L1L^1 contraction for bounded (non-integrable) solutions of degenerate parabolic equations

We obtain new $L^1$ contraction results for bounded entropy solutions of Cauchy problems for degenerate parabolic equations. The equations we consider have possibly strongly degenerate local or non-local diffusion terms. As opposed to previous results, our results apply without any integrability assumption on the %(the positive part of the difference of) solutions. They take the form of partial Duhamel formulas and can be seen as quantitative extensions of finite speed of propagation local $L^1$ contraction results for scalar conservation laws. A key ingredient in the proofs is a new and non-trivial construction of a subsolution of a fully non-linear (dual) equation. Consequences of our results are maximum and comparison principles, new a priori estimates, and in the non-local case, new existence and uniqueness results

A model for the X-ray nova A0620-00

The model involves a white dwarf accreting mass from a late-type subgiant companion. The transient behavior of the X-ray source is explained by the instability to mass loss of the companion (as in Algol-type binaries). The brightening, spectrum, and decay timescale of the optical counterpart are explained in terms of re-emission of X-radiation intercepted by the subgiant. It was concluded that A0620-00 can provide an excellent test case for numerical models of stellar atmospheres irradiated by an external X-ray flux

Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory

Abstract. We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations ∂tu − Lσ,μ[φ(u)] = f(x,t) in RN × (0,T), where Lσ,μ is a general symmetric diffusion operator of L ́evy type and φ is merely continuous and non-decreasing. We then use this theory to prove con- vergence for many different numerical schemes. In the nonlocal case most of the results are completely new. Our theory covers strongly degenerate Stefan problems, the full range of porous medium equations, and for the first time for nonlocal problems, also fast diffusion equations. Examples of diffusion op- σ,μ α are the (fractional) Laplacians ∆ and −(−∆)2 for α ∈ (0,2), erators L discrete operators, and combinations. The observation that monotone finite difference operators are nonlocal L ́evy operators, allows us to give a unified and compact nonlocal theory for both local and nonlocal, linear and nonlinear diffusion equations. The theory includes stability, compactness, and conver- gence of the methods under minimal assumptions – including assumptions that lead to very irregular solutions. As a byproduct, we prove the new and general existence result announced in [28]. We also present some numerical tests, but extensive testing is deferred to the companion paper [31] along with a more detailed discussion of the numerical methods included in our theory

On the evolutionary status of Be stars. I. Field Be stars near the Sun

A sample of 97 galactic field Be stars were studied by taking into account the effects induced by the fast rotation on their fundamental parameters. All program stars were observed in the BCD spectrophotometric system in order to minimize the perturbations produced by the circumstellar environment on the spectral photospheric signatures. This is one of the first attempts at determining stellar masses and ages by simultaneously using model atmospheres and evolutionary tracks, both calculated for rotating objects. The stellar ages ($\tau$) normalized to the respective inferred time that each rotating star can spend in the main sequence phase ($\tau\_{\rm MS}$) reveal a mass-dependent trend. This trend shows that: a) there are Be stars spread over the whole interval 0 \la \tau/\tau\_{\rm MS} \la 1 of the main sequence evolutionary phase; b) the distribution of points in the ($\tau/\tau\_{\rm MS},M/M\_{\odot}$) diagram indicates that in massive stars (M \ga 12M\_{\odot}) the Be phenomenon is present at smaller $\tau/\tau\_{\rm MS}$ age ratios than for less massive stars (M \la 12M\_{\odot}). This distribution can be due to: $i$) higher mass-loss rates in massive objets, which can act to reduce the surface fast rotation; $ii$) circulation time scales to transport angular momentum from the core to the surface, which are longer the lower the stellar mass.Comment: 18 pages, 6 figures, A&A, in pres

Observational indicators of the transition from fully convective stars to stars with radiative cores

We present a discussion of the similarities and key differences between the transition onto (at the turn-on) and away from (at the turn-off) the main sequence, the latter termed the Hertzsprung gap. Using a set of model isochrones and adopting an initial mass function leads us to predict a dearth of G-type stars for any star forming region. This is caused by the (relatively) constant spectral type at which the transition from a fully convective star to a star with a radiative core begins. We also present analysis of the details of this transition in the ONC. In particular we show that a gap in the photometric and spectral type distributions is centred on, and a change in the fractional X-ray luminosity and rotation rate distribution occurs approximately at, the position of a peak in radiative core size as a function of mass. Whilst photometric signatures of this transition are lost at ages over ~20 Myrs, we show that changes in fractional X-ray luminosity and magnetic field configuration persist to older ages. Analysis of literature data show that the mass at which the change in fractional X-ray luminosity is observed decreases with age.Comment: 9 pages and 6 figures. Accepted for publication in MNRA

Effects of gravitational darkening on the determination of fundamental parameters in fast rotating B-type stars

