On the scaling of molecular weight distribution functionals J. Rheol. 45, 891 (2001) On the nonlinear rheology of a wormlike micellar system in the presence of sodium salicylate salt J. Rheol. 41, 307 (1997) The density dependence of fluid properties and nonNewtonian flows: The Weissenberg effecta) J. Rheol. 39, 1343Rheol. 39, (1995 High Weissenberg number simulation of die swell for differential type viscoelastic model by the streamlineupwind finite element method SynopsisThe model of isothermal diffusion in a polymeric medium derived by El Afil et al. ͓A. El Afif, M. Grmela, and G. Lebon, J. Non-Newtonian Fluid Mech. 86, 253 ͑1999͔͒ is investigated in the absence of an overall flow and in mechanical equilibrium. First, we derive its more macroscopic reduced versions and compare them with the models introduced previously in the literature. Next, we investigate the wave propagation of disturbances in the solvent concentration. Subsequently, we specify the free energy and kinetic coefficients that appear in the general governing equations and solve ͑using both qualitative and numerical methods͒ the governing equations expressed in the material coordinates. In this way we obtain the time evolution of the solvent concentration, the diffusion flux, the swelling, the internal deformations and stresses, and the internal viscosity associated with the solvent penetration and the swelling. The governing equations involve three parameters that express the individual nature of the mixture: the relaxation time of the polymeric structure, the relaxation time of the diffusion flux, and one parameter that expresses coupling of the polymeric structure and the solvent concentration in free energy. As an illustration, we show that with these three characteristic parameters we can reproduce results of observations that we have selected from the literature ͓N. L. Thomas and A. H. Windle, Polymer 19, 255 ͑1978͔͒. In particular, we reproduce the case II type diffusion observed in the absence of a glass-rubber transition.

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The authors investigate the contribution of the unseparated Rydberg states which are usually neglected, in atomic K-edge X-ray spectra. They suppose that the core hole broadening is large, so that the global contribution of all unresolved Rydberg levels introduces an apparent threshold shift with a value nearly equal to the separation of the first unresolvable Rydberg line from the series limit. The apparent threshold has the same dependence on the photon energy as the true one. The region of unresolvable Rydberg lines can be described by means of a quasi-particle approach, by introducing a pseudo-wave vector formalism. The authors perform an analysis of Ne and Ar K-edge absorption spectra. Using the present theory, they derive a very simple procedure for the evaluation of the instrumental and the core hole broadening in X-ray spectra.

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