Locally supersymmetric D=3 non-linear sigma models

We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it generally decomposes into two separate quaternionic spaces, associated with inequivalent supermultiplets. For N=5,6,8 there is a unique (symmetric) space for any given number of supermultiplets. Beyond that there are only theories based on a single supermultiplet for N=9,10,12 and 16, associated with coset spaces with the exceptional isometry groups $F_{4(-20)}$, $E_{6(-14)}$, $E_{7(-5)}$ and $E_{16(+8)}$, respectively. For $N=3$ and $N\geq5$ the $D=2$ theories obtained by dimensional reduction are two-loop finite.Comment: 35 pages plain tex, CERN-TH.6612/92 THU-92-1

3-D facial expression representation using statistical shape models

This poster describes a methodology for facial expressions representation, using 3-D/4-D data, based on the statistical shape modelling technology. The proposed method uses a shape space vector to model surface deformations, and a modified iterative closest point (ICP) method to calculate the point correspondence between each surface. The shape space vector is constructed using principal component analysis (PCA) computed for typical surfaces represented in a training data set. It is shown that the calculated shape space vector can be used as a significant feature for subsequent facial expression classification. Comprehensive 3-D/4-D face data sets have been used for building the deformation models and for testing, which include 3-D synthetic data generated from FaceGen Modeller® software, 3-D facial expression data caputed by a static 3-D scanner in the BU-3DFE database and 3-D video sequences captured at the ADSIP research centre using a 3dMD® dynamic 3-D scanner

2-D and 3-D Radiation Transfer Models of High-Mass Star Formation

2-D and 3-D radiation transfer models of forming stars generally produce bluer 1-10 micron colors than 1-D models of the same evolutionary state and envelope mass. Therefore, 1-D models of the shortwave radiation will generally estimate a lower envelope mass and later evolutionary state than multidimensional models. 1-D models are probably reasonable for very young sources, or longwave analysis (wavelengths > 100 microns). In our 3-D models of high-mass stars in clumpy molecular clouds, we find no correlation between the depth of the 10 micron silicate feature and the longwave (> 100 micron) SED (which sets the envelope mass), even when the average optical extinction of the envelope is >100 magnitudes. This is in agreement with the observations of Faison et al. (1998) of several UltraCompact HII (UCHII) regions, suggesting that many of these sources are more evolved than embedded protostars. We have calculated a large grid of 2-D models and find substantial overlap between different evolutionary states in the mid-IR color-color diagrams. We have developed a model fitter to work in conjunction with the grid to analyze large datasets. This grid and fitter will be expanded and tested in 2005 and released to the public in 2006.Comment: 10 pages, 8 figures, to appear in the proceedings of IAU Symp 227, Massive Star Birth: A Crossroads of Astrophysics, (Cesaroni R., Churchwell E., Felli M., Walmsley C. editors

Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models

Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic d=3 physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers, are obtained for Ising, XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.Comment: 7 pages, 12 figures. Corrected typos, added publication informatio

Numerical approach for high precision 3-D relativistic star models

A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a regularization procedure is introduced to deal with the infinite derivatives on the boundary that may appear in the density field when stiff equations of state are used. Consequently all the physical fields are smooth functions on each domain and the spectral method is absolutely free of any Gibbs phenomenon, which yields to a very high precision. The power of this method is demonstrated by direct comparison with analytical solutions such as MacLaurin spheroids and Roche ellipsoids. The relative numerical error reveals to be of the order of $10^{-10}$. This approach has been developed for the study of relativistic inspiralling binaries. It may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres