Scaling Limits for Internal Aggregation Models with Multiple Sources

We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, all three models are found to have the same scaling limit, which we describe as the solution to a certain PDE free boundary problem in R^d. In particular, internal DLA has a deterministic scaling limit. We find that the scaling limits are quadrature domains, which have arisen independently in many fields such as potential theory and fluid dynamics. Our results apply both to the case of multiple point sources and to the Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in v2: added "least action principle" (Lemma 3.2); small corrections in section 4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version); expanded section 6.

Atomic Diffusion and Mixing in Old Stars I. VLT/FLAMES-UVES Observations of Stars in NGC 6397

We present a homogeneous photometric and spectroscopic analysis of 18 stars along the evolutionary sequence of the metal-poor globular cluster NGC 6397 ([Fe/H] = -2), from the main-sequence turnoff point to red giants below the bump. The spectroscopic stellar parameters, in particular stellar-parameter differences between groups of stars, are in good agreement with broad-band and Stroemgren photometry calibrated on the infrared-flux method. The spectroscopic abundance analysis reveals, for the first time, systematic trends of iron abundance with evolutionary stage. Iron is found to be 31% less abundant in the turnoff-point stars than in the red giants. An abundance difference in lithium is seen between the turnoff-point and warm subgiant stars. The impact of potential systematic errors on these abundance trends (stellar parameters, the hydrostatic and LTE approximations) is quantitatively evaluated and found not to alter our conclusions significantly. Trends for various elements (Li, Mg, Ca, Ti and Fe) are compared with stellar-structure models including the effects of atomic diffusion and radiative acceleration. Such models are found to describe the observed element-specific trends well, if extra (turbulent) mixing just below the convection zone is introduced. It is concluded that atomic diffusion and turbulent mixing are largely responsible for the sub-primordial stellar lithium abundances of warm halo stars. Other consequences of atomic diffusion in old metal-poor stars are also discussed.Comment: 20 pages (emulateapj), 11 figures, accepted for publication in Ap

Observation of Parity Nonconservation in Møller Scattering

We report a measurement of the parity-violating asymmetry in fixed target electron-electron (Møller) scattering: A_(PV) = [-175 ± 30(stat)± 20(syst)] X 10^(-9). This first direct observation of parity nonconservation in Møller scattering leads to a measurement of the electron’s weak charge at low energy Q^e_W = -0:053 ± 0:011. This is consistent with the standard model expectation at the current level of precision: sin^2θ_W = (M_Z)_(MS) = 0:2293 ± 0:0024(stat) ± 0:0016(syst) ± 0:0006(theory)

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

The spherical probe electric field and wave experiment

The experiment is designed to measure the electric field and density fluctuations with sampling rates up to 40,000 samples/sec. The description includes Langmuir sweeps that can be made to determine the electron density and temperature, the study of nonlinear processes that result in acceleration of plasma, and the analysis of large scale phenomena where all four spacecraft are needed

The Chemical Compositions of the SRd Variable Stars-- II. WY Andromedae, VW Eridani, and UW Librae

Chemical compositions are derived from high-resolution spectra for three stars classed as SRd variables in the General Catalogue of Variable Stars. These stars are shown to be metal-poor supergiants: WY And with [Fe/H] = -1.0, VW Eri with [Fe/H] = -1.8, and UW Lib with [Fe/H] = -1.2. Their compositions are identical to within the measurement errors with the compositions of subdwarfs, subgiants, and less evolved giants of the same FeH. The stars are at the tip of the first giant branch or in the early stages of evolution along the asymptotic giant branch (AGB). There is no convincing evidence that these SRd variables are experiencing thermal pulsing and the third dredge-up on the AGB. The SRds appear to be the cool limit of the sequence of RV Tauri variables.Comment: 14 pages, 1 figure, 4 table

Skyrmions from a Born-Infeld Action

We consider a geometrically motivated Skyrme model based on a general covariant kinetic term proposed originally by Born and Infeld. We introduce this new term by generalizing the Born-Infeld action to a non-abelian $SU(2)$ gauge theory and by using the hidden gauge symmetry formalism. The static properties of the Skyrmion are then analyzed and compared with other Skyrme-like models.Comment: 11 pages, 4 figures (not included), revtex v3, LAVAL-PHY-11-9

