Asymptotics of the mean-field Heisenberg model

We consider the mean-field classical Heisenberg model and obtain detailed information about the total spin of the system by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cramer- and Sanov-type large deviations principles for the total spin and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the total spin throughout the phase transition using Stein's method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.Comment: 44 page

Solution of coupled vertex and propagator Dyson-Schwinger equations in the scalar Munczek-Nemirovsky model

In a scalar $\phi^2\chi$ model, we exactly solve the vertex and $\phi$ propagator Dyson-Schwinger equations under the assumption of a spatially constant (Munczek-Nemirovsky) propagator for the $\chi$ field. Various truncation schemes are also considered.Comment: 7 pages,4 figures, minor changes, reference added for published versio

Adaptive Density Estimation on the Circle by Nearly-Tight Frames

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the so-called Mexican needlets, which describe a nearly-tight frame on the circle. We study the asymptotic behaviour of the $L^{2}$-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.Comment: 30 pages, 3 figure

YREC: The Yale Rotating Stellar Evolution Code

The stellar evolution code YREC is outlined with emphasis on its applications to helio- and asteroseismology. The procedure for calculating calibrated solar and stellar models is described. Other features of the code such as a non-local treatment of convective core overshoot, and the implementation of a parametrized description of turbulence in stellar models, are considered in some detail. The code has been extensively used for other astrophysical applications, some of which are briefly mentioned at the end of the paper.Comment: 10 pages, 2 figures, ApSS accepte

Imprints of the Quantum World in Classical Mechanics

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless particles is a classical equation which is equivalent to Hamilton's equations.Comment: Paper submitted to Foundations of Physic

Presupernova Structure of Massive Stars

Issues concerning the structure and evolution of core collapse progenitor stars are discussed with an emphasis on interior evolution. We describe a program designed to investigate the transport and mixing processes associated with stellar turbulence, arguably the greatest source of uncertainty in progenitor structure, besides mass loss, at the time of core collapse. An effort to use precision observations of stellar parameters to constrain theoretical modeling is also described.Comment: Proceedings for invited talk at High Energy Density Laboratory Astrophysics conference, Caltech, March 2010. Special issue of Astrophysics and Space Science, submitted for peer review: 7 pages, 3 figure

Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds

Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}\}$ describing a localised projection onto the space of eigenfunctions of the Laplace operator on $\mathbf M$ with corresponding eigenvalues less than $2^{2j}$, as constructed in \cite{GP10}. We prove non-asymptotic concentration inequalities for the uniform deviations of the linear needlet density estimator $f_n(j)$ obtained from an empirical estimate of the needlet projection $\sum_\eta \phi_{j \eta} \int f \phi_{j \eta}$ of $f$. We apply these results to construct risk-adaptive estimators and nonasymptotic confidence bands for the unknown density $f$. The confidence bands are adaptive over classes of differentiable and H\"{older}-continuous functions on $\mathbf M$ that attain their H\"{o}lder exponents.Comment: Probability Theory and Related Fields, to appea

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

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe