The New Theory for Rogue Waves featured in SPIE Newsroom !
Last Updated (Wednesday, 19 August 2015 14:26)
Irreversibility of Shock Waves Explained by Nonlinear Gamow Vectors
Editors of Physical Review A have retained among their suggestions a paper published by Silvia Gentilini, Maria Chiara Braidotti, Giulia Marcucci, Eugenio Del Re and Claudio Conti about a novel theoretical approach for the description of shock waves in nonlinear nonlocal media.
The novel theory is based on ideas retained from Irreversible Quantum Mechanics, a novel formulation of quantum mechanics based on the so-called Rigged Hilbert Space that include explonential decaying wavefuctions.
The theory describes the shock and wave-breaking scenario beyond the limits of the usual hydrodynamic approach, and allows to derive closed forms for the degree of irreversibility. This approach also introduces the "nonlinear Gamow Vectors," a novel kind of nonlinear waves with many possible applications in nonlinear physics.
Last Updated (Wednesday, 05 August 2015 08:28)
Three-dimensional rogue waves by random media go through obstacles
Last Updated (Sunday, 19 July 2015 10:13)
Relativistic analogue in non-paraxial shock waves
Shock generation and wave-breaking are effects largely investigated in nonlinear optics. They are always occurring in extreme regimes with a variety of fundamental physical implications, and a number of applications, ranging from particle and material manipulation, to supercontinuum and X-ray generation.
In nonlinear optics, one studies shocks in space and time. Concerning the spatial case, shock waves are observed as highly irregular wave-fronts that originate upon the propagation of a smooth Gaussian beam in a strongly nonlinear medium like, for example, a thermal liquid.
So far, the analysis of spatial shock waves has been limited by the paraxial approximation. The validity of this approximation, however, is questioned by the large spatial bandwidth that is observed at the shock formation.
In a manuscript published in Optics Communications (arXiv:1412.8602) Silvia Gentilini, Eugenio Del Re and Claudio Conti study theoretically and computationally the effects of the non-paraxial regime on the shocks. The result is a predicted correction to the maximal spatial bandwidth after the shock generation, which is within experimentally measurable values, and which is also relevant for temporal shock waves.
The analysis is fascinating, as it shows that non-paraxial terms can be mapped to the relativistic corrections that occur when one considers the propagation of particles with velocity comparable with the speed of light. In other words, the mathematical treatment of the non-paraxial shock is analogue to the treatment of the relativistic particle motion. The trajectories of the particles corresponds to the so-called characteristic lines.
This problem is also relevant for mathematical investigations concerning wave-breaking in high-order nonlinear partial differential equations.
The picture below shows an example of the calculation of the relativistic shock wave front.
Last Updated (Sunday, 19 July 2015 09:45)