| title: | Statistical topography for dynamical dissipative systems at self-organized criticality. |
|---|---|
| reg no: | ETF5036 |
| project type: | Estonian Science Foundation research grant |
| subject: |
1.1. Mathematics 2.3. Mechanics |
| status: | completed |
| institution: | Institute of Cybernetics at Tallinn Technical University |
| head of project: | Jaan Kalda |
| duration: | 01.01.2002 - 31.12.2004 |
| description: | The project addresses the generic geometrical aspects of dynamical dissipative systems at self-organized criticality. As a particular aim, it is to be shown that 1+1 dimensional [(1+1)D] and 2D rough surfaces belong to the same universality class. Also, the relationship between the scaling laws for (1+1)D and 2D mono-scale surfaces will be clarified. The fractal dimension of the "oceanic coastline" will be calculated numerically as a function of the roughness exponent H. The relationship between the scaling exponents describing the size-distribution of avalanches of dynamical processes on random surfaces (e.g. flooding a random surface with water) and various fractal dimensions of the contour loops of the random surface will be derived analytically. The statistical topography of gradient-limited surfaces will be studied. The relevance of the model of gradient-limited surfaces to the fracture surfaces will be clarified. Nonlinear time series (heart beat intervals, financial data) will be analysed using the measures of statistical topography. Multifractal properties of the geometric pattern of contour lines produced by passive scalar turbulence will be analysed. Wave propagation in complex solids with fractal interfaces will be studied analytically. Project as a whole helps to create a general approach to studying the geometrical aspects of systems at self-organized criticality. The research results will have environmental applications (problems related to the transport of contamination) and will help to enhance novel methods of heart rate variability analysis. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Jaan Kalda | Institute of Cybernetics, TTU | senior researher | |
| 2. | Robert Kitt | Tallinn Technical University | PhD student | |
| 3. | Maksim Säkki | Institute of Cybernetics, TTU | PhD student | |