Simulations of core convection in rotating A-type stars: Differential rotation and overshooting

We present the results of 3--D simulations of core convection within A-type stars of 2 solar masses, at a range of rotation rates. We consider the inner 30% by radius of such stars, thereby encompassing the convective core and some of the surrounding radiative envelope. We utilize our anelastic spherical harmonic (ASH) code, which solves the compressible Navier-Stokes equations in the anelastic approximation, to examine highly nonlinear flows that can span multiple scale heights. The cores of these stars are found to rotate differentially, with central cylindrical regions of strikingly slow rotation achieved in our simulations of stars whose convective Rossby number (R_{oc}) is less than unity. Such differential rotation results from the redistribution of angular momentum by the nonlinear convection that strongly senses the overall rotation of the star. Penetrative convective motions extend into the overlying radiative zone, yielding a prolate shape (aligned with the rotation axis) to the central region in which nearly adiabatic stratification is achieved. This is further surrounded by a region of overshooting motions, the extent of which is greater at the equator than at the poles, yielding an overall spherical shape to the domain experiencing at least some convective mixing. We assess the overshooting achieved as the stability of the radiative exterior is varied, and the weak circulations that result in that exterior. The convective plumes serve to excite gravity waves in the radiative envelope, ranging from localized ripples of many scales to some remarkable global resonances.Comment: 48 pages, 16 figures, some color. Accepted to Astrophys. J. Color figures compressed with appreciable loss of quality; a PDF of the paper with better figures is available at http://lcd-www.colorado.edu/~brownim/core_convectsep24.pd

Struggling Students\u27 Use of Representation When Developing Number Sense and Problem Solving Abilities

Through my experience I have found students often rely on concrete or pictorial strategies to solve mathematical problems. These strategies are great to build an understanding in mathematical concepts. However, using these strategies becomes a tedious task when working with multi-digit numbers to solve problems involving mathematical operations. For example, a student who relies on drawing base ten blocks to solve three-digit addition problems may experience fatigue, as this is not the most efficient means to solve problems everyday. Through my experience I have found that these strategies may hinder students\u27 abilities to solve a problem correctly because they focus on their drawing and become overwhelmed with how many blocks they have to draw. Concrete manipulatives allow students opportunities to manipulate concrete objects, which help build a strong foundational understanding of mathematical concepts, such as place value (Wai Lan Chan, Au, & Tang, 2014). When students use their understanding of place value with concrete manipulatives they are able to extend this understanding in their mental math abilities, which will help them abstractly compute problems correctly (Bobis, 2008). If students are able to abstractly solve a problem they would then be able to mentally compute a problem, instead of having to use concrete objects or draw a picture. This would help students be able to focus on what a problem features instead of focusing on drawing a picture. The purpose of this study was to help me understand how my students’ flexible engagement with concrete experiences can help construct flexibility abstractly. Furthermore, I wondered if this flexibility would help improve students’ problem-solving abilities in mathematical experiences. Specifically, the purpose of this project was to determine how third grade students (ages 8-9 years old), identified as struggling, flexibly used their concrete experiences to construct flexible abstract strategies when solving mathematical problems involving addition, subtraction, and estimation. Student flexibility was measured through assessments given that involved story problems and numbers lines. It was also measured by student dialogue (Shumway, 2011; Yang & Wu, 2010), whole class counting routines (Shumway, 2011), and number line tasks (Siegler & Booth, 2004.

How Preservice Teachers Develop Awareness and Beliefs About Design Features and Academic Language Features When Choosing and Evaluating Digital Math Games for English Language Learners

This mixed methods study examined how preservice teachers developed awareness and beliefs about design features and academic language features when choosing and evaluating digital math games for English language learners. The overarching research question for this study was, “How do preservice teachers develop awareness and beliefs about design features and academic language features when choosing and evaluating digital math games for English language learners (ELLs)?” During the study, 21 elementary preservice teachers participated in online learning modules about design features and academic language features in digital math games. During the modules, preservice teachers chose and evaluated three digital math games for ELLs based on their awareness of the design features and academic language features in the games. Preservice teachers completed a pre- and post-belief survey, a pre- and post-evaluation rubric, two module reflections, and participated in semistructured interviews. I analyzed qualitative and quantitative data by identifying common themes among open-ended responses on the surveys and evaluation rubrics, module reflections, and responses to the semi-structured interviews. I then used frequency tables to count the themes that emerged and visualized the frequency counts using bar graphs. I then examined the changes in beliefs from pre- to post-surveys and scores from pre- to post- evaluation rubrics. Finally, I compared the results from these analyses to examine how the qualitative and quantitative results agreed or disagreed. Results showed a positive change in preservice teachers’ beliefs about using digital math games to enhance mathematics instruction for ELLs after they participated in the learning modules. Results also showed an increase in preservice teachers’ awareness of design features and academic language features. This indicates that using the learning modules, and the opportunity to choose and evaluate the digital math games, supported a positive impact on preservice teachers’ beliefs and awareness of design features and academic language features

