Nearest q-Flat to m Points

Recently, Bradley and Mangasarian studied the problem of finding the nearest plane to m given points in ⁿ in the least square sense. They showed that the problem reduces to finding the least eigenvalue and associated eigenvector of a certain n×n symmetric positive-semidefinite matrix. We extend this result to the general problem of finding the nearest q-flat to m points, with 0qn–1.     

Molecular mobility in polymer thin films

Fluorescence recovery after photobleaching was used to measure in-plane dye-probe diffusion coefficients, D, in thin films of monodisperse polystyrene supported on fused quartz substrates. The substrates were prepared with a high density of surface hydroxyl groups which interact favorably with repeat units of the polymer. The effects of temperature and film thickness were investigated, at temperatures above the bulk glass transition of the polymer, T(g), and in the range of film thicknesses from 1-10(2) times the radius of gyration (R(g)) of individual polymer molecules. As the film thickness decreases towards R(g) the value of D increases above the bulk values, with significant effects first appearing in films approximately 20R(g). In the thinnest films studied, about 4R(g), the values of D lie as much as two orders over bulk values. At the same time, the temperature dependence of D becomes much weaker than in bulk. Analysis by free volume theory indicates that apparent values of both T(g) and the thermal expansion coefficient for liquid state, alpha(L), decrease as the film thickness decreases. The possible effects of surface segregation of the dye probe are discussed.     

Search for color singlet technicolor particles in p&pmacr; collisions at radicals = 1.8 TeV

We search for color singlet technirho and technipion production in p&pmacr; collisions at sqrt[s] = 1.8 TeV recorded with the Collider Detector at Fermilab. These exotic technimesons are present in a model of walking technicolor. The signatures studied are lepton plus two jets plus E(T) and multijet final states. No excess of events is seen in either final state. We set an upper limit on the technirho production cross section and exclude a region in the technipion mass versus technirho mass plane.     

Diffractive dijets with a leading antiproton in &pmacr;p collisions at sqrt

We report results from a study of events with a leading antiproton of beam momentum fraction 0.9057 GeV. Using the dijet events, we evaluate the diffractive structure function of the antiproton and compare it with expectations based on results obtained in diffractive deep inelastic scattering experiments at the DESY ep collider HERA.     

Two-phase flow pressure change subject to sudden contraction in small rectangular channels

This study investigates the pressure change and flow pattern subject to the influence of sudden contractions. The air and water mixture flows from small rectangular channels (2 × 4, 2 × 6, 4 × 4 and 4 × 6 mm, respectively) into a 2 mm diameter tube. The total mass flux (G) ranges from 100 to 700 kg/m² s with gas quality (x) being varied from 0.001 to 0.8. In general the contraction pressure change increases with the rise of mass flux, and gas quality but an unique deflection of contraction pressure change pertaining to liquid vena contracta at a very low gas quality is encountered at a very low gas quality in the 4 ± 6 mm test section. For a low gas quality, elongated bubble prevails after the contraction, yet the size of elongated bubbles is reduced when the aspect ratio is increased. Comparisons amid the pressure change data of this study and available literature data with the predictions of existing model/correlations indicate that none of them can accurately predict the data. It is found that the influence of surface tension and outlet tube size, or equivalently the Bond number plays a major role for the departure of various models/correlations. Among the models/correlations being examined, the homogeneous model shows a little better than the others. Hence by taking account the influences of gas quality, Bond number, Weber number and area contraction ratio into the homogeneous model, a modified homogeneous correlation is proposed that considerably improves the predictive ability over existing correlations with a mean deviation of 30% to all the data.     

Evaluation of runaway thermal reactions of di-<Emphasis Type="Italic">tert</Emphasis>-butyl peroxide employing calorimetric approaches

Di-tert-butyl peroxide (DTBP) is an organic peroxide (OP) which has widespread use in the various chemical industries. In the past, thermal runaway reactions of OPs have been caused by their general thermal instability or by reactive incompatibility in storage or operation, which can create potential for thermal decomposition reaction. In this study, differential scanning calorimetry was applied to measure the heat of decomposition reactions, which can contribute to understand the reaction characteristics of DTBP. Vent sizing package 2 was also employed to evaluate rates of increase for temperature and pressure in decomposition reactions, and then the thermokinetic parameters of DTBP were estimated. Finally, hazard characteristics of the gassy system containing DTBP, specifically with respect to thermal criticality, were clearly identified.     

Crystallization kinetics and crystallization behavior of syndiotactic polystyrene/clay nanocomposites

We investigated the effects of montmorillonite (clay) on the crystallization kinetics of syndiotactic polystyrene (sPS) with isothermal differential scanning calorimetry analyses. The clay was dispersed into the sPS matrix via melt blending on a scale of 1–2 nm or up to about 100 nm, depending on the surfactant treatment. For a crystallization temperature of 240 °C, the isothermal crystallization data were fitted well with the Avrami crystallization equation. Crystallization data on the kinetic parameters (i.e., the crystallization rate constant, Avrami exponent, clay content, and clay/surfactant cation‐exchange ratio) were also investigated. Experimental results indicated that the crystallization rate constant of the sPS nanocomposite increased with increasing clay content. The clay played a vital role in facilitating the formation on the thermodynamically more favorable all‐β‐form crystal when the sPS was melt‐crystallized. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2097–2107, 2001     

Polymerization and nanocomposites properties of multifunctional methylmethacrylate POSS

Thermally induced polymerization of multifunctional methylmethacrylate POSS (MMA‐POSS) was studied in this work for preparation of polymer/POSS nanocomposites. The polymerization of MMA‐POSS could be promoted with benzoyl peroxide (BPO). Self‐assembly of POSS into a layer‐by‐layer structure in the MMA‐POSS polymer (TP‐MMA‐POSS) is observed with a transmission electron microscopy. An ultra‐low‐k value of about 1.85 is measured with TP‐MMA‐POSS. In addition, polyimide‐POSS nanocomposites are also prepared. These nanocomposites demonstrate good homogeneity and enhanced mechanical properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5157–5166, 2008