Critical power for self-focusing in bulk media and in hollow waveguides

We determine the threshold power for self-focusing collapse both in a bulk medium and in a hollow-core waveguide for various spatial profiles. We find that the threshold power for collapse in the waveguide is always equal to the lower-bound prediction for a bulk medium.     

A quantitative approach to soliton instability

We present an approach for instabilities of solitons that is based on the spectrum of a fourth-order linearized operator. Unlike the standard approach which is based on the slope (Vakhitov-Kolokolov) condition, this approach provides the quantitative value of the instability rate and the qualitative nature of the instability dynamics.     

Synthesis and optimization of a new calcium phosphate ceramic using a design of experiments

The main objective of this work is to understand the effects caused by particle size, temperature, and sintering time on ceramic formation and development of its surface hardness (Vickers hardness Vk) in order to extend its use in medical applications. The ceramic consists of a biphasic calcium phosphates mixture (beta-tricalcium phosphate and hydroxylapatite) to which we have added zinc oxide, silica, and zirconia in order to improve the biological and mechanical profiles of this ceramic. The ceramization process is made by partial melting, which the melt agent is an amorphous aluminum phosphate added by small quantities to the last mixture. In fact, when the aluminum phosphate is under high temperature, it causes the formation of a melt which facilitates the adhesion of particles during the solidification process. In this study, we adopted an experimental strategy such as central composite design. This plan lets us optimize the mechanical hardness of the ceramic, involving a polynomial form derived from the Taylor–Mac Lorrain equation. The isoresponses curves obtained give us the estimated responses and empirical possibilities for obtaining ceramics with an optimum hardness, which can then be used for each type or intervention place in reconstructive surgery.