<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.     

The Asymptotic Behavior of the Ergodic Measure of a Glauber + Kawasaki model

We consider an interacting particle system given by the Glauber + Kawasaki dynamics. It is known that this process has a reaction diffusion equation as hydrodynamic limit. The ergodicity of this process in the presence of a metastable state (double well potential) was recently proved by S. Brassesco et al. In this Letter we prove that, in the limit, as ε → 0, the expected value of each spin converges to the global minimizer of the potential. We also prove decay of correlations of the ergodic measure.AMS Subject Classification (2000). 60K35 (82C22, 82C31)This work was partially supported by CNPq     

An Example of Embedded Singular Continuous Spectrum for One-Dimensional Schrödinger Operators

We present a new example of a potential such that the corresponding Schrödinger operator in the halfaxis has singular continuous spectrum embedded in the absolutely continuous spectrum. The singular part is supported in an essentialy dense set. This generalizes a result of C. Remling [3].Mathematics Subject Classification: 34L40, 81Q10.     

The Doss Trick on Symmetric Spaces

The Doss trick is employed to find solutions of Schrüdinger equations on symmetric spaces of compact type. The potentials and initial conditions are taken from an algebra of functions which admit an holomorphic extension to the complexification of the considered symmetric spaces.     

On Conformal Jordan Cells of Finite and Infinite Rank

This work concerns, in part, the construction of conformal Jordan cells of infinite rank and their reductions to conformal Jordan cells of finite rank. How a procedure similar to Lie algebra contractions may reduce a conformal Jordan cell of finite rank to one of lower rank is also discussed. A conformal Jordan cell of rank one corresponds to a primary field. This offers a picture in which any finite conformal Jordan cell of a given conformal weight may be obtained from a universal covering cell of the same weight but infinite rank. MSC (2000): 81T40     

Visualization of shock-wave formation processes during shock reflection at obstacles with multiple steps

According to standard textbooks on compressible fluid dynamics, a shock wave is formed by an accumulation of compression waves. However, the process by which an accumulated compression wave grows into a shock wave has never been visualized. In the present paper, the authors tried to visualize this process using a model wedge with multiple steps. This model is useful for generating a series of compression waves and can simulate a compression process that occurs in a shock tube. By estimating the triple-point trajectory angle, we demonstrated visually that an accumulated compression wave grows into a shock wave. Further reflection experiments over a rough-surface wedge confirmed the tendency for the triple point trajectory angle to reach the asymptotic value _s in the end.This work was first presented at the Symposium on Shock Waves, Japan 2002     

Pressure recovery in a radiused sudden expansion

Experiments on a steady flow through a nominally 2-D exit geometry with rounded edges are presented for the Reynolds number range 300<Re<25,000. The results indicate that the channel flow expands and decelerates upstream of the exit plane resulting in large pressure recovery, especially for turbulent channel flow. It is shown that pressure recovery is a function of the dimensionless edge radius and Re. Pressure recoveries of up to 20% are reported at large Re for dimensionless radii as small as r/h=0.625. It is also found that the rounded exit results in turbulence levels as much as 25% higher than sharp-edged exits.     

The thermal structure of a wind-driven Reynolds ridge

In this study, we investigate the nature of a Reynolds ridge formed by wind shear. We have simultaneously imaged the water surface, with a deposit of a monolayer of the surfactant, oleyl alcohol, subject to different wind shears, by using a high-resolution infrared (IR) detector and a high-speed (HS) digital camera. The results reveal that the regions around the wind-driven Reynolds ridge, which have subtle manifestations in visual imagery, possess surprisingly complex hydrodynamical and thermal structures when observed in the infrared. The IR measurements reveal a warm, clean region upstream of the ridge, which is composed of the so called fishscale structures observed in earlier investigations. The region downstream of the ridge is composed of colder fluid which forms two counter-rotating cells. A region of intermediate temperature, which we call the mixing (wake) region, forms immediately downstream of the ridge near the channel centerline. By measuring the velocity of the advected fishscales, we have determined a surface drift speed of about 2% of the wind speed. The spanwise length-scale of the structures has also been used to estimate the wind shear. In addition, a comparison of IR and visual imagery shows that the thermal field is a very sensitive indicator of the exact position of the ridge itself.     

On the Path of a Quasi-static Crack in Mode III

A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path. Mathematics Subject Classifications (2000) 74R05, 74B05, 74G70.Gerardo E. Oleaga: Supported by EU-Project Front Singularities University of Leipzig and the Max Planck Institute MIS. Partial support was also provided by the Spanish DGES project BFM2000-0605.