In this paper we develop a calculation code to account for the effects carried by fast rotation on the observed spectra of early-type stars. Stars are assumed to be in rigid rotation and the grid of plane-parallel model atmospheres used to represent the gravitational darkening are calculated by means of a non-LTE approach. Attention is paid on the relation between the apparent and parent non-rotating counterpart stellar fundamental parameters and apparent and true vsini parameters as a function of the rotation rate Omega/Omega_c, stellar mass and inclination angle. It is shown that omission of gravitational darkening in the analysis of chemical abundances of CNO elements can produce systematic overestimation or underestimation, depending on the lines used, rotational rate and inclination angle. The proximity of Be stars to the critical rotation is re-discussed by correcting not only the vsini of 130 Be stars, but also their effective temperature and gravity to account for stellar rotationally induced geometrical distortion and for the concomitant gravitational darkening effect. We concluded that the increase of the vsini estimate is accompanied by an even higher value of the stellar equatorial critical velocity, so that the most probable average rate of angular velocity of Be stars attains Omega/Omega_c ~ 0.88.Comment: 20 pages, 16 figures. Submitted for publication in A&

Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

Rotational velocities of A-type stars. III. Velocity distributions

Aim - In this work, a sample of vsini of B9 to F2-type main sequence single stars has been built from highly homogeneous vsini parameters determined for a large sample cleansed from objects presenting the Am and Ap phenomenon as well as from all known binaries. The aim is to study the distributions of rotational velocities in the mass range of A-type stars for normal single objects. Methods - Robust statistical methods are used to rectify the vsini distributions from the projection effect and the error distribution. The equatorial velocity distributions are obtained for an amount of about 1100 stars divided in six groups defined by the spectral type, under the assumption of randomly orientated rotational axes. Results - We show that late B and early A-type main-sequence stars have genuine bimodal distributions of true equatorial rotational velocities due probably to phenomena of angular momentum loss and redistribution the star underwent before reaching the main sequence. A striking lack of slow rotators is noticed among intermediate and late A-type stars. The bimodal-like shape of their true equatorial rotational velocity distributions could be due to evolutionary effects.Comment: 16 pages, 10 figures, accepted in A&

Diagnoses to unravel secular hydrodynamical processes in rotating main sequence stars

(Abridged) We present a detailed analysis of the main physical processes responsible for the transport of angular momentum and chemical species in the radiative regions of rotating stars. We focus on cases where meridional circulation and shear-induced turbulence only are included in the simulations. Our analysis is based on a 2-D representation of the secular hydrodynamics, which is treated using expansions in spherical harmonics. We present a full reconstruction of the meridional circulation and of the associated fluctuations of temperature and mean molecular weight along with diagnosis for the transport of angular momentum, heat and chemicals. In the present paper these tools are used to validate the analysis of two main sequence stellar models of 1.5 and 20 Msun for which the hydrodynamics has been previously extensively studied in the literature. We obtain a clear visualization and a precise estimation of the different terms entering the angular momentum and heat transport equations in radiative zones. This enables us to corroborate the main results obtained over the past decade by Zahn, Maeder, and collaborators concerning the secular hydrodynamics of such objects. We focus on the meridional circulation driven by angular momentum losses and structural readjustements. We confirm quantitatively for the first time through detailed computations and separation of the various components that the advection of entropy by this circulation is very well balanced by the barotropic effects and the thermal relaxation during most of the main sequence evolution. This enables us to derive simplifications for the thermal relaxation on this phase. The meridional currents in turn advect heat and generate temperature fluctuations that induce differential rotation through thermal wind thus closing the transport loop.Comment: 16 pages, 18 figures. Accepted for publication in A&

Physical exercise augmented cognitive behaviour therapy for older adults with generalised anxiety disorder (PEXACOG): a feasibility study for a randomized controlled trial

Background Generalised anxiety disorder (GAD) is a frequent and severe disorder among older adults. For older adults with GAD the effect of the recommended treatment, cognitive behaviour therapy (CBT), is reduced. Physical exercise (PE) may enhance the effect of CBT by improving cognitive function and increasing levels of brain-derived neurotrophic factor (BDNF), a predictor of the effect of CBT in patients with anxiety. The aim of the study was to assess the feasibility of a randomized controlled trial (RCT) investigating treatment effect of the combination of CBT and PE for GAD in a sample of older adults, including procedures for assessment and treatment. Methods Four participants aged 62–70 years (M = 65.5, SD = 3.2) with a primary diagnosis of GAD were included. Participants received 15 weeks of PE in combination with 10 weeks of CBT. Participants completed self-report measures, and clinical, biological, physiological and neuropsychological tests at pre-, interim- and post-treatment. Results Procedures, protocols, and results are presented. One participant dropped out during treatment. For the three participants completing, the total adherence to PE and CBT was 80% and 100%, respectively. An independent assessor concluded that the completers no longer fulfilled the criteria for GAD after treatment. Changes in self-report measures suggest symptom reduction related to anxiety and worry. The sample is considered representative for the target population. Conclusions The results indicate that combining CBT and PE for older adults with GAD is feasible, and that the procedures and tests are suitable and manageable for the current sample.publishedVersio