Global minimization of a generalized convex multiplicative function

This paper discusses an algorithm for generalized convex multiplicative programming problems, a special class of nonconvex minimization problems in which the objective function is expressed as a sum ofp products of two convex functions. It is shown that this problem can be reduced to a concave minimization problem with only 2p variables. An outer approximation algorithm is proposed for solving the resulting problem.     

A Polyhedral Approach for Nonconvex Quadratic Programming Problems with Box Constraints

We apply a linearization technique for nonconvex quadratic problems with box constraints. We show that cutting plane algorithms can be designed to solve the equivalent problems which minimize a linear function over a convex region. We propose several classes of valid inequalities of the convex region which are closely related to the Boolean quadric polytope. We also describe heuristic procedures for generating cutting planes. Results of preliminary computational experiments show that our inequalities generate a polytope which is a fairly tight approximation of the convex region.     

Permeation of high-pressure gases in poly(ethylene-co-vinyl acetate)

A previously proposed theoretical treatment to elucidate the pressure dependence of gas permeability is improved in order to apply it to polymer-gas systems in which gas dissolution follows the Flory-Huggins equation. Permeation rates of N₂, CH₄, and CO₂ in poly(ethylene-co-vinyl acetate) are measured in the pressure range below 90 atm at 10–40°C, and the effect of pressure on permeability is found for each gas. The data are analyzed using the improved method to estimate the contributions of concentration and hydrostatic pressure to the pressure dependence of permeability. The concentration effect decreases with increasing temperature, whereas the hydrostatic-pressure effect is almost independent of temperature. Crystallinity dependence of the concentration effect is discussed in connection with high-pressure permeation data of other semicrystalline polymers reported elsewhere. © 1993 John Wiley & Sons, Inc.     

Sorption,diffusion, and partial molar volumes of C4 hydrocarbons in rubbery polymers

Sorption and dilation isotherms and diffusion coefficients for seven hydrocarbons (n-butane, isobutane, 1-butene, cis-2-butene, trans-2-butene, isobutylene, and 1,3-butadiene) in two rubbery polymers, 1,2-polybutadiene (PB) and poly(ethylene-co-vinyl acetate) (EVAc), were measured at 25°C. Dissolution parameters (Henry's law coefficient and Flory-Huggins interaction parameter), partial molar volumes, and diffusion coefficients were determined. PB exhibited greater affinity and lower diffusivity than EVAc to the C₄ gases, although the gases showed nearly the same partial molar volumes in the two polymers. The diffusivity of such elongated molecules as trans-2-butene in both polymers was higher than that of bulky molecules with similar partial molar volume, such as cis-2-butene and isobutylene. Pressure-dependent permeabilities of PB and EVAc films to the hydrocarbons were predicted and discussed based on the dissolution parameters and the diffusivities. © 1995 John Wiley & Sons, Inc.