Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

Obituary Gilbert Grynberg (1948-2003)

We mourn the death of Professor Dr. Gilbert Grynberg, April 17, 1948 - January 27, 2003. We have lost an excellent and highly esteemed scientist, an outstanding character and a good friend. He has been a very active colleague in the merger of Zeitschrift für Physik and Journal de Physique in the early days. As one of the Co-Editors-in-Chief of The European Physical Journal D, from its start, he has formed the scienti.c standards of EPJ. Untiringly he has served our Journal with greatest dedication. We are grateful that he has been with us. The editorial board and o.ce of EPJ B Siegfried Grossmann, Denis Jérome, Antonio Paoletti     

Fully adaptive multiresolution finite volume schemes for conservation laws

The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation. In this approach the solution is still represented at each time step on the finest grid, resulting in an inherent limitation of the potential gain in memory space and computational time. The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid. A crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages. Several solutions to this problem are proposed, analyzed, and compared in terms of accuracy and complexity.

     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

Syntheses of Macrocyclic Amides from L-Amino Acid Esters by RCM

IntroductionThe discovery of stable and defined carbenecomplexes of molybdenum and ruthenium as efficientprecatalysts for olefin metathesis has made this transfor-mation one of the most important C—C bond formingreactions[1—11]. Specifically, ring-closi…     

Ring‐Rearrangement Metathesis

Ring‐rearrangement metathesis (RRM) refers to the combination of several metathesis transformations into a domino process, in which an endocyclic double bond of a cycloolefin reacts with an exocyclic alkene. RRM has proven to be a powerful method for the rapid construction of complex structures. The extension of the basic ring‐opening–ring‐closing metathesis process by further metathesis steps as well as an examination of the driving forces, limits, scope, recent advantages, and future perspectives of these domino sequences is presented with various examples, thus reflecting the high efficiency and utility of RRM in organic synthesis.     

Selective metal promoted hydrolysis of nitrile groups in the side chain of tetraazamacrocyclic Cu2+-complexes

The metal promoted hydrolysis of nitrile groups in the side chains of tetraazamacrocyclic Cu2+ complexes has been studied by stopped-flow techniques. It is shown that the reaction proceeds by an intramolecular attack of an axially coordinated OH- onto the nitrile group to give the corresponding amide. In alkaline solution the amide then deprotonates and binds to the axial position of the Cu2+ thus preventing further coordination of an OH-. This explains mechanistically that in the Cu2+ complexes of macrocycles carrying two nitrile functions only one is selectively hydrolysed. The nitrile hydrolysis has also been used on a preparative scale to synthesize tetraazamacrocycles with two different side chains. X-Ray diffractions of several products are presented to confirm the structures and the results from the kinetics and equilibria measurements.