No abstract

No abstract

Optical solitons which remain radiationless in spite of having wavenumbers immersed in the spectrum of linear waves are rather unusual. This article shows that moving solitons of this type are solutions of an extended NLS equation with third and fourth-order dispersion, and a quintic nonlinearity. The mechanism which prevents the emission of radiation in these solitons is presented. The radiation emitted when these solitons are perturbed is also studied. This radiation exhibits four propagating fronts, and the velocities of these fronts are calculated and explained.

Inspired by the locomotion mechanism of sea urchins, we study the locomotion of an irregular echinoid by means of a simplified dynamical model. We prove that if two conjectures are assumed, the geometrical arrangement of the five ambulacral petals of irregular echinoids should form a eutactic star in order to optimize motility. We firstly propose an adequate "measure" of eutacticity that allows us to to verify the statistical tendency to such a property for a representative collection of fossil specimens. Next, regarding dynamics, the biological advantage of eutactic stars is addressed as a minimal path problem. Finally, we study the stability of some eutactic stars under small perturbations.

In this work, a modified version of the cut and projection approach is proposed to describe the structure of graphene bilayers with twist angles. With this method, the rotation between two graphene layers is viewed as a rotation of the projection space and the resulting projected structure is interpreted as the set of points of best fit between the two rotated structures. Additionally, focus is given to the pertinence of the many algebraic and geometric tools used in grain boundaries and in quasicrystals to graphene bilayer system (or any other bilayer system, for that matter) case.