Fractal tracer distributions in turbulent field theories

We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary the two Lyapunov exponents for the particle motion and thereby find a regime in which the particle distribution is a strange attractor. We compare the Lyapunov dimension to the information dimension of actual particle distributions and show that there is good agreement with the Kaplan-Yorke conjecture. Similar phenomena have been observed experimentally.Comment: 17 pages, 7 figures, elsart.sty, psfig.sty, LaTe

A multiscale view on inverse statistics and gain/loss asymmetry in financial time series

Researchers have studied the first passage time of financial time series and observed that the smallest time interval needed for a stock index to move a given distance is typically shorter for negative than for positive price movements. The same is not observed for the index constituents, the individual stocks. We use the discrete wavelet transform to illustrate that this is a long rather than short time scale phenomenon -- if enough low frequency content of the price process is removed, the asymmetry disappears. We also propose a new model, which explain the asymmetry by prolonged, correlated down movements of individual stocks

Large Scale Structures and Particle Motion in Chaotic Dynamical Systems.

This article is appended to this thesis. The article is long and tells a coherent story, which will not be repeated here. This chapter will tell something about the physical background of the article. It is meant as to make the article accessible to a broader audience. 2.1 Surface Wave

Growth shapes and pulses in a generalized Kuramoto-Sivashinsky equation

We examine the growth shapes that arise as solutions to a generalized Kuramoto-Sivashinsky equation, when a small perturbation expands into a linearly unstable uniform flat regime. We show how, by including both the linear instabilities and the coherent structures, i.e. pulses, the growth shapes can be predicted for a large range of parameters. 1 Introduction We study the growth shapes which appear when a small localized perturbation expands into an unstable uniform medium. There are many examples of deterministic growth, i.e. growth where noise plays no role. These examples include propagating flames fronts [1], chemical turbulence [2] and localized turbulent spots in pipe flows or boundary layers [3]. To study these growth phenomena, we study a generalized version of the Kuramoto-Sivashinsky equation. The equation has been derived in a number of different physical contexts including chemical turbulence [4], surface waves [5] and flame fronts [6]. 2 The Generalized Kuramoto-Sivashi..