Stochastic analysis of ocean wave states with and without rogue waves

This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale dependent complexity of ocean waves by means of a Fokker-Planck equation, providing stochastic information of multi-scale processes. In particular we show evidence of Markov properties for increment processes, which means that a three point closure for the complexity of the wave structures seems to be valid. Furthermore we estimate the parameters of the Fokker-Planck equation by parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction. This work presents a new approach where the coherent structure of rogue waves seems to be integrated into the fundamental statistics of complex wave states.Comment: 18 pages, 13 figure

Orientational transition in nematic liquid crystals under oscillatory Poiseuille flow

We investigate the orientational behaviour of a homeotropically aligned nematic liquid crystal subjected to an oscillatory plane Poiseuille flow produced by an alternating pressure gradient. For small pressure amplitudes the director oscillates within the flow plane around the initial homeotropic position, whereas for higher amplitudes a spatially homogeneous transition to out-of-plane director motion was observed for the first time. The orientational transition was found to be supercritical and the measured frequency dependence of the critical pressure amplitude in the range between 2 and 20 Hz was in quantitative agreement with a recent theory.Comment: 11 pages, 4 figures, submitted to Europhys. Let

Improved estimation of Fokker-Planck equations through optimisation

An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems (L-BFGS-B) is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimisation routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this new optimisation routine