A numerical study of a rotationally degenerate hyperbolic system. Part I. The Riemann problem

We study numerically the Riemann problem for a 2 x 2 system of conservation laws with a cubic flux function, a particular case of the class of models introduced by Keyfitz and Kranzer. The system is not strictly hyperbolic, and the classical Lax theory for hyperbolic systems is not directly applicable. Correspondingly, some numerical schemes which are accurate for strictly hyperbolic systems are not well behaved for this example. When they do work, different schemes yield markedly different results for certain data. We explain this effect by observing that, near these data, viscous regularization is non-uniform as the viscosity tends to zero. This fact does not contradict the well-posedness of the hyperbolic model; it does imply that precise control of the viscosity introduced into a computational method is crucial for generating the correct numerical solutions. We examine all of these issues and comment on their implications for similar systems which arise in continuum mechanics.     

Latex Fractionation by Sedimentation and Colloidal Crystallization: The Case of Poly(styrene-co-acrylamide)

Poly(styrene-co-acrylamide) (PS-AAM) latex was prepared, fractionated by sedimentation under gravity, and characterized by PCS, infrared spectra, secondary and backscattered electron imaging in the scanning electron microscope, and electron spectroscopy imaging in an analytical transmission electron microscope. Three latex fractions were obtained. The lower fraction was opalescent and its particles were the more uniform, concerning size, chemical composition, and topochemical features. This lower fraction was still further fractionated by zonal centrifugation in a density gradient, yielding two fractions with similar macrocrystal-forming abilities but different sizes and chemical compositions. These results confirm those previously obtained for the PS-HEMA latex. Copyright 2000 Academic Press.