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Discrete scale invariance and stochastic Loewner evolution

Ghasemi Nezhadhaghighi, M ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevE.82.061101
  3. Publisher: 2010
  4. Abstract:
  5. In complex systems with fractal properties the scale invariance has an important rule to classify different statistical properties. In two dimensions the Loewner equation can classify all the fractal curves. Using the Weierstrass-Mandelbrot (WM) function as the drift of the Loewner equation we introduce a large class of fractal curves with discrete scale invariance (DSI). We show that the fractal dimension of the curves can be extracted from the diffusion coefficient of the trend of the variance of the WM function. We argue that, up to the fractal dimension calculations, all the WM functions follow the behavior of the corresponding Brownian motion. Our study opens a way to classify all the fractal curves with DSI. In particular, we investigate the contour lines of two-dimensional WM function as a physical candidate for our new stochastic curves
  6. Keywords:
  7. Brownian motion ; Complex systems ; Contour line ; Diffusion Coefficients ; Discrete scale invariances ; Fractal curves ; Fractal properties ; Large class ; Scale invariance ; Statistical properties ; Stochastic Loewner evolution ; Two-dimension ; Weierstrass-mandelbrot functions ; Brownian movement ; Invariance ; Partial discharges ; Stochastic systems ; Fractal dimension
  8. Source: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; 2010 , Volume 82, Issue 6 ; 15393755 (ISSN)
  9. URL: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.82.061101