Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.     

Use of reactable light stabilizers to prevent migration and to improve durability of coatings on plastic substrates

One of the challenges of coating plastic substrates for exterior automotive applications involves the tendency for light stabilizers, which inhibit UV degradation of the coating, to migrate out of the topcoat and into the underlying plastic substrate. The consequent depletion of the stabilizer from the topcoat could account for significantly poorer durability for coatings applied on plastic than on a nonpermeable substrate such as steel. These studies investigate the migration of both nonreactable and reactable UV absorbers (UVAs) and hindered amine light stabilizers (HALS) in fully formulated 2K urethane coatings applied on thermoplastic olefin (TPO) and steel substrates. Extensive migration of the nonreactable stabilizers occurs during accelerated exposure of the cured coating, and this migration correlates with poorer performance on TPO. Functionalization of the stabilizer with a group which covalently reacts into the coating will prevent much of this migration, and the improved degree of retention of the reactable light stabilizers in the topcoat correlates with improved performance on TPO substrates. In addition, stabilizer variables, such as the type and extent of functionalization as well as their chemical structure, have an effect on both the migration and performance of the stabilizers.     

Effect of Nanoparticles on the Hysteresis Loop in Mixed Convection within a Two-Sided Lid-Driven Inclined Cavity Filled with a Nanofluid

The present work deals with numerical modeling of mixed convection flow in a two-sided lid driven inclined square enclosure filled with water-Al₂O₃ nanofluid. The limiting cases of a cavity heated from below and cooled from above and the one differentially heated are recovered respectively for inclination angles 0° and 90°. The moving walls of the cavity are pulled in opposite directions with the same velocity and maintained at constant but different temperatures while the remaining walls are kept insulated. The numerical resolution of the studied problem is based on the lattice Boltzmann method. A parametric study is conducted and a set of graphical results is presented and discussed to illustrate the effects of the presence of nanoparticles and enclosure inclination angle on fluid flow and heat transfer characteristics. The governing parameters of this problem are the Richardson number (varied from 0.1 to 10⁶), the nanoparticles volume fraction (varied from 0 to 0.04) and the inclination angle (varied from 0° to 180°). The critical conditions leading to the transition from monocellular flow to multicellular flow and vice versa are determined. In the common ranges of Richardson number and inclination angle where both monocellular and tri-cellular patterns coexist, the heat transfer is seen to be strongly reduced by the latter.     

Heat-transfer corrosion behaviour of cast Al alloy

Heat-transfer corrosion behaviour of an ISO 2379 cast Al alloy was studied in antifreeze radiator coolant under heat-rejecting condition. Extensive analyses of microstructures and corroded surfaces were carried out under the optical microscope, scanning electron microscope equipped with energy dispersive spectroscopy and X-ray diffractometer. Heat-rejecting condition led to a cavitation process and cavities were observed within the α-Al matrix. Crevice corrosion was predominant at oxygen depleted regions in heat-transfer corrosion cell. Al₂Cu, Al₁₅(Fe,Mn)₃Si₂ dendrites, Al₄Cu₂Mg₈Si₇ and Si phases served as the effective cathodes resulting microgalvanic corrosion at the anodic site of α-Al matrix.     

Migration of reactable UVAs and HALS in automotive plastic coatings

Loss of light stabilizers from automotive finishes can significantly reduce the durability of coatings on plastic substrates. Minimizing movement by retaining the stabilizers in the targeted layer can greatly improve coating longevity. This article examines the migratory patterns of a series of traditional UVA and HALS additives in fully formulated 1K silane crosslinked coatings applied over both plastic and steel substrates, comparing their migratory patterns to that of reactable light stabilizers containing hydroxyl functionality. Analysis of the coating layers with the various UVAs and HALS revealed that functionalization of the light stabilizer with reactable hydroxy groups can prevent migration into the plastic; whereas nonreactable light stabilizers migrate into lower coating system layers and even into the plastic substrate. The greatest extent of migration does not occur during initial cure of the wet coating, but during exposure. Significant depletion of the nonreactable light stabilizers from the topcoat occurs as early as 1500 hours of Xenon boro/boro exposure. This paper was awarded first place in the Shelby F. Thames Best Paper Award, at the 30th International Waterborne, High-Solids and Powder Coatings Symposium, February 26–28, 2003, in New Orleans, LA.     

On magnetization dynamics with inertial effects

We consider a mathematical model describing magnetization dynamics with inertial effects. The model consists of a modified form of the Landau–Lifshitz–Gilbert equation for the evolution of the magnetization vector in a rigid ferromagnet. We discuss global existence of weak solutions and characterize the \(\omega \) -limit set for the model.