An electromagnetic study of the staircase approximation of arbitrary shaped gratings is conducted with three different grating theories. Numerical results on a deep aluminum sinusoidal grating show that the staircase approximation introduces sharp maxima in the local field map close to the edges of the profile. These maxima are especially pronounced in TM polarization and do not exist with the ...

Rapid Prototyping technologies are able of generating physical objects from CAD models. An important aspect of these technologies is the achieved surface quality of manufactured parts. The surface quality is strongly associated with the layered manufacturing. The surface roughness which depends by the staircase effect is a consequence of the layered manufacturing. The staircase effect vary acco...

We consider a relatively new combinatorial structure called staircase tableaux. They were introduced in the context of the asymmetric exclusion process and Askey–Wilson polynomials; however, their purely combinatorial properties have gained considerable interest in the past few years. We will be interested in a general model of staircase tableaux in which symbols that appear in staircase tablea...

Auditory scene analysis describes the ability to segregate relevant sounds out from the environment and to integrate them into a single sound stream using the characteristics of the sounds to determine whether or not they are related. This study aims to contrast task performances in objective threshold measurements of segregation and integration using identical stimuli, manipulating two variabl...

We define a combinatorial structure, a tiling of the staircase in the R plane, that will allow us, when restricted in different ways, to create direct bijections to Dyck paths of length 2n, Motzkin paths of lengths n and n−1, as well as Schröder paths and little Schröder paths of length n.