The nature of p-modes and granulation in HD 49933 observed by CoRoT

Context: Recent observations of HD49933 by the space-photometric mission CoRoT provide photometric evidence of solar type oscillations in a star other than our Sun. The first published reduction, analysis, and interpretation of the CoRoT data yielded a spectrum of p-modes with l = 0, 1, and 2. Aims: We present our own analysis of the CoRoT data in an attempt to compare the detected pulsation modes with eigenfrequencies of models that are consistent with the observed luminosity and surface temperature. Methods: We used the Gruberbauer et al. frequency set derived based on a more conservative Bayesian analysis with ignorance priors and fit models from a dense grid of model spectra. We also introduce a Bayesian approach to searching and quantifying the best model fits to the observed oscillation spectra. Results: We identify 26 frequencies as radial and dipolar modes. Our best fitting model has solar composition and coincides within the error box with the spectroscopically determined position of HD49933 in the H-R diagram. We also show that lower-than-solar Z models have a lower probability of matching the observations than the solar metallicity models. To quantify the effect of the deficiencies in modeling the stellar surface layers in our analysis, we compare adiabatic and nonadiabatic model fits and find that the latter reproduces the observed frequencies better.Comment: accepted to be published in A&A, 9 pages, 5 figure

Renal function in Palestine sunbirds: elimination of excess water does not constrain energy intake

Copyright © 2004 Company of BiologistsAlthough the renal responses of birds to dehydration have received significant attention, the consequences of ingesting and processing large quantities of water have been less studied. Nectar-feeding birds must often deal with exceptionally high water intake rates in order to meet their high mass-specific energy demands. Birds that ingest large volumes of water may either eliminate excess water in the kidney or regulate the volume of water absorbed in the gastrointestinal tract. Because water absorption in the gastrointestinal tract of Palestine sunbirds (Nectarinia osea) decreases with increasing water ingestion rate, we predicted that glomerular filtration rate (GFR) in these birds would not be unusually high in spite of large ingested water loads. When feeding on dilute sucrose solutions, sunbirds ingested between 4 and 6 times their body mass in nectar per day, yet they were able to compensate for varying nectar energy density and increased thermoregulatory energy demands with no apparent difficulty. GFR was lower than predicted (1976.22±91.95 µl h-1), and was not exceptionally sensitive to water loading. Plasma glucose concentrations were high, and varied 1.8-fold between fasted (16.08± 0.75 mmol l-1) and fed (28.18±0.68 mmol l-1) sunbirds, but because GFR was low, glucose filtered load also remained relatively low. Essentially the entire glucose filtered load (98%) was recovered by the kidney. Renal fractional water reabsorption (FWR) decreased from 0.98 to 0.64 with increasing water intake. The ability of Palestine sunbirds to reduce the absorption of ingested water in the gastrointestinal tract may resolve the potential conflict between filtering a large excess of absorbed water in the kidney and simultaneously retaining filtered metabolites.Todd J. McWhorter, Carlos Martínez del Rio, Berry Pinshow and Lizanne Roxburg

Global asteroseismic properties of solar-like oscillations observed by Kepler : A comparison of complementary analysis methods

We present the asteroseismic analysis of 1948 F-, G- and K-type main-sequence and subgiant stars observed by the NASA {\em Kepler Mission}. We detect and characterise solar-like oscillations in 642 of these stars. This represents the largest cohort of main-sequence and subgiant solar-like oscillators observed to date. The photometric observations are analysed using the methods developed by nine independent research teams. The results are combined to validate the determined global asteroseismic parameters and calculate the relative precision by which the parameters can be obtained. We correlate the relative number of detected solar-like oscillators with stellar parameters from the {\em Kepler Input Catalog} and find a deficiency for stars with effective temperatures in the range $5300 \lesssim T_\mathrm{eff} \lesssim 5700$\,K and a drop-off in detected oscillations in stars approaching the red edge of the classical instability strip. We compare the power-law relationships between the frequency of peak power, $\nu_\mathrm{max}$, the mean large frequency separation, $\Delta\nu$, and the maximum mode amplitude, $A_\mathrm{max}$, and show that there are significant method-dependent differences in the results obtained. This illustrates the need for multiple complementary analysis methods to be used to assess the robustness and reproducibility of results derived from global asteroseismic parameters.Comment: 14 pages, 9 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ

Open issues in probing interiors of solar-like oscillating main sequence stars: 2. Diversity in the HR diagram

We review some major open issues in the current modelling of low and intermediate mass, main sequence stars based on seismological studies. The solar case was discussed in a companion paper, here several issues specific to other stars than the Sun are illustrated with a few stars observed with CoRoT and expectations from Kepler data.Comment: GONG 2010 - SoHO 24, A new era of seismology of the Sun and solar-like stars, To be published in the Journal of Physics: Conference Series (JPCS

Alfven node-free vibrations of white dwarf in the model of solid star with toroidal magnetic field

In the context of the white dwarf asteroseismology, we investigate vibrational properties of a non-convective solid star with an axisymmetric purely toroidal intrinsic magnetic field of two different shapes. Focus is laid on regime of node-free global Lorentz-force-driven vibrations about symmetry axis at which material displacements have one and the same form as those for nodeless spheroidal and torsional vibrations restored by Hooke's force of elastic shear stresses. Particular attention is given to the even-parity poloidal Alfven modes whose frequency spectra are computed in analytic form showing how the purely toroidal magnetic fields completely buried beneath the star surface can manifest itself in seismic vibrations of non-magnetic white dwarfs. The obtained spectral formulae are discussed in juxtaposition with those for Alfven modes in the solid star model with the poloidal, homogeneous internal and dipolar external, magnetic field whose inferences are relevant to Alfven vibrations in magnetic white dwarfs.Comment: Accepted for publication in Astrophysics & Space Scienc