Periodicity of Two-Dimensional Bonding of Main Group Elements

In the periodic table the position of each atom follows the ‘aufbau’ principle of the individual electron shells. The resulting intrinsic periodicity of atomic properties determines the overall behavior of atoms in two-dimensional (2D) bonding and structure formation. Insight into the type and strength of bonding is the key in the discovery of innovative 2D materials. The primary features of 2D bonding and the ensuing monolayer structures of the main-group II–VI elements result from the number of valence electrons and the change of atom size, which determine the type of hybridization. The results reveal the tight connection between strength of bonding and bond length in 2D networks. The predictive power of the periodic table reveals general rules of bonding, the bonding-structure relationship, and allows an assessment of published data of 2D materials.     

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.     

Ueber die Biegung und Drillung eines unendlich dünnen elastischen Stabes,dessen eines Ende von einem Kräftepaar angegriffen wird

Ohne ZusammenfassungMit einer lithographirten Tafel.Ein Auszug aus dieser Untersuchung ist erschienen in den Sitzungsberichten der bayer. Acad. d. Wissensch. 1883, 82–110.     

Iterative regularization methods for atmospheric remote sensing

In this paper we present different inversion algorithms for nonlinear ill-posed problems arising in atmosphere remote sensing. The proposed methods are Landweber's method (LwM), the iteratively regularized Gauss-Newton method, and the conventional and regularizing Levenberg-Marquardt method. In addition, some accelerated LwMs and a technique for smoothing the Levenberg-Marquardt solution are proposed. The numerical performance of the methods is studied by means of simulations. Results are presented for an inverse problem in atmospheric remote sensing, i.e., temperature sounding with an airborne uplooking high-resolution far-infrared spectrometer.     

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.