Stellar turbulence and mode physics

An overview of selected topical problems on modelling oscillation properties in solar-like stars is presented. High-quality oscillation data from both space-borne intensity observations and ground-based spectroscopic measurements provide first tests of the still-ill-understood, superficial layers in distant stars. Emphasis will be given to modelling the pulsation dynamics of the stellar surface layers, the stochastic excitation processes and the associated dynamics of the turbulent fluxes of heat and momentum.Comment: Proc. HELAS Workshop on 'Synergies between solar and stellar modelling', eds M. Marconi, D. Cardini, M. P. Di Mauro, Astrophys. Space Sci., in the pres

Gluon contribution to the structure function g_2(x,Q^2)

We calculate the one-loop twist-3 gluon contribution to the flavor-singlet structure function g_2(x,Q^2) in polarized deep-inelastic scattering and find that it is dominated by the contribution of the three-gluon operator with the lowest anomalous dimension (for each moment N). The similar property was observed earlier for the nonsinglet distributions, although the reason is in our case different. The result is encouraging and suggests a simple evolution pattern of g_2(x,Q^2) in analogy with the conventional description of twist-2 parton distributions.Comment: 26 pages, Latex style, 4 figures (two references added, a few typos corrected

Stochastic excitation of acoustic modes in stars

For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances ...). Excitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich & Keely (1977), more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modeled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions. We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.Comment: Notes associated with a lecture given during the fall school organized by the CNRS and held in St-Flour (France) 20-24 October 2008 ; 39 pages ; 11 figure

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Stein's method on Wiener chaos

We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. We also prove results concerning random variables admitting a possibly infinite Wiener chaotic decomposition. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-It\^o integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre, Peccati and Tudor. We apply our techniques to prove Berry-Ess\'een bounds in the Breuer-Major CLT for subordinated functionals of fractional Brownian motion. By using the well-known Mehler's formula for Ornstein-Uhlenbeck semigroups, we also recover a technical result recently proved by Chatterjee, concerning the Gaussian approximation of functionals of finite-dimensional Gaussian vectors.Comment: 39 pages; Two sections added; To appear in PTR

Significant suppression of weak ferromagnetism in (La1.8{}_{1.8}Eu0.2{}_{0.2})CuO4{}_4

The magnetic structure of (La${}_{1.8}$Eu${}_{0.2}$)CuO${}_4$ has been studied by magnetization measurements of single crystals, which show antiferromagnetic long-range order below $T_N$ = 265 K and a structural phase transition at $T_s$ = 130 K. At $T_s < T < T_N$, the Cu spin susceptibility exhibits almost the same behavior as that of La${}_2$CuO${}_4$ in the low-temperature orthorhombic phase, which indicates the existence of finite spin canting out of the CuO${}_2$ plane. At $T < T_s$, the magnitude of the weak-ferromagnetic moment induced by the spin canting is suppressed approximately by 70{%}. This significant suppression of the weak-ferromagnetic moment is carefully compared with the theoretical analysis of weak ferromagnetism by Stein {\it et al.} (Phys. Rev. B {\bf 53}, 775 (1996)), in which the magnitude of weak-ferromagnetic moments strongly depend on the crystallographic symmetry. Based on such comparison, below $T_s$ (La${}_{1.8}$Eu${}_{0.2}$)CuO${}_4$ is in the low-temperature less-orthorhombic phase with a space group of $Pccn$. We also discuss the possible magnetic structure of the pure low-temperature tetragonal phase with space group $P4_2/{ncm}$, which is relevant for rare-earth and alkaline-earth ions co-doped La${}_2$CuO${}_4$.Comment: 16 pages including 5 figures, submitted to Phys. Rev. B. Fig. 4 is newly adde

Radiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona

We present a series of numerical simulations of the quiet Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun's atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy.Comment: 20 pages, 5 figures, Solar Physics, in pres