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

DESIGN CONSIDERATIONS FOR DIGITAL IMAGE LIBRARIES

Design of digital image libraries requires choices for numerous configuration aspects, such as resolution and display settings. These aspects can be categorized into different types of design criteria based on whether they are a human viewing and usage factor, or a stage in the image library management process. The criteria can also be applied in a hierarchy of nested versions of access to the library to suit different usage circumstances. Here we present a framework for design criteria using this approach, and apply it to some example cases

Structure Formation Inside Triaxial Dark Matter Halos: Galactic Disks, Bulges and Bars

We investigate the formation and evolution of galactic disks immersed in assembling live DM halos. Disk/halo components have been evolved from the cosmological initial conditions and represent the collapse of an isolated density perturbation. The baryons include gas (which participates in star formation [SF]) and stars. The feedback from the stellar energy release onto the ISM has been implemented. We find that (1) The growing triaxial halo figure tumbling is insignificant and the angular momentum (J) is channeled into the internal circulation; (2) Density response of the disk is out of phase with the DM, thus diluting the inner halo flatness and washing out its prolateness; (3) The total J is neathly conserved, even in models accounting for feedback; (4) The specific J for the DM is nearly constant, while that for baryons is decreasing; (5) Early stage of disk formation resembles the cat's cradle -- a small amorphous disk fueled via radial string patterns; (6) The initially puffed up gas component in the disk thins when the SF rate drops below ~5 Mo/yr; (7) About 40%-60% of the baryons remain outside the SF region; (8) Rotation curves appear to be flat and account for the observed disk/halo contributions; (9) A range of bulge-dominated to bulgeless disks was obtained; Lower density threshold for SF leads to a smaller, thicker disk; Gravitational softening in the gas has a substantial effect on various aspects of galaxy evolution and mimics a number of intrinsic processes within the ISM; (10) The models are characterized by an extensive bar-forming activity; (11) Nuclear bars, dynamically coupled and decoupled form in response to the gas inflow along the primary bars.Comment: 18 pages, 16 figures, accepted by the Astrophysical Journal. Minor revisions. The high-resolution figures can be found at http://www.pa.uky.edu/~shlosman/research/galdyn/figs07a

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&