Simultaneous measurement of viscoelastic changes and cell opening during processing of flexible polyurethane foam

A parallel-plate rheomete was constructed and used to study the development of dynamic shear modulus and cell opening under forced adiabatic conditions for a series of flexible slabstock polyurethane foams. Typical industrial formulations were used. The plates were heated to follow the adiabatic temperature profile of a real foam bun during foaming. The rheometer overcomes difficulties encountered in other methods such as heat loss and bubble damage caused by the probe.A four-stage modulus development profile was observed: initial bubble growth, bubble network, polymer stiffening and final curing. Chemical structure development was also studied under forced adiabatic conditions, using Fourier transform infrared spectroscopy. Polymer stiffening coincided with bidentate (hydrogen-bonded) urea formation.The normal force exerted by the expanding foam on the plates was found to be a function of the rate of foam expansion and the foam modulus. A sudden drop in the normal force typically coincides with the visually observed blow-off in the reacting foam bun, thus the normal force profile is a new and accurate indicator of cell opening. The normal force profile clearly shows that cell opening occurs just after the onset of polymer stiffening, thus illustrating the role of polymer rheology in the cell opening mechanism.Dedicated to the memory of Professor Tasos C. PapanastasiouPortions presented at the SPI Polyurethanes Technical/Marketing Conference, October 9–12, 1994, Boston, massachusetts, USA (Best paper award) and at the XIIth International Congress on Rheology, August 18–23, 1996, Québec City, Québec, Canada.     

Study on the absolute configuration of (−)-palau’amine

The absolute stereochemistry of the immunosuppressive pyrrole-imidazole alkaloid (−)-palau’amine from the marine sponge Stylotella aurantium is analyzed by CD spectroscopy. With the help of a series of model compounds it is shown that the CD spectrum of (−)-palau’amine can be explained based on the assumption that the pyrrolopyrazinone partial structure is planar in 2,2,2-trifluoroethanol (TFE). Surprisingly, the natural product (−)-dibromophakellin shows the opposite Cotton effect, despite exhibiting the same absolute configuration.     

Thermodynamic Stability Versus Kinetic Lability of ZnS4 Core

Density Functional Theory and post‐Hartree Fock calculations reveal an unusual energy profile for Zn? S and Zn? N bond dissociation reactions in several [Zn(SR)₄]^2? and [Zn(Im)(SR)₃]^? complexes. The Zn? S bond dissociation in tetrathiolate dianions, which is highly exothermic in the gas phase, proceeds through a late transition state which can be rationalized on the basis of an avoided crossing resulting from Coulomb repulsion between the anionic fragments and ligand‐to‐metal charge‐transfer in the [Zn(SR)₄]^2? complexes. When solvation models for water, DMSO, or acetonitrile are included, some complexes become stable while others are metastable, so this constitutes the first theoretical model which is in full agreement with the experimental data for various [Zn(SR)₄]^2?, [Zn(SR)₃]^?, and [Zn(Im)(SR)₃]^? complexes. The analysis given here indicates that the Zn(Cys)₄ and Zn(His)(Cys)₃ cores of numerous proteins are metastable with respect to Zn? S and Zn? N bond dissociation, respectively. This is consistent with the kinetic lability at the zinc‐centers and illustrates that in nature, thermodynamic stability is imparted upon the zinc cores by the protein environment.     

Frequency down-conversion using cascading arrays of coupled nonlinear oscillators

A novel coupling scheme using M≥2 arrays of coupled nonlinear elements arranged in a specific configuration can produce multifrequency patterns or a frequency down-converting effect on an external (input) signal. In such a configuration, each array contains N≥3 nonlinear elements with similar dynamics and each element is coupled unidirectionally within the array. The subsequent arrays in the cascade are coupled in a similar fashion except that the coupling direction is arranged in the opposite direction with respect to that of the preceding array. Previous theoretical work and numerical results have already been reported in [P. Longhini, A. Palacios, V. In, J. Neff, A. Kho, A. Bulsara, Exploiting dynamical symmetry in coupled nonlinear elements for efficient frequency down-conversion, Phys. Rev. E 76 (2007) 026201]. This paper is focused on results of experiments implemented on two distinct systems: the first system is fabricated using discrete component circuits to approximate an overdamped bistable Duffing oscillator described by a quartic potential system, and the second system is built in a microcircuit, where the nonlinearity is described by a hyperbolic tangent function, with the option of applying an external signal to investigate resonant effects. In particular, the circuit implementations for each case use M=2 arrays, but their voltage oscillations already demonstrate that the frequency relations between each of the successive arrays decrease by a rational factor, conforming to earlier theoretical and numerical results for the general case containing M arrays. This behavior is important for efficient frequency down-converting applications which are essential in many communication systems where heterodyning is typically used and it involves multi-step processes with complicated circuitry.     

Rank-one convexity and polyconvexity of Hencky-type energies

We investigate a family of isotropic volumetric-isochorically decoupled strain energies based on the Hencky-logarithmic (true, natural) strain tensor log U. The main result of this note is that for n = 2 the considered energies are rank-one convex for suitable values of two material parameters. We also conjecture that there are values of the material parameters such that the corresponding energies are polyconvex. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

We propose an extension of the cyclic hardening plasticity model formulated by Armstrong and Frederick which includes micropolar effects. Our micropolar extension establishes coercivity of the model which is otherwise not present. We study then existence of solutions to the quasistatic, rate-independent Armstrong–Frederick model with Cosserat effects which is, however, still of non-monotone, non-associated type. In order to do this, we need to relax the pointwise definition of the flow rule into a suitable weak energy-type inequality. It is shown that the limit in the Yosida approximation process satisfies this new solution concept. The limit functions have a better regularity than previously known in the literature, where the original Armstrong–Frederick model has been studied.     

Error estimation in nonlinear optimization

Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality conditions hold. A second estimate, based on the solution of an unconstrained nonconvex, nonsmooth optimization problem, is valid even when strict complementary slackness is violated. Both estimates are valid in a neighborhood of a local minimizer. An active set algorithm is developed for computing a stationary point of the nonsmooth error estimator. Each iteration of the algorithm requires the solution of a symmetric, positive semidefinite linear system, followed by a line search. Convergence is achieved in a finite number of iterations. The error bounds are based on stability properties for nonlinear programs. The theory is illustrated by some numerical examples.     

Local existence and uniqueness for a geometrically exact membrane‐plate with viscoelastic transverse shear resistance

We prove the local existence and uniqueness to a geometrically exact, observer‐invariant membrane‐plate model introduced by the author. The model consists of an elliptic partial differential system of equations describing the equilibrium response of the membrane which is non‐linearly coupled with a viscoelastic evolution equation for exact rotations, taking on the role of an orthonormal triad of directors. This coupling introduces a viscoelastic transverse shear resistance. Refined elliptic regularity results together with a new extended Korn's first inequality for plates and shells allow to proceed by a fixed point argument in appropriately chosen Sobolev‐spaces in order to prove existence and uniqueness. Copyright © 2004 John Wiley & Sons, Ltd.