A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems

Summary Consider the solution of one-dimensional linear initial-boundary value problems by a finite element method of lines using a piecewiseP ^th -degree polynomial basis. A posteriori estimates of the discretization error are obtained as the solutions of either local parabolic or local elliptic finite element problems using piecewise polynomial corrections of degreep+1 that vanish at element ends. Error estimates computed in this manner are shown to converge in energy under mesh refinement to the exact finite element discretization error. Computational results indicate that the error estimates are robust over a wide range of mesh spacings and polynomial degrees and are, furthermore, applicable in situations that are not supported by the analysis.This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 90-0194; by the U.S. Army Research Office under Contract Number DAAL03-91-G-0215; and by the National Science Foundation under Institutional Infrastructure Grant Number CDA-8805910     

Linearization of column responses by correlation chromatography. Separation improvement and reduction of undesired adsorption effects

Summary Experiments and simulations prove that correlation chromatography can greatly reduce the disadvantage of a non-linear response of the chromatographic column. A factor that has been accepted as being an important source of error in correlation or multiplex chromatography, has been shown not to be. Separations affected, improve dramatically when correlation chromatography is used, and a substantial amount of correlation noise only arises when there is a large difference in separation between a conventional chromatogram and a correlogram.A model has been developed for simulating these nonlinearities. It is shown that, especially for correlation chromatography, the simulation results match the practical measurements very well.     

Recent developments in the chemistry of stable doubly bonded germanium compounds

During the last 10 years, several compounds of the type Ge=X (X = C, Ge, N, P, S) have been isolated as monomers. The stabilization of such derivatives, which are generally highly polymerizable, was achieved by using very bulky groups both on the germanium atom and on the heteroelement X. Conjugation (particularly in a few germenes and germaimines) and intramolecular or intermolecular coordination with oxygen or nitrogen, also contributes, in some cases, to the stabilization. The X-ray analyses of such compounds show a significant bond shortening of the double bond (8–10%) relative to the corresponding single bond and a planar or nearly planar germanium. These doubly bonded germanium derivatives are usually thermally stable but must be handled in an inert atmosphere because of their high sensitivity to oxygen and moisture; they are extremely reactive, much more than the corresponding carbon analogues. Nearly quantitative additions on the double bond have been observed with electrophiles and nucleophiles, and various types of cycloadditions also occur. Except in one case, a germylene behavior has not been observed, proving that such compounds retain their structural integrity in solution.     

Energy levels of small titanium oxide clusters obtained from SCF calculations

The energy levels of small titanium oxide clusters [(TiO₂)₂, and (TiO₂H)₃, and (TiO₂H)₂] have been calculated using ab initio SCF methods. Both crystal and relaxed geometries have been considered. Systematic changes in the valencelevel structure resulting from geometry relaxation are found, which may be related to band-gap changes experimentally observed for small titanium oxide particles. In addition, a Ti? OH local surface state is found to be well described within a limited cluster model. © 1994 John Wiley & Sons, Inc.     

Why define atoms in real space?

The physics of a system is determined by a variation of the action integral, i.e., by a variation of the space–time volume integral of the Lagrange function. If one demands that the properties of an atom in a molecule be derived from physics, the atom must generate its own space–time volume, requiring that its boundaries be defined in real space. The variations in the action are related to the actions of generators of infinitesimal unitary transformations. In the general case, the action integral is altered by generators acting in both the spacelike and timelike surface bounding the space–time volume, whereas for a total isolated system, the physics is totally determined by their action in just the spacelike surfaces at the two time endpoints. It is shown and illustrated for a one-dimensional system that the definition of an atom corresponds to the possibility of choosing a subsystem in such a way that the contributions to the change in action resulting from the evolution in time of its spatial boundaries vanishes identically. The properties of these subsystems and of the total system of which they are a part are, therefore, determined by one and the same action principle. This choice of subsystem corresponds to the possibility of augmenting the Lagrange function by the divergence of the gradient of the electron density a step that, while leaving the equations of motion unchanged, modifies the generating operators in the required manner. © 1994 John Wiley & Sons, Inc.     

Three-dimensional atom probe study of the segregation behaviour of Ni91Pt9 alloy after sputtering

To investigate local ordering and segregation phenomenon in a Ni91Pt9-alloy after sputtering and annealing a 3D optical atom probe (OAP) has been used. The specimen tips have been prepared from polycrystalline samples. To sputter the samples a separate preparation chamber with a scannable Ar-sputter-gun is connected to the OAP vessel. When necessary, the sample can be electrically heated to induce segregation and cure the altered layer. After a heat treatment of a Ni91 at. %Pt 9 at.% specimen at 1100 K the surface of a (111)-oriented specimen is enriched in platinum by a factor of two in relation to the bulk. The phenomenon of short-range ordering has been investigated on the surface and in the subsurface volume. A 3D reconstruction of this annealed NiPt specimen shows regions with high concentration of platinum that gives an indication at short-range ordering. Uniform sputtering of the tip without a heat treatment induces a decisive depletion of Pt on the surface and the following subatomic layers. The atom-probe results of specimens in thermal equilibrium are in close agreement to further surface sensitive results obtained from Ion Scattering Spectroscopy (ISS) and Auger Electron Spectroscopy (AES).     

Spin effects in instanton models

Nonperturbative nolocal structure of QCD vacuum is well described by instanton model. Specific helicity and flavor structure of zero modes of quarks, in instanton field allows simultaneously to explain some important features of low-and high-energy hadron phenomemology. The basic characteristics of hadron spectrum, partonic sum rules, heavyquark potential etc within the instanton liquid model are briefly discussed.     

Study of the charge-exchange reactions\pi ^ - p \to (\pi ^0 ,\eta ,\eta \prime )n at 63 GeV

Muon electron pairs were detected in an Al multiplate spark chamber, exposed to a neutrino beam from the CERN PS. The leptons were not accompanied by other particles, except occasionally by protons. The background came mainly from muon associated π⁰ production, with one decay gamma lost. It was determined empirically, together with the small contribution from υ _e reactions. For electron energies above 2 GeV the background is 5.7±1.5 events, whereas 18 (μe)-candidates have been observed. Hence the effect is established, with a rate of about 10^?4 as compared to the muonic reactions above 3 GeV. Charm creation as the origin of this (μe)-production process is excluded; heavy neutral lepton production does not fit the kinematics observed. Instead the events are compatible with the two-body decay of an object with variable invariant mass of order 1 GeV, possibly resulting from axion interactions.