Note on log-periodic description of 2008 financial crash

We analyze the financial crash in 2008 for different financial markets from the point of view of log-periodic function model. In particular, we consider Dow Jones index, DAX index and Hang Seng index. We shortly discuss the possible relation of the theory of critical phenomena in physics to financial markets.Comment: 13 pages, 7 figures; references and few comments added

Linguistic complexity: English vs. Polish, text vs. corpus

We analyze the rank-frequency distributions of words in selected English and Polish texts. We show that for the lemmatized (basic) word forms the scale-invariant regime breaks after about two decades, while it might be consistent for the whole range of ranks for the inflected word forms. We also find that for a corpus consisting of texts written by different authors the basic scale-invariant regime is broken more strongly than in the case of comparable corpus consisting of texts written by the same author. Similarly, for a corpus consisting of texts translated into Polish from other languages the scale-invariant regime is broken more strongly than for a comparable corpus of native Polish texts. Moreover, we find that if the words are tagged with their proper part of speech, only verbs show rank-frequency distribution that is almost scale-invariant

Efficient finite element modelling of ultrasound waves in elastic media

The aim of the work presented in this thesis is to provide tools to extend modelling capacities and improve quality and reliability of bulk and guided wave propagation models using commercially available finite element (FE) packages. During the development process of NDT inspection techniques, the knowledge of the interaction of waves with defects is key to the achievement of robust and efficient techniques as well as identifying potential weaknesses. The reflection of ultrasound from cracks and notches of simple geometry anq'orientation is already well understood, but there are few results for more complex c~es. A discrete approach is needed to model how the waves interact with discontinuities, including structural features, cracks, corrosion or other forms of defects. FE methods have been used to model a wide range of bulk and guided waves problems and have successfully provided important information about wave interaction with discontinuities. In these studies, defects were strongly simplified. One reason for this is that initial work is bound to focus on the simplest cases, but many modellers are ready to go on to more complex problems. The reason that so little of that is happening is that, despite rapid growth in computer power, many of the more complex realistic problems are still beyond the capacity of the models. The more complex problems require much larger models than the simplified ones, and so have remained out of reach. This can be changed by using innovative techniques and improving the quality and reliability ofmodelling by taking the right decisions during the modelling process. Perfectly matched layers (pML) and absorbing layers using increasing damping (ALID) enabling a reduction in the model geometric size are implemented in commercially available FE packages. Analytical models are developed in order to facilitate the achievement of high computational efficiency. Demonstrator cases highlight the gains achieved by the use of these techniques. As the choice of mesh density is crucial in defining the resources necessary to solve a model, a study of the influence of meshing parameters for various element types and numerical schemes on the propagation velocity is performed. This provides information helping modellers to reach the right modelling compromises thanks to an improved understanding ofthe consequences of the decisions made. The accuracy of defect modelling is investigated for a range of situations and modelling strategy. The weight ofthe choice ofthe right strategies is demonstrated. The potential implementation of local mesh refinement in commercially available FE packages is considered and discussed in the context of the choices open to the modellers. The outcome of the use of the techniques and information presented in this thesis is a significant improvement in FE modelling of waves in elastic media.Imperial Users onl