Evolutionary variations of solar luminosity

The Theoretical arguments for a 30% increase in the solar luminosity over the past 4.7 billion years are reviewed. A scaling argument shows that this increase can be predicted without detailed numerical calculations. The magnitude of the increase is independent of nuclear reaction rates, as long as conversion of hydrogen to helium provides the basic energy source of the Sun. The effect of the solar luminosity increase on the terrestrial climate is briefly considered. It appears unlikely that an enhanced greenhouse effect, due to reduced gases (NH3, CH4), can account for the long-term paleoclimatic trends

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

The evolution of rotating stars. 1: Method and exploratory calculations for a 7 solar mass star

A method was developed which allows us to study the evolution of rotating stars beyond the main sequence stage. Four different cases of redistribution of angular momentum in an evolving star are considered. Evolutionary sequences for a 7 solar mass star, rotating according to these different cases, were computed from the ZAMS to the double shell source stage. Each sequence was begun with a (typical) equatorial velocity of 210 km/sec. On the main sequence, the effects of rotation are of minor importance. As the core contracts during later stages, important effects arise in all physically plausible cases. The outer regions of the cores approach critical velocities and develop unstable angular velocity distributions. The effects of these instabilities should significantly alter the subsequent evolution

Influence of magnetic pressure on stellar structure: A Mechanism for solar variability

A physical mechanism is proposed that couples the Sun's dynamo magnetic field to its gravitational potential energy. The mechanism involves the isotropic field pressure resulting in a lifting force on the convective envelope, thereby raising its potential energy. Decay of the field due to solar activity allows the envelop to subside and releases this energy, which can augment the otherwise steady solar luminosity. Equations are developed and applied to the Sun for several field configurations. The best estimate model suggests that uniform luminosity variations as large as 0.02% for half a sunspot cycle may occur. Brief temporal variations or the rotation of spatial structures could allow larger excursions in the energy released

Thermal perturbation of the Sun

Thermal perturbations of the solar convection zone can be modeled (to the first order) by perturbing the mixing length parameter alpha (equal to the ratio of the mixing length to the pressure scale height) used in the standard mixing length theory of convection. Results of such an analysis are presented and discussed in relation to recent work by others

Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type

We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ can be any nonlocal symmetric degenerate elliptic operator including the fractional Laplacian and numerical discretizations of this operator. The function $\varphi:\mathbb{R} \to \mathbb{R}$ is only assumed to be continuous and nondecreasing. The class of equations include nonlocal (generalized) porous medium equations, fast diffusion equations, and Stefan problems. In addition to very general uniqueness and existence results, we obtain $L^1$-contraction and a priori estimates. We also study local limits, continuous dependence, and properties and convergence of a numerical approximation of our equations.Comment: To appear in "Advances in Mathematics

On distributional solutions of local and nonlocal problems of porous medium type

We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of $$\partial_tu-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=g(x,t)\quad\quad\text{in}\quad\quad \mathbb{R}^N\times(0,T),$$ where $\varphi$ is merely continuous and nondecreasing and $\mathfrak{L}^{\sigma,\mu}$ is the generator of a general symmetric L\'evy process. This means that $\mathfrak{L}^{\sigma,\mu}$ can have both local and nonlocal parts like e.g. $\mathfrak{L}^{\sigma,\mu}=\Delta-(-\Delta)^{\frac12}$. New uniqueness results for bounded distributional solutions of this problem and the corresponding elliptic equation are presented and proven. A key role is played by a new Liouville type result for $\mathfrak{L}^{\sigma,\mu}$. Existence and a priori estimates are deduced from a numerical approximation, and energy type estimates are also obtained.Comment: 6 pages. Minor revision. Added details to Step 2 of the proof of Theorem 3.

Collaboration, a Creative Catalyst

An insight into developing the "Warehouse" project through Producer Mediation, Band Influence, and Facilitation for Musical Practice

Høyde og kroppsbilde- en studie av unge kvinner som spiller håndball

English abstract: Purpose: the purpose of this study is to look into how the participants of the study feel about their body image in relation to their height, and if handball can prove tall girls with an enclave or social network. Going through literature on body-image, sport, health and public health it became apparent that many studies have been done based on weight and BMI. Height on the other hand, is a factor which is hardly examined at all in the literature on body-image, especially regarding adolescent girls. Method: The methodology of this study is based upon grounded theory, and is used through the entire research process. 12 girls participating in a national “tall girl” project conducted by the Norwegian Handball Association (NHF) were interviewed about their body image, seen in relation to their height and the fact they are all handball players. Results: The results from the empirical data show a clear distinction between talking about body image and talking about height. The participants were talking more about “general issues” regarding their body image such as: what they liked or disliked about their bodies, media impact and if they would change something on their body or not. When they were talking about their height, they talked more specific about benefits and disadvantages being tall in everyday life and on the handball court. The girls distinguish between being tall in everyday life and being tall at the handball court. Playing handball was important to them in order to feel confident and proud of their height, however, this did not translate into everyday life. The findings in this study shows there are several factors having an impact on the participants and how they view themselves. Being participants in NHF’s “tall girl’s project” has helped them to take advantage of their height in the handball court and for some it has even raised their level of confidence as tall girls in everyday life. However, even though handball does provide a suitable enclave for the tall girls, handball is only temporarily able to elleviate the pressure on girls to conform to gender stereotypes of the female body as tiny and petite.Norsk sammendrag: Hensikt: Hensikten med denne studien, har vært å se på hvordan deltakerne i denne studien ser på sitt kroppsbilde i forhold til høyden sin, og om håndball kan gi jenter som er høyere enn gjennomsnittlig, et sosialt nettverk å lene seg på. Etter å ha sett på litteratur om kroppsbilde, sport, helse og folkehelse, har det kommet klart frem at mange studier har blitt gjort på bakgrunn av vekt og BMI- relaterte utfordringer. Høyde derimot er en faktor som ikke har vært undersøkt i særlig grad i sammenheng med kroppsbilde, hvert fall ikke sett i sammenheng med unge jenter. Metode: I denne studien er Grounded Theory brukt som gjennomgående metode. 12 jenter som allerede er deltakere i Norges Håndballforbund sitt «høye jenter» prosjekt har blitt intervjuet angående deres kroppsbilde, sett i sammenheng med høyden deres og at de alle spiller håndball. Resultat: Resultatet fra de empiriske dataene, viser at jentene skiller klart mellom å prate om kroppsbilde generelt og høyde. Deltakerne pratet mer om «generelle problemer» når de pratet om kroppsbilde som: hva de eller ikke liker med kroppene sine, medias innvirkning og om de ville forandret noe på kroppene sine eller ikke. Når de snakket om høyden sin, kommenterte de mer om fordeler og ulemper med å være høg i hverdagen og på håndballbanen. Jentene skilte veldig på å være høy i hverdagen og det å være høg på håndballbanen. Funnene som ble gjort viser at det er mange ulike faktorer som spiller inn på hvordan deltakerne ser på seg selv. Det å være deltaker i NHF sitt prosjekt har bidratt til at mange har fått utbytte fordelene av å være høy på håndballbanen, i tillegg til at prosjektet har bidratt med at noen har fått bedre selvtillit som høy jente i hverdagen. Selv om håndball gir de høge jentene et sosialt nettverk de kan lene seg på, kan det bare midlertidig ta vekk presset jentene føler. For dem er det en utfordring å passe inn i det typiske kjønnsstyrte bilde laget av kvinnekroppen som liten og nett

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