Multivalued differential equations on closed convex sets in Banach spaces

New derivation results for integrands and multifunctions via the Lipschitzean approximations are obtained. Applications to multivalued differential equations on closed convex sets are presented.     

Aspects of the transpiration model for aerofoil design

Transpiration is a technique in which extra non-physical normal flows are created on an aerofoil surface in order to form a new streamline pattern such that the surface streamlines no longer follow the aerofoil surface under inviscid flow. The transpiration model is an important technique adopted in aerofoil design either to avoid mesh regeneration when aerofoil profile co-ordinates are adjusted or to find shape corrections in inverse design methods. A first-order approximation (with respect to the normal streamline displacement) to the transpiration model is commonly adopted; it is shown that this can be a poor approximation especially in regions of high curvature. In this paper more accurate approximations are developed to address this problem and improve the accuracy.     

Distribution of melamine in polyester–melamine surface coatings cured under nonisothermal conditions

The influence of experimental cure parameters on the diffusion of reactive species in polyester–melamine thermoset coatings during curing has been investigated with X‐ray photoelectron spectroscopy and attenuated total reflectance Fourier transform infrared. The diffusion of melamine plays a vital role in the curing process and, therefore, in the ultimate properties of coatings. At a low (<20%) hexamethoxymethylmelamine (HMMM) crosslinker concentration, the matrix composition is uniform, but at high HMMM concentrations, excess HMMM rapidly segregates to the air–coating interface. The rate of migration is governed by the difference in the surface free energies of polyester and HMMM and the concentration gradient of HMMM between the bulk and the surface. An increased rate of energy absorption also increases the rate of migration of HMMM to the surface. A physical model has been proposed to explain this surface segregation phenomenon in terms of cocondensation and self‐condensation reactions. It suggests that an appropriate amount of melamine can be segregated on the surface and allowed to self‐condense to form a desired thickness of a melamine topcoat through the control of the binder composition and cure conditions. This technique can be implemented to apply a melamine topcoat during cure. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 83–91, 2004     

UV curing of a novel resin derived from poly(ethylene terephthalate)

The synthesis and characterization of photopolymerizable unsaturated polyester resins based on PET waste are described. The resins came from a depolymerization process based on the glycolysis of PET by diethylene glycol (DEG). Different molecular weights of glycolysates were synthesized. Then, the latter was functionalized by a methyl hemiester of maleic acid to obtain unsatured α,ω‐bismaleate PET oligomers. In the presence of an electron donor monomer, such as triethylene glycol divinyl ether, these electron acceptor oligomers were copolymerized by way of charge‐transfer complexes under UV irradiation. The reaction was monitored in situ by real‐time IR spectroscopy to study the kinetics of photopolymerization. This one was studied in relation with the physical and chemical characteristics of oligoesters and the composition of mixtures containing divinyl ethers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1324–1335, 2007     

Elevation of the glass transition temperature in flexible‐chain semicrystalline polymers

In the idealized two‐phase model of a semicrystalline polymer, the amorphous intercrystalline layers are considered to have the same properties as the fully‐amorphous polymer. In reality, these thin intercrystalline layers can be substantially influenced by the presence of the crystals, as individual polymer molecules traverse both crystalline and amorphous phases. In polymers with rigid backbone units, such as poly(etheretherketone), PEEK, previous work has shown this coupling to be particularly severe; the glass transition temperature (T_g) can be elevated by tens of degrees celsius, with the magnitude of the elevation correlating directly with the thinness of the amorphous layer. However, this connection has not been explored for flexible‐chain polymers, such as those formed from vinyl‐type monomers. Here, we examine T_g in both isotactic polystyrene (iPS) and syndiotactic polystyrene (sPS), crystallized under conditions that produce a range of amorphous layer thicknesses. T_g is indeed shown to be elevated relative to fully‐amorphous iPS and sPS, by an amount that correlates with the thinness of the amorphous layer; the magnitude of the effect is severalfold less than that in PEEK, consistent with the minimum lengths of polymer chain required to make a fold in the different cases. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1198–1204, 2007     

The force on a lattice defect in an elastic body

It is shown that the force on a lattice defect in an elastic body is, like the force on a disclination in a nematic liquid crystal, a real force which, for equilibrium, must be balanced by an external force applied to the closed surface enclosing the defect.     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

Serial magnetic resonance imaging in patients following acute myocardial infarction.

The detection of serial changes in magnetic resonance (MR) signal intensity of the heart following acute myocardial infarction may provide a useful method of characterizing tissue healing. Fourteen patients with acute Q-wave infarction underwent T2-weighted, spin-echo cardiac imaging during hospitalization, followed by one or more additional MR studies (total 31) over a 6- to 27-wk period (mean: 3 mo). Visual assessment of the images demonstrated a gradual reduction in signal intensity and localization of the bright signal to the subendocardium of the infarction region over the three-mo study period. A quantitative measurement of signal intensity (infarction/normal myocardium) fell from 1.81 +/- 0.42 on the initial study to 1.34 +/- 0.37 (p less than 0.05) at a mean of 14 wk. Two patients had an increase in signal intensity on the follow-up study and both patients had been readmitted with acute coronary syndromes. In summary, characterization of changes in signal intensity may provide a useful method of assessing myocardial healing following acute myocardial infarction. Further studies are indicated to determine the prognostic significance of these parameters.