Brief of Amici Curiae 65 Professors of Law, Business, Economics, and Sports Management in Support of Respondents

The Alston plaintiffs are college athletes who successfully challenged the NCAA\u27s amateurism rules, convincing the lower courts that the rules should be modestly relaxed to limit their effect on competition for athletic talent. Nearly 60 professors of law, business, and economics from around the country joined the brief

An observational asteroseismic study of the pulsating B-type stars in the open cluster NGC 884

Recent progress in the seismic interpretation of field β Cep stars has resulted in improvements of the physical description in the stellar structure and evolution model computations of massive stars. Further asteroseismic constraints can be obtained from studying ensembles of stars in a young open cluster, which all have similar age, distance and chemical composition. We present an observational asteroseismic study based on the discovery of numerous multi-periodic and mono-periodic B-type stars in the open cluster NGC 884 (χ Persei). Our study illustrates the current status of ensemble asteroseismology of this young open cluste

Atmospheric parameters and chemical properties of red giants in the CoRoT asteroseismology fields

A precise characterisation of the red giants in the seismology fields of the CoRoT satellite is a prerequisite for further in-depth seismic modelling. High-resolution FEROS and HARPS spectra were obtained as part of the ground-based follow-up campaigns for 19 targets holding great asteroseismic potential. These data are used to accurately estimate their fundamental parameters and the abundances of 16 chemical species in a self-consistent manner. Some powerful probes of mixing are investigated (the Li and CNO abundances, as well as the carbon isotopic ratio in a few cases). The information provided by the spectroscopic and seismic data is combined to provide more accurate physical parameters and abundances. The stars in our sample follow the general abundance trends as a function of the metallicity observed in stars of the Galactic disk. After an allowance is made for the chemical evolution of the interstellar medium, the observational signature of internal mixing phenomena is revealed through the detection at the stellar surface of the products of the CN cycle. A contamination by NeNa-cycled material in the most massive stars is also discussed. With the asteroseismic constraints, these data will pave the way for a detailed theoretical investigation of the physical processes responsible for the transport of chemical elements in evolved, low- and intermediate-mass stars.Comment: Accepted for publication in A&A, 25 pages, 13 colour figures (revised version after language editing

Oscillating red giants in the CoRoT exo-field: Asteroseismic mass and radius determination

Context. Observations and analysis of solar-type oscillations in red-giant stars is an emerging aspect of asteroseismic analysis with a number of open questions yet to be explored. Although stochastic oscillations have previously been detected in red giants from both radial velocity and photometric measurements, those data were either too short or had sampling that was not complete enough to perform a detailed data analysis of the variability. The quality and quantity of photometric data as provided by the CoRoT satellite is necessary to provide a breakthrough in observing p-mode oscillations in red giants. We have analyzed continuous photometric time-series of about 11 400 relatively faint stars obtained in the exofield of CoRoT during the first 150 days long-run campaign from May to October 2007. We find several hundred stars showing a clear power excess in a frequency and amplitude range expected for red-giant pulsators. In this paper we present first results on a sub-sample of these stars. Aims. Knowing reliable fundamental parameters like mass and radius is essential for detailed asteroseismic studies of red-giant stars. As the CoRoT exofield targets are relatively faint (11-16 mag) there are no (or only weak) constraints on the star's location in the H-R diagram. We therefore aim to extract information about such fundamental parameters solely from the available time series. Methods. We model the convective background noise and the power excess hump due to pulsation with a global model fit and deduce reliable estimates for the stellar mass and radius from scaling relations for the frequency of maximum oscillation power and the characteristic frequency separation.Comment: 10 pages, 7 figures, accepted for publication in A&

Non-radial oscillations in the red giant HR7349 measured by CoRoT

Convection in red giant stars excites resonant acoustic waves whose frequencies depend on the sound speed inside the star, which in turn depends on the properties of the stellar interior. Therefore, asteroseismology is the most robust available method for probing the internal structure of red giant stars. Solar-like oscillations in the red giant HR7349 are investigated. Our study is based on a time series of 380760 photometric measurements spread over 5 months obtained with the CoRoT satellite. Mode parameters were estimated using maximum likelihood estimation of the power spectrum. The power spectrum of the high-precision time series clearly exhibits several identifiable peaks between 19 and 40 uHz showing regularity with a mean large and small spacing of Dnu = 3.47+-0.12 uHz and dnu_02 = 0.65+-0.10 uHz. Nineteen individual modes are identified with amplitudes in the range from 35 to 115 ppm. The mode damping time is estimated to be 14.7+4.7-2.9 days.Comment: 8 pages, A&A accepte

Models of red giants in the CoRoT asteroseismology fields combining asteroseismic and spectroscopic constraints

