Numerical method for a model of inhomogeneous muscle fibers

The numerical solution of a nonlinear and nonlocal system of integro-differential equations that models the contraction of a single heterogeneous muscle fiber is studied. The method proposed is a form of the finite difference method of characteristics. Optimal error bounds are established for the resulting approximation. © 1993 John Wiley & Sons, Inc.     

On finite element approximation and stabilization methods for compressible viscous flows

This work is devoted to the numerical solution of the Navier–Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. We present methods to implement discontinuous approximations for the pressure and the density. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov–Galerkin method and the flux limiter methods aiming to introduce numerical diffusion only where it is necessary.     

Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields

A representation in the form of a functional integral is obtained for the partition function of the inhomogeneous 2D Ising model on a triangular lattice where the coupling parameters are arbitrary functions of coordinates. The method for transforming the partition function into an integral uses an auxiliary six-component Grassmann field in which the Grassmann fields corresponding to one of the components commute with the others. Thus, one pair of components realizes a representation of the q-deformed group SL_q(2, R) with q=–1 and the other two pairs correspond to the usual Grassmann spinors (q=1). An explicit expression in terms of the modified Pfaffian is found for the Gaussian integral over these fields and its relation to the ordinary Grassmann functional integral is established.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 441–463, December, 1996.     

THE USE OF THERMOELASTICITY TO EVALUATE STRESS REDISTRIBUTION AND NOTCH SENSITIVITY IN CERAMIC MATRIX COMPOSITES

Thermoelastic stress analysis was used to document the effect of composite damage on the stress distribution in three ceramic matrix composites. Composite damage was found to significantly alter the thermoelastic response of each material, with the greatest effect noted in SiC/CAS. Thermoelastic imaging of these materials affords a more complete picture of how the various damage mechanisms affect the stress distribution. In particular, a stress concentration factor computed from thermoelastic images, serves as an indicator of stress redistribution. The stress concentration factors were computed by comparing notch root to far field temperatures, and monitored after the introduction of various amounts of damage. In each material, the stress concentration factor diminished as the damaging load approached the ultimate stress. Reduction in the stress concentration is associated with local changes in modulus, mechanistically arising from combinations of fiber, matrix and interface fracture. Stress redistribution occurs as a consequence of modulus changes, leading to lower notch sensitivity in each of the tested composites.     

Miscible blends of modified poly(aryl ether ketones) with aromatic polyimides

The phase behavior of binary blends of poly(ether ether ketone) (PEEK), sulfonated PEEK, and sulfamidated PEEK with aromatic polyimides is reported. PEEK was determined to be immiscible with a poly(amide imide) (TORLON 4000T). Blends of sulfonated and sulfamidated PEEK with this poly(amide imide), however, are reported here to be miscible in all proportions. Blends of sulfonated PEEK and a poly(ether imide) (ULTEM 1000) are also reported to be miscible. Spectroscopic investigations of the intermolecular interactions suggest that formation of electron donoracceptor complexes between the sulfonated/sulfamidated phenylene rings of the PEEKs and the n-phenylene units of the polyimides are responsible for this miscibility. © 1993 John Wiley & Sons, Inc.     

The amplitude and phase of a transmission holographic grating due to four-wave interaction in a photorefractive medium

Based on a previously developed two-level model of four-wave interaction in photorefractive crystals, expressions for the amplitude and phase of a transmission holographic grating have been obtained. The analysis of these expressions points to the dependence of both the amplitude and the phase of the grating on the intensity of the readout beam.     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007