3-Dimensional Core-Collapse

In this paper, we present the results of 3-dimensional collapse simulations of rotating stars for a range of stellar progenitors. We find that for the fastest spinning stars, rotation does indeed modify the convection above the proto-neutron star, but it is not fast enough to cause core fragmentation. Similarly, although strong magnetic fields can be produced once the proto-neutron star cools and contracts, the proto-neutron star is not spinning fast enough to generate strong magnetic fields quickly after collapse and, for our simulations, magnetic fields will not dominate the supernova explosion mechanism. Even so, the resulting pulsars for our fastest rotating models may emit enough energy to dominate the total explosion energy of the supernova. However, more recent stellar models predict rotation rates that are much too slow to affect the explosion, but these models are not sophisticated enough to determine whether the most recent, or past, stellar rotation rates are most likely. Thus, we must rely upon observational constraints to determine the true rotation rates of stellar cores just before collapse. We conclude with a discussion of the possible constraints on stellar rotation which we can derive from core-collapse supernovae.Comment: 34 pages (5 of 17 figures missing), For full paper, goto http://qso.lanl.gov/~clf/papers/rot.ps.gz accepted by Ap

Towards 3-Dimensional Rewriting Theory

String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is confluent and terminating, they provide one with a notion of canonical representative of the elements of the presented monoid. Polygraphs are a higher-dimensional generalization of this notion of presentation, from the setting of monoids to the much more general setting of n-categories. One of the main purposes of this article is to give a progressive introduction to the notion of higher-dimensional rewriting system provided by polygraphs, and describe its links with classical rewriting theory, string and term rewriting systems in particular. After introducing the general setting, we will be interested in proving local confluence for polygraphs presenting 2-categories and introduce a framework in which a finite 3-dimensional rewriting system admits a finite number of critical pairs

The 3-dimensional oscillon equation

On a bounded three-dimensional smooth domain, we consider the generalized oscillon equation with Dirichlet boundary conditions, with time-dependent damping and time-dependent squared speed of propagation. Under structural assumptions on the damping and the speed of propagation, which include the relevant physical case of reheating phase of inflation, we establish the existence of a pullback global attractor of optimal regularity, and finite-dimensionality of the kernel sections

Approximate 3-Dimensional Electrical Impedance Imaging

We discuss a new approach to three-dimensional electrical impedance imaging based on a reduction of the information to be demanded from a reconstruction algorithm. Images are obtained from a single measurement by suitably simplifying the geometry of the measuring chamber and by restricting the nature of the object to be imaged and the information required from the image. In particular we seek to establish the existence or non-existence of a single object (or a small number of objects) in a homogeneous background and the location of the former in the (x,y)-plane defined by the measuring electrodes. Given in addition the conductivity of the object rough estimates of its position along the z-axis may be obtained. The approach may have practical applications.Comment: 12 pages, 4 figures, LaTeX, Appendix added and other minor change