critical comparison between stellar and solar r-process abundance mixes.Comment: 48 pages, 11 figures, 12 tables: To appear in the Astrophysical Journal Supplemen