Context. The availability of asteroseismic constraints for a large sample of red giant stars from the CoRoT and Kepler missions paves the way for various statistical studies of the seismic properties of stellar populations. Aims. We use the first detailed spectroscopic study of 19 CoRoT red-giant stars (Morel et al 2014) to compare theoretical stellar evolution models to observations of the open cluster NGC 6633 and field stars. Methods. In order to explore the effects of rotation-induced mixing and thermohaline instability, we compare surface abundances of carbon isotopic ratio and lithium with stellar evolution predictions. These chemicals are sensitive to extra-mixing on the red-giant branch. Results. We estimate mass, radius, and distance for each star using the seismic constraints. We note that the Hipparcos and seismic distances are different. However, the uncertainties are such that this may not be significant. Although the seismic distances for the cluster members are self consistent they are somewhat larger than the Hipparcos distance. This is an issue that should be considered elsewhere. Models including thermohaline instability and rotation-induced mixing, together with the seismically determined masses can explain the chemical properties of red-giants targets. However, with this sample of stars we cannot perform stringent tests of the current stellar models. Tighter constraints on the physics of the models would require the measurement of the core and surface rotation rates, and of the period spacing of gravity-dominated mixed modes. A larger number of stars with longer times series, as provided by Kepler or expected with Plato, would help for ensemble asteroseismology.Comment: Accepted 03/05/201

An Arbitrary Curvilinear Coordinate Method for Particle-In-Cell Modeling

A new approach to the kinetic simulation of plasmas in complex geometries, based on the Particle-in- Cell (PIC) simulation method, is explored. In the two dimensional (2d) electrostatic version of our method, called the Arbitrary Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are carried out in 2d on a uniform grid on the unit square logical domain, and mapped to a nonuniform boundary-fitted grid on the physical domain. As the resulting logical grid equations of motion are not separable, we have developed an extension of the semi-implicit Modified Leapfrog (ML) integration technique to preserve the symplectic nature of the logical grid particle mover. A generalized, curvilinear coordinate formulation of Poisson's equations to solve for the electrostatic fields on the uniform logical grid is also developed. By our formulation, we compute the plasma charge density on the logical grid based on the particles' positions on the logical domain. That is, the plasma particles are weighted to the uniform logical grid and the self-consistent mean electrostatic fields obtained from the solution of the logical grid Poisson equation are interpolated to the particle positions on the logical grid. This process eliminates the complexity associated with the weighting and interpolation processes on the nonuniform physical grid and allows us to run the PIC method on arbitrary boundary-fitted meshes.Comment: Submitted to Computational Science & Discovery December 201

Vector-soliton collision dynamics in nonlinear optical fibers

We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions, described by a coupled pair of nonlinear Schroedinger equations. We study a low-dimensional model system of Hamiltonian ODE derived by Ueda and Kath and also studied by Tan and Yang. We derive a further simplified model which has similar dynamics but is more amenable to analysis. Sufficiently fast solitons move by each other without much interaction, but below a critical velocity the solitons may be captured. In certain bands of initial velocities the solitons are initially captured, but separate after passing each other twice, a phenomenon known as the two-bounce or two-pass resonance. We derive an analytic formula for the critical velocity. Using matched asymptotic expansions for separatrix crossing, we determine the location of these "resonance windows." Numerical simulations of the ODE models show they compare quite well with the asymptotic theory.Comment: 32 pages, submitted to Physical Review

Modelling a high-mass red giant observed by CoRoT

The G6 giant HR\,2582 (HD\,50890) was observed by CoRoT for approximately 55 days. Mode frequencies are extracted from the observed Fourier spectrum of the light curve. Numerical stellar models are then computed to determine the characteristics of the star (mass, age, etc...) from the comparison with observational constraints. We provide evidence for the presence of solar-like oscillations at low frequency, between 10 and 20\,$\mu$Hz, with a regular spacing of $(1.7\pm0.1)\mu$Hz between consecutive radial orders. Only radial modes are clearly visible. From the models compatible with the observational constraints used here, We find that HR\,2582 (HD\,50890) is a massive star with a mass in the range (3--\,5\,$M_{\odot}$), clearly above the red clump. It oscillates with rather low radial order ($n$ = 5\,--\,12) modes. Its evolutionary stage cannot be determined with precision: the star could be on the ascending red giant branch (hydrogen shell burning) with an age of approximately 155 Myr or in a later phase (helium burning). In order to obtain a reasonable helium amount, the metallicity of the star must be quite subsolar. Our best models are obtained with a mixing length significantly smaller than that obtained for the Sun with the same physical description (except overshoot). The amount of core overshoot during the main-sequence phase is found to be mild, of the order of 0.1\,$H_{\rm p}$.Comment: Accepted in A&

The underlying physical meaning of the νmax−νc\nu_{\rm max}-\nu_{\rm c} relation

Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum ($\nu_{\rm max}$) of solar-like oscillations and the cut-off frequency ($\nu_{\rm c}$). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called \emph{plateau} of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between $\nu_{\rm max}$ and $\nu_{\rm c}$, with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter.Comment: 8 pages, 11 figures. Accepted in A&