The numerical integration of relative equilibrium solutions. The nonlinear Schrodinger equation

We analyse different error propagation mechanisms for conservativeand nonconservative time-integrators of nonlinear Schrödingerequations. We use a geometric approach based on interpretingwaves as relative equilibria.     

Analysis of Depolarized Light Scattering from a Solution of Rod-Like Macromolecules Through A Laplace Transform Method

In this work, an analysis is made of the depolarized component of the light scattered by a solution of rod-like macromolecules by measuring the Laplace Transform (LT) of the time interval probability between successive photoelectrons, P(t). The study was performed in forward scattering conditions, which allows direct evaluation of the Rotational Diffusion Coefficient, Dr. Results were obtained by means of computer simulation and are compared with those obtained through the measurement of the second order correlation function, g⁽²⁾(τ), for the same experimental conditions.     

Stress-optical behavior of polydimethylsilmethylene [?Si(CH3)2CH2?], a hydrocarbon analog of polydimethylsiloxane,and a silicon analog of polyisobutylene

Elastomeric networks were prepared from polydimethylsilmethylene (PDMSM) [? Si(CH₃)₂CH₂? ], a polymer closely related to polydimethylsiloxane (PDMSO) [? Si(CH₃)₂O? ] and polyisobutylene (PIB) [? C(CH₃)₂CH₂? ]. The birefringence of PDMSM in elongation was found to be qualitatively similar to that of PDMSO, in that there was no evidence for strain-induced crystallization. However, the values of the optical-configuration parameter Δa were considerably larger, and both Δa and its temperature coefficient are essentially the same as those of PIB. Swelling the PDMSM networks generally decreased Δa; the largest decreases, obtained as expected with the most nearly symmetrical diluent, were also approximately the same as those observed for PIB. Use of cyclic PDMSO pentamer as diluent in a PDMSM network was found to increase the birefringence, presumably because of orientational effects. Various network-diluent combinations involving the significantly anisotropic PDMSM and the more nearly isotropic PDMSO should be extremely useful for elucidating the nature of these intermolecular correlations. Results obtained from rotational isomeric state theory considerably underestimate both Δa and its temperature coefficient for PDMSM, as they do for PIB. Although the origin of the discrepancy is not necessarily the same for both polymers, the results on PDMSM suggest that the discrepancy for PIB is not due to the severe steric congestion known to be present in this polymer.     

Strain birefringence studies on poly(vinyl acetate) networks

Atactic poly(vinyl acetate) prepared in a free-radical polymerization was crosslinked by means of benzoyl peroxide. The resulting elastomeric networks were studied in elongation, both unswollen and swollen with triethylbenzene, over the range 0–90°C. The most important experimental results obtained were values of the network birefringence, which is negative, as was recently also found to be the case for networks of atactic poly(methyl acrylate).Calculations carried out to interpret the birefringence were based on Monte Carlo simulations of the atactic structure, and on the rotational isomeric-state theory of chain configurations. The agreement between theory and experiment was very good, in fact much better than has usually been observed for other polymers studied to date.     

Influence of local inhomogeneities induced in corneal ablation on the evolution of contrast sensitivity

The presence of local inhomogeneities in corneal tissue after refractive surgery has an influence on visual performance. Here we focus on the corneal ablation associated with Lasik surgery and its effect on the modulation transfer function (MTF) that we obtained by modifying a personalized Kooijman model. Inhomogeneities induced by the ablation occur in the form of Gaussian-distributed refractive-index variations of a given correlation length. We show how variation of refractive-index deviation and correlation length (size) of the inhomogeneities allows us to obtain pairs of values that are able to achieve a MTF evolution similar to that observed for contrast sensitivity in the same patients. An estimate of the characteristics of the local effects is obtained.     

Determination of molecular parameters of hydroxyethyl and hydroxypropyl celluloses by chromatography with dual detection

Hydroxyethylcellulose (HEC) and hydroxypropylcellulose (HPC) were studied by means of size exclusion chromatography with dual detection, i.e. employing simultaneously a refractive index (concentration sensitive) and a multiangle light scattering (molecular weight sensitive) detectors. The eluent was water and water solutions containing different concentrations of ionic salts. Molecular weight distributions and averages, coefficients of the scaling law of molecular dimensions and unperturbed dimensions were thus obtained from a single polydisperse sample of each polymer. Measurements were performed at 25 degrees C and the anomalous chromatographic behaviour, due to a combination of ion and size exclusion mechanisms, found when using pure water as eluent is transformed into a size exclusion mechanism by the addition of ionic salts. However, the two polymers behave on a different way in presence of salts. Thus, HEC, which is of low degree of substitution (DS), is close to theta conditions in the aqueous salt solutions (i.e. the q exponent of the scaling law has a value close to 0.5), whereas in the case of HPC the addition of salt improves the quality of the solvent up to a value of q around 0.6. Unperturbed dimensions are also calculated for both celluloses.     

Intramolecular formation of excimers in model compounds for polymers of 2,6-naphthalene dicarboxylic acid and five glycols in media of different viscosity

Steady-state fluorescence has been used to study the dependence of the intramolecular formation of excimers in media of differing viscosity, η, for model compounds of polyesters containing naphthalene groups. The model compounds are derived from 2-naphthalene carboxylic acid as rigid units and glycols, HO (SINGLEBOND) (CH₂)_m (SINGLEBOND) OH, m = 2(SINGLEBOND) 6, as flexible spacers. The ratio of the intensity of excimer and monomer emissions, I_D/I_M, exhibits two regimes: a regime at high η where I_D/I_M shows an odd(SINGLEBOND) even effect with m, with maxima at odd m, and a regime at low η where the odd-even effect is lost, and the maximum values are obtained for m = 3 and 6. Calculations performed for the equilibrium state using the rotational isomeric state model and Molecular Dynamics (MD) simulations allow the rationalization of the behavior of I_D/I_M with m in the media of high and low η, respectively. © 1996 John Wiley & Sons, Inc.