Diffusion–dispersion limits for multidimensional scalar conservation laws with source terms

AbstractIn this paper we consider conservation laws with diffusion and dispersion terms. We study the convergence for approximation applied to conservation laws with source terms. The proof is based on the Hwang and Tzavaras's new approach [Seok Hwang, Athanasios E. Tzavaras, Kinetic decomposition of approximate solutions to conservation laws: Application to relaxation and diffusion–dispersion approximations, Comm. Partial Differential Equations 27 (5–6) (2002) 1229–1254] and the kinetic formulation developed by Lions, Perthame, and Tadmor [P.-L. Lions, B. Perthame, E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc. 7 (1) (1994) 169–191]

Singular Limit of the Rotational Compressible Magnetohydrodynamic Flows

We consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the stratified flows of the rotational compressible magnetohydrodynamic flows with the well-prepared initial data and the tool of proof is based on the relative entropy. Furthermore, the convergence rates are obtained

Effects of Particle Sizes on Sintering Behavior of 316L Stainless Steel Powder

In rapidly evolving powder injection molding technology, the wide prevalence of various microstructures demands the powders of smaller particle sizes. The effects of particle size on the sintering behavior are critical to not only shape retention of microstructure but also its mechanical properties. This study investigates the effects of three different particle sizes on the sintering behavior of the 316L stainless steel (STS316L) samples, prepared by powder injection molding, via the dilatometry experiments. For this purpose, the STS316L powders of three different mean particle sizes, i.e., 2.97, 4.16, and 8.04 mu m, were produced for STS316L. The samples for the dilatometry test were prepared through powder-binder mixing, injection molding, and solvent and thermal debinding. Dilatometry experiments were carried out with the samples in a H-2 atmosphere at three different heating rates of 3, 6, and 10 K/min. The shrinkage data obtained by dilatometry experiments was collected and analyzed to help understand the densification and the sintering behaviors in terms of particles size and heating rate. The master sintering curve (MSC) model was used to quantify the effects of particle sizes. In addition, we investigated the microstructure evolutions in terms of particles sizes.open1186sciescopu