Taylor-Galerkin algorithms for viscoelastic flow: Application to a model problem

Coupled and decoupled Taylor-Galerkin algorithms are considered for viscoelastic flow and a model problem—transient startup Poiseuille flow in a channel under a fixed pressure gradient. All algorithms reproduce the steady-state solutions and are stable at high elasticity numbers (E). For a fixed mesh, the coupled and decoupled versions (TGC and TGD) give exceptional time-accuracy at low elasticity numbers [to within O(1%) at E = 1] and reasonable accuracy at high elasticity numbers [to within O(10%) at E = 10, 100]. By definition, the decoupled false-transient scheme (TGF), which uses different time scales for velocity and stress time stepping, provides a poor transient history. Where the main requirement is to compute a steady-state algorithm efficiency is crucial. The TGF scheme attains a steady state between six to eight times faster than does the TGC scheme, and the latter is over twice as fast as the TGD form. © 1994 John Wiley & Sons, Inc.     

Inhomogeneities in silicon p-n-junctions

Latent macroscopic defects in silicon are detected by electrical and electron microscope measurements. They lead to anomalous temperature dependence of the Fermi level position and growth in the hole capture coefficient. A level with energy of 0.55 eV measured from the conduction zone controls the recombination process. It is proposed that macroscopic defects develop upon association of oxygen-silicon vacancy complexes. Action of an electron beam leads to reversible changes which increase upon multiple scanning, affecting the value of the diffusion length.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 71–75, April, 1991.     

Approximation of solutions of operator-differential equations by operator polynomials

We prove theorems that characterize the classes of functions whose best approximations by algebraic polynomials tend to zero with given order. We construct approximations of solutions of operator-differential equations by polynomials in the inverse operator. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1506–1516, November, 1998.     

Asymptotic behavior of neutron small-angle multiple scattering spectra

The asymptotic behavior of the spectra for large values of the scattering vector for the case of elastic multiple small-angle neutron scattering (SANS) is investigated theoretically and experimentally. An expansion of the spectrum in terms of the reciprocal of the magnitude of the momentum transfer is obtained taking account of the influence of the instrumental line. It is shown that, to within some factor, the leading term of the expansion is identical to the differential single-scattering cross section averaged over a statistical ensemble of particles; several subsequent terms in the expansion are calculated and the range of applicability of the resulting expressions is determined. The asymptotic behavior of the multiple SANS spectrum is measured, using a two-crystal neutron spectrometer, for samples of an HTSC ceramic, the alloy Fe-Ni, and Al powder. The agreement between the experimental results and the theoretical predictions is analyzed. Zh. éksp. Teor. Fiz. 114, 2194–2203 (December 1998)