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  • 1
    Electronic Resource
    Electronic Resource
    On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions (1994)
    Springer
    Mathematische Annalen 298 (1994), S. 543-556 
    Details
    ISSN: 1432-1807
    Keywords: 35J65 ; 60J65 ; 53C21
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459750
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  • 2
    Electronic Resource
    Electronic Resource
    On the existence of positive solutions for semilinear elliptic equations with Neumann boundary conditions (1995)
    Springer
    Probability theory and related fields 101 (1995), S. 251-276 
    Details
    ISSN: 1432-2064
    Keywords: 35J65 ; 60J65 ; 53C21
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We give sufficient conditions for the existence of positive solutions to some semilinear elliptic equations in unbounded Lipschitz domainsD ⊂ ℝ d (d≥3), having compact boundary, with nonlinear Neumann boundary conditions on the boundary ofD. For this we use an implicit probabilistic representation, Schauder's fixed point theorem, and a recently proved Sobolev inequality forW 1,2(D). Special cases include equations arising from the study of pattern formation in various models in mathematical biology and from problems in geometry concerning the conformal deformation of metrics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01375828
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  • 3
    Electronic Resource
    Electronic Resource
    Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant (1993)
    Springer
    Probability theory and related fields 96 (1993), S. 283-317 
    Details
    ISSN: 1432-2064
    Keywords: 60J60 ; 60J65 ; 60G44 ; 60K25 ; 58G32
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of ℝ d . Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this “pushing” at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01292674
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  • 4
    Electronic Resource
    Electronic Resource
    Cure of epoxy resins containing epoxidized polyols (1992)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 32 (1992), S. 836-840 
    Details
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A commercial epoxy resin, consisting of a mixture of diepoxides based on diglycidyl ether of bisphenol-A (DGEBA) and containing an epoxidized polypropylene glycol as reactive diluent, was characterized by 1HNMR, FTIR, SEC, and chemical analysis. The kinetics of the cure with ethylenediamine (EDA) was catalyzed by the (OH) groups present in a large amount in the commercial formulation. A second order kinetic behavior gave an accurate fitting of results obtained by different experimental techniques (DSC in dynamic and isothermal modes and SEC in the pregel stage). The activation energy was E = 59.1 kJ/mol (14.1 kcal/mol), in very close agreement with values reported for the catalytic mechanism of the DGEBA-EDA polymerization. From the gel conversion and the critical stoichiometric ratio for samples containing an epoxy excess it was found that the average functionality of epoxidized species was f = 1.58.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760321211
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  • 5
    Electronic Resource
    Electronic Resource
    Criteria for selecting cure cycles in autoclave processing of graphite/epoxy composites (1990)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 1140-1145 
    Details
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Room temperature mechanical properties, such as flexural strength and impact resistance, of epoxies and graphite/epoxy composites go through a maximum as a function of epoxy conversion. For tetraglycidyl 4,4′-diaminodiphenylmethane (TGDDM)-4,4′-diamlnodiphenylsulfone (DDS) formulations, the recommended cure cycle prescribes a maximum temperature close to 177°C. The maximum extent of reaction that may be obtained at this temperature is determined from the vitrification curve. At this maximum conversion, balanced mechanical and physical properties are attained in the partially cured specimen. However, if the standard cycle is used to cure thick parts, the maximum temperature inside the sample increases beyond 177°C. This leads to a complete conversion in most of the part and a consequent impairment of resulting physical and mechanical properties. It is shown how numerical solutions of differential energy and mass balances may be used to propose alternative cure cycles such that the maximum conversion at every point remains bounded by the vitrification curve. An illustration for a particular thickness is provided.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760301805
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  • 6
    Electronic Resource
    Electronic Resource
    Analysis of the thermodynamic compatibility of interpenetrating networks during their synthesis (1988)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 26 (1988), S. 1735-1749 
    Details
    ISSN: 0887-6266
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A thermodynamic analysis of interpenetrating polymer networks (IPNs), at any extent of reaction during their synthesis, is presented for both simultaneous and sequential procedures. A model IPN is assumed to be built up by the independent stepwise homopolymerization of two monomers: a tetrafunctional one, A4, and a trifunctional one, A3. No reaction of copolymerization or grafting is allowed between the two types of polymers. For the case of semi-IPNs, A3 is replaced by A2, i.e., a bifunctional monomer leading to a linear polymer. The free energy of mixing is described by a Flory-Huggins lattice model, whereas the elastic contribution is calculated by assuming affine deformation of an ideal elastic network. Results show that a sequential polymerization gives a more incompatible system (i.e., it enters the metastable region at lower conversions) than a simultaneous polymerization starting from the same monomers. In every case, a semi-IPN is shown to be more compatible than an IPN owing to the fact that the average size of the bifunctional monomer increases less with conversion than the size of the trifunctional monomer. When a sequential polymerization begins from a swollen gel at equilibrium, any increase in the extent of reaction of the solvent monomer will lead to its segregation from the swollen gel. The critical Flory-Huggins interaction parameter provides a simple way to ascertain the possibility of phase separation during a simultaneous polymerization.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1988.090260813
