Adaptive boundary element methods for strongly elliptic integral equations

Summary Integral operators are nonlocal operators. The operators defined in boundary integral equations to elliptic boundary value problems, however, are pseudo-differential operators on the boundary and, therefore, provide additional pseudolocal properties. These allow the successful application of adaptive procedures to some boundary element methods. In this paper we analyze these methods for general strongly elliptic integral equations and obtain a-posteriori error estimates for boundary element solutions. We also apply these methods to nodal collocation with odd degree splines. Some numerical examples show that these adaptive procedures are reliable and effective.This work was carried out while Dr. De-hao Yu was an Alexander-von-Humboldt-Stiftung research fellow at the University of Stuttgart in 1987, 1988     

Wide-angle one-way wave equations

A one-way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy-absorbing numerical boundary conditions. The design of a one-way wave equation is connected with the approximation of (1-s2)1/2 on [-1,1] by a rational function, which has usually been carried out by Padé approximation. This article presents coefficients for L2, L infinity, and other alternative classes of approximants that have better wide-angle behavior. For theoretical results establishing the well posedness of these wide-angle equations, see the work of Trefethen and Halpern ["Well-posedness of one-way wave equations and absorbing boundary conditions," Math. Comput. 47, 421-435 (1986)].     

Evaluating the effect of whiskerization of the fibers of composites on the fundamental frequency of a laminated cylindrical shell

Conclusion The calculations showed that whiskerization of the reinforcement of the structural material of multilaminate shells makes it possible in some cases to increase the fundamental vibration frequency of the structure up to 15–20%. In combination with the well-known [1] effect of improved strength characteristics for a whiskerized composite in the transverse and shear directions, this finding allows us to conclude that whiskerized structural materials are more efficient than ordinary laminated composites in shell-type load-bearing structures. Here, the greatest benefit can be expected in the case of whiskers which have higher elastic moduli than the main reinforcement. Since considerably higher reinforcement intensities can be achieved in whiskerized laminated composites than in composites with a reinforcement characterized by an arbitrary three-dimensional structure, it can be concluded on the basis of the results obtained here that, at least for shells of moderate thickness (10 < R/h 50), whiskerized composites are the optimum structural material for load-bearing shells.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1022–1027, November–December, 1987.     

Effect of pressure on the behavior of nontransition metallic superconductors

An explicit expression has been derived for the volume dependence of electron-phonon coupling strength () by using a recently proposed quadratic form of the screened pseudopotential and by considering the variation of Fermi momentum with volume. Variation of Coulomb pseudopotential ( ^*) has also been explicitly considered by varying the Fermi momentum. Dependence of transition temperatureT _c and the logarithm of the effective interaction strength (N ₀ V) on the volume has been studied for eight nontransition metallic superconductors. A linear drop inT _c for small values of (–/ ₀) as well as the calculated values of= InN ₀ V/ In, exhibits better matching with the experimental data, as compared to the earlier theoretical results.     

Softening during and after the hot deformation of the AISI 321 steel with respect to practical applications

The softening processes during and after the hot deformation (850–1180 C) in AISI 321 stainless steel were studied with respect to true strains _D and true strain rates . The analysis of deformation curves indicates the occurrence of dynamic recrystallization for values of Zener-Hollomon parameterZ10¹⁵ s^–1. The retardation of static recrystallization by fine Ti(N, C) precipitates is documented by microstructure studies and by variations of annealing conditions.     

Precipitation structure in an Al-2·0 at. % Zn-1·0 at. % Mg alloy within and close to the grain boundaries and its effects on mechanical properties

During ageing the Al-2·0 at. %Zn-1·0 at. % Mg alloy at elevated temperatures the width of the precipitation free zone (PFZ) at both sides of the grain boundaries (GB) is identical with that free of quenched-in dislocation loops (DL). After sufficiently long ageing a band of precipitates is growing inside the former PFZ and the DLs in the midgrain regions act as sites for the heterogeneous nucleation of the-phase. Two precipitation processes significantly affect the mechanical properties. TEM correlates grain boundary precipitate density and morphology with grain boundary misorientation.     

WKB properties of the time-dependent Schrödinger system

It is shown that the time-dependent WKB expansion highlights some of the hidden properties of the Schrödinger equation and forms a natural bridge between that equation and the functional integral formulation of quantum mechanics. In particular it is shown that the leading (zero- and first-order in ) terms in the WKB expansion are essentially classical, and the relationship of this result to the classical nature of the WKB partition function, and of the anomalies in quantum field theory, is discussed.     

One-dimensional harmonic lattice caricature of hydrodynamics: Second approximation

The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived.     

Effects of small external magnetic fields on the hyperfine field of iron in iron metal above the curie temperature: A new method for studying critical phenomena

By applying magnetic fields up to 2 kG, the equation of state and the critical dynamics of a spin system near its critical point can be studied with the Mössbauer effect. As an example, the equation of state near the Curie temperature of iron is investigated yielding the critical exponent =4.84±0.15.