Reducing Huge Gyroscopic Eigenproblems by Automated Multi-level Substructuring

Simulating numerically the sound radiation of a rolling tire requires the solution of a very large and sparse gyroscopic eigenvalue problem. Taking advantage of the automated multi-level substructuring (AMLS) method it can be projected to a much smaller gyroscopic problem, the solution of which however is still quite costly since the eigenmodes are non-real and complex arithmetic is necessary. This paper discusses the application of AMLS to huge gyroscopic problems and the numerical solution of the AMLS reduction. A numerical example demonstrates the efficiency of AMLS.     

Stability testing in an integrated scheme

ISO Guide 35 deals with RM stability issues and scrutinizes the evaluation of stability testing results under the assumption that either there is no trend at all (a rather rare situation), or any observed deterministic change is insignificant and thus can be neglected. However, market demands for reliable reference materials are obviously not limited to stable or at least seemingly stable materials. In many analytical applications, analytes and measurands under consideration are known, or at least suspected, to be unstable on time scales that may vary widely from measurand to measurand. The Federal Institute for Materials Research and Testing (BAM) has developed (and successfully uses) an integrated approach in its certification practice. The approach is based on an initial stability study and subsequent post-certification monitoring. Data evaluation is model-based and takes advantage of all information collected in the stability testing scheme(s). It thus allows one to deal with any kind of instability observed, to assess limiting time intervals at any stress condition in the range tested, to estimate a final expiry date for materials with detected instabilities or the maximum admissible re-testing interval for seemingly stable materials, and to assess maximum admissible stress loads during delivery of the material to the customer. The article describes (and exemplifies) typical study layout, the model selection, and the integrated data assessment.     

Probability Collectives for Unstable Particles

Unstable particles, together with their stable decay products, constitute probability collectives that are defined as Hilbert spaces with dimension higher than one, nondecomposable in a particle basis. Their structure is considered in the framework of Birkhoff-von Neumann's Hilbert subspace lattices. Bases with particle states are related to bases with a diagonal scalar product by a Hilbert-bein involving the characteristic decay parameters (in some analogy to the n-bein structures of metrical manifolds). Probability predictions as expectation values, involving unstable particles, have to take into account all members of the higher dimensional collective. For example, the unitarity structure of the S-matrix for an unstable particle collective can be established by a transformation with its Hilbert-bein.     

Der Berührungstensor zweier Flächen und die Affingeometrie derF p imA n

Ohne Zusammenfassung     

Eine Schwefelbestimmungsmethode von allgemeiner Anwendbarkeit

Ohne Zusammenfassung     

Bücherbesprechungen

Ohne Zusammenfassung     

Differential scanning calorimetry and thermogravimetric analysis investigation of the thermal properties and degradation of some radiation‐grafted films and membranes

The influence of irradiation and grafting on the crystallinity of three base polymers has been investigated with differential scanning calorimetry. Grafting has the largest effect on the base polymer crystallinity and results in a reduction of the crystallinity. The thermal degradation of the base polymers and grafted films has been investigated with thermogravimetric analysis. The extent of the fluorination of the base polymer, the irradiation method, and the graft level all influence the thermal degradation and its activation energy. It is proposed that the variation of the chain lengths of the grafted polystyrene chains is actually a primary underlying factor responsible for the influence of these various parameters on the degradation process. The first results of a comparative thermal analysis of some fuel‐cell membranes are also presented, and the promise and shortcomings of this method are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2612–2624, 2004     

Regularity of multiwavelets

The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L _p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.     

Correlated polarization propagator calculations of static polarizabilities

We present a systematic comparison of the correlation contribution at the level of the second-order polarization propagator approximation (SOPPA ) and MP 2 to the static dipole polarizability of (1) Be, BeH^?, BH, CH⁺, MgH^?, AIH, SiH⁺, and GeH⁺; (2) BH₃, CH₄, NH₃, H₂O, HF, BF, and F₂; and (3) N₂, CO, CN^?, HCN, C₂H₂, and HCHO . Fairly extended basis sets were used in the calculations. We find that the agreement with experimental values is improved in SOPPA and MP .2 over the results at the SCF level. The signs and magnitudes of the correlation contribution in SOPPA are similar to those obtained in analytical derivative MP 2 calculations. However, it is not possible to say, in general, which method gives the largest correlation contribution or the best agreement with experiment, nor is it possible to make a priori prediction of the sign of the correlation contribution. For the first group of molecules, which have a quasi-degenerate ground state, additional CCDPPA and CCSDPPA calculations were performed and compared with polarizabilities obtained as analytical/numerical derivatives of the CCD and CCSD energies. The CCSDPPA results were found to be in better agreement with other calculations than were the SOPPA results, demonstrating the necessity of using methods based on infinite-order perturbation theory for these systems. © 1994 John Wiley & Sons, Inc.