One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

WASAN : the development of a facilitated methodology for structuring a waste minimisation problem

This paper contributes a new methodology called Waste And Source-matter ANalyses (WASAN) which supports a group in building agreeable actions for safely minimising avoidable waste. WASAN integrates influences from the Operational Research (OR) methodologies/philosophies of Problem Structuring Methods, Systems Thinking, simulation modelling and sensitivity analysis as well as industry approaches of Waste Management Hierarchy, Hazard Operability (HAZOP) Studies and As Low As Reasonably Practicable (ALARP). The paper shows how these influences are compiled into facilitative structures that support managers in developing recommendations on how to reduce avoidable waste production. WASAN is being designed as Health and Safety Executive Guidance on what constitutes good decision making practice for the companies that manage nuclear sites. In this paper we report and reflect on its use in two soft OR/problem structuring workshops conducted on radioactive waste in the nuclear industry. Crown Copyright © 2010.