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  • 7
    Electronic Resource
    Electronic Resource
    Glass transition temperature versus conversion relationships for thermosetting polymers (1990)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 28 (1990), S. 85-95 
    Details
    ISSN: 0887-6266
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Owing to enthalpy relaxation, values of the glass transition temperature (Tg) for partially reacted polymers may depend on the thermal history of samples and the heating rate used for measurements. Use of theoretical relations between Tg and the extent of reaction (x) of a thermoset must take this fact into account. The original DiBenedetto equation has been reevaluated as a convenient constitutive equation for expressing Tg versus x. An extension of Couchman's approach for the expression of the compositional variation of Tg enabled us to derive the same functionality as given by the DiBenedetto equation. Thus, the DiBenedetto equation may be regarded as based on entropic considerations applied to a model of the thermosetting polymer consisting of a random mixture of a fully reacted network with the initial monomers in an amount which depends on the particular conversion level. These two equations have been applied with success to different diepoxy-diamine copolymers.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/polb.1990.090280107
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  • 8
    Electronic Resource
    Electronic Resource
    Thermodynamic analysis of the phase separation in polyetherimide-modified epoxies (1996)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 34 (1996), S. 349-356 
    Details
    ISSN: 0887-6266
    Keywords: phase separation ; thermoplastic-modified epoxies ; polyetherimide-modified epoxies ; Flory-Huggins equation ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The miscibility of polyetherimides (PEIs) with epoxy monomers based on diglycidylether of bisphenol-A (DGEBA), and with reactive mixtures based on stoichiometric amounts of DGEBA and an aromatic diamine (DA) {either 4,4′-diaminodiphenylsulfone (DDS) or 4,4′-methylenebis[3-chloro 2,6-diethylaniline] (MCDEA)}; was experimentally studied. Cloud-point curves (temperature vs. composition) are reported for PEI-DGEBA and PEI-DGEBA-DA initial mixtures. Cloud-point conversions are reported for the reactive mixtures, for various PEI amounts and polycondensation temperatures. A thermodynamic model based on the Flory-Huggins-Staverman approach, taking polydispersity of both components into account, was used to analyze the experimental information. A single relationship between the interaction parameter and temperature, χ(T), could fit experimental results of mixtures of two commercial PEIs with DGEBA. The addition of DDS led to a decrease in miscibility whereas MCDEA improved the initial miscibility. In both cases, the interaction parameter decreased with conversion, meaning that PEI was more compatible with oligomeric species than with the mixture of starting monomers. The phase separation process in initially miscible rubber- or thermoplastic-modified thermosetting polymers is the result of two factors: increase in the average molar size of the thermosetting oligomer (main driving force favoring demixing), and variation of the interaction parameter with conversion, which may act to increase or decrease the cloud-point conversion determined by the first factor. © 1996 John Wiley & Sons, Inc.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Thermal conductivity of plastic foams (1983)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 23 (1983), S. 293-298 
    Details
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A simple equation enabling the prediction of the thermal conductivity of plastic foams, without the aid of adjustable parameters, is proposed. The equation is based on a recurrent method, previously developed, that showed reasonable agreement with experimental results. Ways of decreasing the thermal radiation contribution are shown. In particular, the influence of cell size, radiation transmission through solid membranes, and low-emissivity boundary surfaces are analyzed. Errors involved in steady techniques of measuring the thermal conductivity associated with radiation are discussed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760230602
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  • 10
    Electronic Resource
    Electronic Resource
    Manufacture of urea-formaldehyde concentrates using a gas-liquid technology (1984)
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 24 (1984), S. 1245-1248 
    Details
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The performance of a laboratory packed-column for the manufacture of urea-formaldehyde (UF) concentrates is analyzed. Gaseous formaldehyde was generated by the thermal decomposition of paraformaldehyde in a carrier nitrogen stream. The UF solution was continuously recirculated through a glass column filled with Raschig rings. No pH control was necessary when the operation was started using a solution with a F/U molar ratio higher than 3.5 to 4. Otherwise, insoluble resins appeared during the operation. The formaldehyde absorption rate was controlled by the gas phase resistance. The vapor composition in equilibrium with a typical UF concentrate is provided as a function of temperature.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pen.760241606
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