Abstract: The present disclosure relates generally to roofing products, for example, suitable for use covering and protecting the roofs of structures. The present disclosure relates more particularly to a roofing product including an upper section and an exposed section. The roofing product includes a substrate having a top surface and a bottom surface, and a plurality of zones of roofing granules disposed on the top surface of the substrate. The plurality of zones includes first, second and third zones within the exposed section. The first zone includes a first collection of algae-resistant roofing granules and has a first algae-resistance intensity. The second zone includes a second collection of algae-resistant roofing granules and has a second algae-resistance intensity. The third zone has a third algae-resistance intensity that is different from the first algae-resistance intensity.

Abstract: A Bi1-xSbx thin film is provided that includes a Dirac-cone with different degrees of anisotropy in their electronic band structure by controlling the stoichiometry, film thickness, and growth orientation of the thin film, so as to result in a consistent inverse-effective mass tensor including non-parabolic or linear dispersion relations.