Small angle neutron scattering from oxygen precipitates in silicon

The formation of silicon oxide precipitates from Czochralski grown silicon depends on the time and temperature of the heat treatment as well as on the initial content of interstitially dissolved oxygen. Samples containing between 5×10¹⁷ O_i/cm³ and 13×10¹⁷ O_i/cm³ have been heated at 750° C for 96 h. SiO₂ precipitates of various shape and size have been obtained and investigated by means of small angle neutron scattering (SANS) in the Q-range 0.05 Å^–1<Q<0.2 Å^–1. The obtained SANS patterns reveal a typical anisotropy of their intensity distribution, which splits into a central peak at Q<0.1 Å^–1 due to the shape of the individual particles and a number of weak intensities for large Q-values, originating from a correlation between defects, possibly between the precipitates. While these correlation peaks in the SANS patterns are seen best for rather low values of about (5–7)×10¹⁷ O_i/cm³ oxygen content, the central peak anisotropy is most pronounced for higher values of ca 10×10¹⁷ O_i/cm³. The integrated intensity of the central peak increases with increasing initial oxygen content. For comparison, untreated samples of the same initial oxygen content do not reveal any anisotropic SAN scattering or a broadened central peak beam.     

Projective-type axioms for the hyperbolic plane

It is shown that the Laws of Pappus and Desargues may replace the Axiom of Projectivities in Menger's development of hyperbolic geometry from axioms of alignment.     

Systematics of flux jumps and the stabilizing effect of flux creep in a La1.86Sr0.14CuO4 single crystal

Flux jumps have been observed in a large (138 mg) single crystal of La_1.86Sr_0.14CuO₄. Both complete and incomplete flux jumps are observed with the energy dissipated by complete flux jumps consistent with temperature rises to nearly T_c. The systematics of these flux jumps with respect to field history, temperature and the time duration of the hysteresis measurements are reported. The field at which flux jumps first occur and their subsequent spacing are not consistent with a simple adiabatic theory of flux jumps for our experimental conditions. Instead, the crystal is observed to be stabilized against flux jumps by flux creep which occurs during the time interval over which field steps are accomplished as well as during imposed time intervals between field steps.     

A Primitive Non-symmetric 3-Class Association Scheme on 36 Elements with p11 = 0 Exists and is Unique

In this paper we construct a primitive, non-symmetric 3-class association scheme with parameters v = 36, v₁ = 7, p¹₁₁ = 0 and p²₁₁ = 4 and show that such a scheme is determined by its parameters.     

The universal nilpotent group compactification of a semigroup

The purpose of this paper is to introduce an algebra of functions on a semitopological semigroup and to study these functions from the point of view of universal semigroup compactification. We show that the corresponding semigroup compactification of this algebra is universal with respect to the property of being a nilpotent group.

     

On finite element approximation and stabilization methods for compressible viscous flows

This work is devoted to the numerical solution of the Navier–Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. We present methods to implement discontinuous approximations for the pressure and the density. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov–Galerkin method and the flux limiter methods aiming to introduce numerical diffusion only where it is necessary.     

Classical solutions to a quadratically nonlinear gauge theory

We present some classical solutions to a gauge theory based on quadratically nonlinear Lie algebras without a central term. We observe that instanton-like and meron-like solutions force the internal fields to behave like solitons.