Computer simulation of the interplay between fractal structures and surrounding heterogeneous multifractal distributions. Applications

In a large number of physical, biological and environmental processes interfaces with high irregular geometry appear separating media (phases) in which the heterogeneity of constituents is present. In this work the quantification of the interplay between irregular structures and surrounding heterogeneous distributions in the plane is made For a geometric set image and a mass distribution (measure) image supported in image, being image, the mass image gives account of the interplay between the geometric structure and the surrounding distribution. A computation method is developed for the estimation and corresponding scaling analysis of image, being image a fractal plane set of Minkowski dimension image and image a multifractal measure produced by random multiplicative cascades. The method is applied to natural and mathematical fractal structures in order to study the influence of both, the irregularity of the geometric structure and the heterogeneity of the distribution, in the scaling of image. Applications to the analysis and modeling of interplay of phases in environmental scenarios are given.

Optimal phase distributions for polygonal Fresnel lenses

Polygonal Fresnel zone plates can be configured in a variety of forms depending on the number of sides of the polygon and the number of phase steps used. This contribution deals with some specific polygonal designs that tessellate the plane: triangles, squares, and hexagons. The phase distribution is chosen as a continuous one to form a polygonal kinoform. The selected designs have been simulated and its behaviour compared. Although their performance is worse than the circular Fresnel plate, they may present some other advantages as the tessellation capability, and the possibility to fabricate them as extruded profiles.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.