SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 45: Poster: Nonlinear Dynamics, Pattern Formation and Networks

DY 45.11: Poster

Donnerstag, 30. März 2023, 13:00–16:00, P1

Randomised mixed labyrinth fractals — •Janett Prehl¹, Ligia Loretta Cristea², and Daniel Dick¹ — ¹Technische Universität Chemnitz, Chemitz, Germany — ²Technische Universität Graz, Graz, Austria

Fractals, introduced by Benoit Mandelbrot in the early 1980s, allow the analysis of physical properties of natural geometries and structures in non-integer dimensions. It has been shown recently, that utilizing fractals structures, for instance for gas sensors made of carbon nanotubes increase their efficiency or give new insights to complex quantum phenomena. Here, we are interested how the effect of randomness, as observed in real materials, alter the topology and thus dynamics of the resulting fractal structures in comparison to the pure cases. We focus on a special class of Sierpinski carpets, i.e., the labyrinth fractals [1], that can be used for dendritic networks or porous materials. Therefore, we mix to fractal patterns, with different properties, i.e., shortest path and random walk dimension, randomly together at different mixing ratios. Surprisingly we found that even in cases where the initial patterns exhibit the same non-integer dimensions the resulting randomised fractals give a different property [2].
[1] L.L. Cristea and B. Steinsky, Proc. Edinburgh Math. Soc. 54.4 (2011) 329.
[2] J. Prehl, D. Dick, and L.L. Cristea, to be submitted to Fractals (2023).