糖心TV

CO904 Stat Mech

Lectures by Ellak Somfai, shared with PX439

Abstract: In the 1960s Mandelbrot developed several fractal models  to describe how the shape of many aspects of the natural  world departs from the Euclidean. One modelled  heavy  tailed jumps-the "Noah effect", typical of economic index  time series-using Levy flights. In the introductory section I will show a few examples of natural systems for  which Levy flights or walks offer a useful model,  including the Earth's auroral electric currents and  the  turbulent solar wind which is their ultimate energy  source. I will also mention recent work where we have  revisited an earlier study which had identified Levy  walks in albatross foraging, using new data and improved  analysis methods.

In my more technical section I will describe studies  using a simple self-affine stable model-linear fractional  stable motion, LFSM, which unifies Levy flights with long  range memory-to give insight into space physics data.  I  will present a newly-derived diffusion equation for LFSM,    and  show work in progress using an LFSM generator and  simple analytic scaling arguments to study the problem of  the area between an LFSM curve and a threshold. Finally I   will discuss how LFSM gives the appearance of multi-affine scaling without having an  underlying turbulent cascade or other multiplicative  process. The importance of this property for the interpretation of natural time series will be discussed.