Norbert Hoffmann

Bio: Norbert Hoffmann is an academic researcher from Hamburg University of Technology. The author has contributed to research in topics: Rogue wave & Nonlinear system. The author has an hindex of 28, co-authored 145 publications receiving 3692 citations. Previous affiliations of Norbert Hoffmann include Bosch & University of Hamburg.

Rogue wave observation in a water wave tank.

Abstract: The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schr\"odinger equation, the most likely candidate satisfying this criterion is the so-called Peregrine solution. It is localized in both space and time, thus describing a unique wave event. Until now, experiments specifically designed for observation of breather states in the evolution of deep water waves have never been made in this double limit. In the present work, we present the first experimental results with observations of the Peregrine soliton in a water wave tank.

Super Rogue Waves: Observation of a Higher-Order Breather in Water Waves

Abstract: How rogue waves in the ocean come about still is a scientific puzzle. But, for the first time, super rogue waves are not only generated in a water-wave tank, but are also understood.

Effects of damping on mode-coupling instability in friction induced oscillations

Abstract: The mode-coupling instability has generally been acknowledged as one of the most prominent mechanisms leading to self-excited oscillations in sliding friction systems. The influence of structural damping on this type of instability mechanism however has not yet been fully clarified. The objective of the present work therefore is to investigate qualitative and quantitative aspects of the mode-coupling instability in the presence of structural damping, which will be assumed as linear viscous. For the sake of simplicity a two-degree-of-freedom minimal model is set up and analyzed. It is shown that under specific conditions the mode-coupling instability may be regarded as a viscous instability in the sense that an increase in structural damping may render a stable system unstable. An explanation for this behavior is given by two lines of argument: First a description and explanation is given in terms of eigenvalue-analysis. Due to the mathematical formality of this approach, the insight gained remains phenomenological. Second, a feedback-loop formalism is developed that allows a more detailed understanding of the underlying mechanical processes. Based on this formalism, necessary and in sum sufficient conditions for the onset of instability can be deduced and also the role of damping can be clarified.

Observation of a hierarchy of up to fifth-order rogue waves in a water tank.

Abstract: We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schr\"odinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the wave-breaking effect of water waves. Due to the strong influence of the wave breaking and relatively small carrier steepness values of the experiment these results for the higher-order solutions do not directly explain the formation of giant oceanic rogue waves. However, our results are important in understanding the dynamics of rogue water waves and may initiate similar experiments in other nonlinear dispersive media such as fiber optics and plasma physics, where the wave propagation is governed by the NLS.

Nonlinear Time Series Analysis.

Abstract: : This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

Instabilities, breathers and rogue waves in optics

Abstract: Curious wave phenomena that occur in optical fibres due to the interplay of instability and nonlinear effects are reviewed.