Solar Oscillations and Convection: II. Excitation of Radial Oscillations

Solar p-mode oscillations are excited by the work of stochastic, non-adiabatic, pressure fluctuations on the compressive modes. We evaluate the expression for the radial mode excitation rate derived by Nordlund and Stein (Paper I) using numerical simulations of near surface solar convection. We first apply this expression to the three radial modes of the simulation and obtain good agreement between the predicted excitation rate and the actual mode damping rates as determined from their energies and the widths of their resolved spectral profiles. We then apply this expression for the mode excitation rate to the solar modes and obtain excellent agreement with the low l damping rates determined from GOLF data. Excitation occurs close to the surface, mainly in the intergranular lanes and near the boundaries of granules (where turbulence and radiative cooling are large). The non-adiabatic pressure fluctuations near the surface are produced by small instantaneous local imbalances between the divergence of the radiative and convective fluxes near the solar surface. Below the surface, the non-adiabatic pressure fluctuations are produced primarily by turbulent pressure fluctuations (Reynolds stresses). The frequency dependence of the mode excitation is due to effects of the mode structure and the pressure fluctuation spectrum. Excitation is small at low frequencies due to mode properties -- the mode compression decreases and the mode mass increases at low frequency. Excitation is small at high frequencies due to the pressure fluctuation spectrum -- pressure fluctuations become small at high frequencies because they are due to convection which is a long time scale phenomena compared to the dominant p-mode periods.Comment: Accepted for publication in ApJ (scheduled for Dec 10, 2000 issue). 17 pages, 27 figures, some with reduced resolution -- high resolution versions available at http://www.astro.ku.dk/~aake/astro-ph/0008048

Improving adaptive bagging methods for evolving data streams

We propose two new improvements for bagging methods on evolving data streams. Recently, two new variants of Bagging were proposed: ADWIN Bagging and Adaptive-Size Hoeffding Tree (ASHT) Bagging. ASHT Bagging uses trees of different sizes, and ADWIN Bagging uses ADWIN as a change detector to decide when to discard underperforming ensemble members. We improve ADWIN Bagging using Hoeffding Adaptive Trees, trees that can adaptively learn from data streams that change over time. To speed up the time for adapting to change of Adaptive-Size Hoeffding Tree (ASHT) Bagging, we add an error change detector for each classifier. We test our improvements by performing an evaluation study on synthetic and real-world datasets comprising up to ten million examples

Synthetic Spectra and Color-Temperature Relations of M Giants

As part of a project to model the integrated spectra and colors of elliptical galaxies through evolutionary synthesis, we have refined our synthetic spectrum calculations of M giants. After critically assessing three effective temperature scales for M giants, we adopted the relation of Dyck et al. (1996) for our models. Using empirical spectra of field M giants as a guide, we then calculated MARCS stellar atmosphere models and SSG synthetic spectra of these cool stars, adjusting the band absorption oscillator strengths of the TiO bands to better reproduce the observational data. The resulting synthetic spectra are found to be in very good agreement with the K-band spectra of stars of the appropriate spectral type taken from Kleinmann & Hall (1986) as well. Spectral types estimated from the strengths of the TiO bands and the depth of the bandhead of CO near 2.3 microns quantitatively confirm that the synthetic spectra are good representations of those of field M giants. The broad-band colors of the models match the field relations of K and early-M giants very well; for late-M giants, differences between the field-star and synthetic colors are probably caused by the omission of spectral lines of VO and water in the spectrum synthesis calculations. Here, we present four grids of K-band bolometric corrections and colors -- Johnson U-V and B-V; Cousins V-R and V-I; Johnson-Glass V-K, J-K and H-K; and CIT/CTIO V-K, J-K, H-K and CO -- for models having 3000 K < Teff < 4000 K and -0.5 < log g < 1.5. These grids, which have [Fe/H] = +0.25, 0.0, -0.5 and -1.0, extend and supplement the color-temperature relations of hotter stars presented in a companion paper (astro-ph/9911367).Comment: To appear in the March 2000 issue of the Astronomical Journal. 60 pages including 15 embedded postscript figures (one page each) and 6 embedded postscript tables (10 pages total