Sigma models with AkA_k singularities in Euclidean spacetime of dimension 0<=D<4 and in the limit N->infinity

For the case of the single-O($N$)-vector linear sigma models the critical behaviour following from any $A_k$ singularity in the action is worked out in the double scaling limit $N \rightarrow \infty$, $f_r \rightarrow f_r^c$, $2 \leq r \leq k$. After an exact elimination of Gaussian degrees of freedom, the critical objects such as coupling constants, indices and susceptibility matrix are derived for all $A_k$ and spacetime dimensions $0 \leq D < 4$. There appear exceptional spacetime dimensions where the degree $k$ of the singularity $A_k$ is more strongly constrained than by the renormalizability requirement.Comment: LaTeX, 25 pages, no figure

Double Scaling Limits, Airy Functions and Multicritical Behaviour in O(N) Vektor Sigma Models

O(N) vector sigma models possessing catastrophes in their action are studied. Coupling the limit N --> infinity with an appropriate scaling behaviour of the coupling constants, the partition function develops a singular factor. This is a generalized Airy function in the case of spacetime dimension zero and the partition function of a scalar field theory for positive spacetime dimension.Comment: 14 pages, LaTe

On the critical behaviour of hermitean f-matrix models in the double scaling limit with f >= 3

An algorithm for the isolation of any singularity of f-matrix models in the double scaling limit is presented. In particular it is proved by construction that only those universality classes exist that are known from 2-matrix models.Comment: 24 pages, LaTex, correction of some notation errors and addition of four reference

Physics of rotation in stellar models

In these lecture notes, we present the equations presently used in stellar interior models in order to compute the effects of axial rotation. We discuss the hypotheses made. We suggest that the effects of rotation might play a key role at low metallicity.Comment: 32 pages, 7 figures, lectures, CNRS school, will be published by Springe

Grids of stellar models. VIII. From 0.4 to 1.0 Msun at Z=0.020 and Z=0.001, with the MHD equation of state

We present stellar evolutionary models covering the mass range from 0.4 to 1 Msun calculated for metallicities Z=0.020 and 0.001 with the MHD equation of state (Hummer & Mihalas, 1988; Mihalas et al. 1988; D\"appen et al. 1988). A parallel calculation using the OPAL (Rogers et al. 1996) equation of state has been made to demonstrate the adequacy of the MHD equation of state in the range of 1.0 to 0.8 Msun (the lower end of the OPAL tables). Below, down to 0.4 Msun, we have justified the use of the MHD equation of state by theoretical arguments and the findings of Chabrier & Baraffe (1997). We use the radiative opacities by Iglesias & Rogers (1996), completed with the atomic and molecular opacities by Alexander & Fergusson (1994). We follow the evolution from the Hayashi fully convective configuration up to the red giant tip for the most massive stars, and up to an age of 20 Gyr for the less massive ones. We compare our solar-metallicity models with recent models computed by other groups and with observations. The present stellar models complete the set of grids computed with the same up-to-date input physics by the Geneva group [Z=0.020 and 0.001, Schaller et al. (1992), Bernasconi (1996), and Charbonnel et al. (1996); Z=0.008, Schaerer et al. (1992); Z=0.004, Charbonnel et al. (1993); Z=0.040, Schaerer et al. (1993); Z=0.10, Mowlavi et al. (1998); enhanced mass loss rate evolutionary tracks, Meynet et al. (1994)].Comment: Accepted for publication in A&A Supplement Serie

The Continuous Series of Critical Points of the Two-Matrix Model at N -> infinity in the Double Scaling Limit

The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.Comment: 24 pages, LaTe

Habitability of Super-Earth Planets around Main-Sequence Stars including Red Giant Branch Evolution: Models based on the Integrated System Approach

In a previous study published in Astrobiology, we focused on the evolution of habitability of a 10 M_E super-Earth planet orbiting a star akin to the Sun. This study was based on a concept of planetary habitability in accordance to the integrated system approach that describes the photosynthetic biomass production taking into account a variety of climatological, biogeochemical, and geodynamical processes. In the present study, we pursue a significant augmentation of our previous work by considering stars with zero-age main sequence masses between 0.5 and 2.0 M_sun with special emphasis on models of 0.8, 0.9, 1.2 and 1.5 M_sun. Our models of habitability consider again geodynamical processes during the main-sequence stage of these stars as well as during their red giant branch evolution. Pertaining to the different types of stars, we identify so-called photosynthesis-sustaining habitable zones (pHZ) determined by the limits of biological productivity on the planetary surface. We obtain various sets of solutions consistent with the principal possibility of life. Considering that stars of relatively high masses depart from the main-sequence much earlier than low-mass stars, it is found that the biospheric life-span of super-Earth planets of stars with masses above approximately 1.5 M_sun is always limited by the increase in stellar luminosity. However, for stars with masses below 0.9 M_sun, the life-span of super-Earths is solely determined by the geodynamic time-scale. For central star masses between 0.9 and 1.5 M_sun, the possibility of life in the framework of our models depends on the relative continental area of the super-Earth planet.Comment: 25 pages, 6 figures, 2 tables; submitted to: International Journal of Astrobiolog

Mitigation and Adaptation Strategies – Organic Agriculture

This psoter presents information on the following - The concept of organic farming in the context of climate change - Carbon sequestration on organic farms - Consequences of an area-wide conversion to organic agricultur