Extinction for two parabolic stochastic PDE's on the lattice

It is well known that, starting with finite mass, the super-Brownian motion dies out in finite time. The goal of this article is to show that with some additional work, one can prove finite time die-out for two types of systems of stochastic differential equations on the lattice Z^d. Our first system involves the heat equation on the lattice Z^d, with a nonlinear noise term u(t,x)^gamma dB_x(t), with 1/2 <= gamma < 1. The B_x are independent Brownian motions. When gamma = 1/2, the measure which puts mass u(t,x) at x is a super-random walk and it is well-known that the process becomes extinct in finite time a.s. Finite-time extinction is known to be a.s. false if gamma = 1. For 1/2 < gamma < 1, we show finite-time die-out by breaking up the solution into pieces, and showing that each piece dies in finite time. Our second example involves the mutually catalytic branching system of stochastic differential equations on Z^d, which was first studied by Dawson and Perkins. Roughly speaking, this process consists of 2 superprocesses with the continuous time simple random walk as the underlying spatial motion. Furthermore, each process stimulates branching and dying in the other process. By using a somewhat different argument, we show that, depending on the initial conditions, finite time extinction of one type may occur with probability 0, or with probability arbitrarily close to 1

The Helios mechanical despin drive assembly for the high-gain antenna reflector

Helios is the German-American solar probe which comes within 0.31 Astronomical Units of the sun. A special thermal design and a dry lubrication system have resulted in successful operation up to now, with Helios having finished its first orbit around the sun

Investigation of the Quantitative Determination of Point and Areal Precipitation by Radar Echo Measurements: Fourth Quarterly Technical Report

published or submitted for publicationis peer reviewedOpe

Man's flight in space

Apollo project - progress and national benefit

Learning to Understand by Evolving Theories

In this paper, we describe an approach that enables an autonomous system to infer the semantics of a command (i.e. a symbol sequence representing an action) in terms of the relations between changes in the observations and the action instances. We present a method of how to induce a theory (i.e. a semantic description) of the meaning of a command in terms of a minimal set of background knowledge. The only thing we have is a sequence of observations from which we extract what kinds of effects were caused by performing the command. This way, we yield a description of the semantics of the action and, hence, a definition.Comment: KRR Workshop at ICLP 201

Non-spherical core collapse supernovae and nucleosynthesis

Motivated by observations of supernova SN 1987A, various authors have simulated Rayleigh-Taylor (RT) instabilities in the envelopes of core collapse supernovae (for a review, see Mueller 1998). The non-radial motion found in these simulations qualitatively agreed with observations in SN 1987A, but failed to explain the extent of mixing of newly synthesized 56Ni quantitatively. Here we present results of a 2D hydrodynamic simulation which re-addresses this failure and covers the entire evolution of the first 5 hours after core bounce.Comment: 4 pages, 1 figure, LaTeX, requires espcrc1.sty. To appear in Nucl. Phys. A., the proceedings of the conference "Nuclei in the Cosmos 2000", held in Aarhus, Denmark, June 27-July 1, 200

Phase diagram of polymer blends in confined geometry

Within self-consistent field theory we study the phase behavior of a symmetrical binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding semi-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surface fields to the interface localization/delocalization transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exhibits two critical points which correspond to the prewetting critical points of the semi-infinite system. Only below a triple point there is a single two phase coexistence region. The crossover between these qualitatively different limiting behaviors occurs gradually, however, the critical temperature and the critical composition exhibit a non-monotonic dependence on the surface field. The dependence of the phase behavior for antisymmetric boundaries is studied as a function of the film thickness and the strength of the surface interactions. Upon reducing the film thickness or decreasing the strength of the surface interactions we can change the order of the interface localization/delocalization transition from first to second. The role of fluctuations is explored via Monte Carlo simulations of a coarse grained lattice model. Close to the (prewetting) critical points we observe 2D Ising critical behavior. At lower temperatures capillary waves of the AB interface lead to a pronounced dependence of the effective interface potential on the lateral system size.Comment: submitted to the Journal of Molecular Liquids and Condensed Matter Physic