Galerkin eigenvector approximations

How close are Galerkin eigenvectors to the best approximation available out of the trial subspace? Under a variety of conditions the Galerkin method gives an approximate eigenvector that approaches asymptotically the projection of the exact eigenvector onto the trial subspace--and this occurs more rapidly than the underlying rate of convergence of the approximate eigenvectors. Both orthogonal-Galerkin and Petrov-Galerkin methods are considered here with a special emphasis on nonselfadjoint problems, thus extending earlier studies by Chatelin, Babuska and Osborn, and Knyazev. Consequences for the numerical treatment of elliptic PDEs discretized either with finite element methods or with spectral methods are discussed. New lower bounds to the of a pair of operators are developed as well.

     

A universal interface for coupling mass spectrometry to thermogravimetry

Techniques for coupling mass spectrometry (MS) to thermogravimetry (TG) have been previously described. A total condensation method is best suited for identification of off-gases at various weight loss steps. For continuous monitoring of evolved components during the weight loss process, a glass-tee interface has been found effective in most applications. The present paper describes a glass tubing-tee interface used in conjunction with a sampler to provide great versatility. Both enrichment and recovery are improved without mass discrimination. The thermogravimetric analyzer can be operated under vacuum or with a gas flow. Examples will be given to illustrate the use of this technique for either qualitative or quantitative analysis of a variety of materials.     

Two-phase hydrodynamic experiments with axial flow through seven-rod clusters

Hydrodynamic experiments have been carried out with upflow of air-water mixtures through vertical seven-rod clusters at atmospheric pressure. Results obtained from measurements of flow characteristics, including pressure drops, local velocity and voidage distribution, are discussed in terms of relations developed for two-phase flow in round tubes. Effects on the flow characteristics of spacer elements and bowing of a cluster are also discussed.     

The radiolysis of mixtures of carbon dioxide and hydrogen

The self-radiolysis of CO₂ in excess tritium (³H₂) has been studied at pressures of 0.1 to 1.0 atm, temperatures of ?80° to +100°C, and in the presence of added H₂O, He, or Ar. The primary products of decomposition are CO and ³H₂O. Secondary products are C³H₄, C₂³H₄, and a white polymer. The rates of disappearance of CO₂ and formation of products and G-;values were measured. The disappearance of CO₂ initially obeys first-order kinetics, then slows down with time at a rate depending upon the initial pressure of ³H₂. The initial rates are proportional to pressures of CO₂ and ³H₂. They are independent of temperature, decreased by addition of H₂O vapor, and increased by addition of He or Ar. The proposed mechanism of decomposition of CO₂ and formation of products involves ionization of CO₂ followed by dissociative recombination forming CO and O. Then the O reacts with a hydrogen-containing species forming OH and H₂O, and a back reaction forms CO₂ from CO and OH.     

Marketing a New Product

Some practical experiences in collaborating with a marketing department in deciding whether or not to test-market before launching a new product. The benefits derived from the use of elementary decision-tree theory are described.     

A thermal evolution — differential trapping — mass spectrometric technique for polymer characterization

The ability of thermal evolution techniques for polymer characterization is greatly enhanced when spectroscopic methods are combined, thus allowing identification of the off-gases. This work describes a thermal evolution—differential trapping—mass spectrometric technique for analysis of polymer systems. The technique involves heating the sample under controlled temperature and pressure conditions, condensing the evolved gases in traps maintained at various temperatures, continuously monitoring the pressure changes at strategic locations, and analyzing the selectivity trapped volatiles by mass spectrometry. Both qualitative and quantitative aspects of the technique will be discussed.     

Single-photon detection mechanism in a quantum dot transistor

We study the transport mechanisms in a quantum dot MODFET by tuning the localization induced by charge stored on the quantum dots with light. The temperature dependence of the resistivity of a macroscopic sample reveals a hopping transport when the dots contain an excess of electrons. The resistance of a mesoscopic sample however, which is capable of detecting single photons, exhibits a much weaker dependence upon temperature. This points towards source-drain tunnelling as a transport mechanism and is confirmed by a statistical analysis of the single-photon-induced conductance steps. The complexity of the conducting paths increases as the average hopping length reduces.