Anomalous diffusion and random walks on random fractals [Elektronische Ressource] / vorgelegt von: Ngoc Ang, Do Hoang

Anomalous diffusion andrandom walks on randomfractalsvon der Fakult¨at fu¨r Naturwissenschaftender Technischen Universitat Chemnitz¨genehmigte Dissertation zur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)vorgelegt von BSc. Ngoc Anh, Do Hoanggeboren am 16. Aug 1979 in Hanoi, Vietnameingereicht am 17. Nov 2009Gutachter: Prof. Dr. Karl Heinz HoffmannProf. Dr. Gu¨nter RadonsTag der Verteidigung: 05. Feb 201023Bibliographische BeschreibungDo Hoang,Ngoc AnhAnomalous diffusion and random walks on random fractalsTechnische Universit¨at Chemnitz, Fakulta¨t fu¨r NaturwissenschaftenDissertation, 2009 (in englischer Sprache)103 Seiten, 67 Abbildungen, 62 Abbildungen im Text, 54 LiteraturzitateAbstractThe purpose ofthis research is toinvestigate properties ofdiffusion processesin porous media. Porous media are modelled by random Sierpinski carpets,each carpet is constructed by mixing two different generators with the sa-me linear size. Diffusion on porous media is studied by performing randomwalks on random Sierpinski carpets and is characterized by the random walkdimension d .wIn the first part of this work we study d as a function of the ratio of consti-wtuents in a mixture. The simulation results show that the resulting d canwbe the same as, higher or lower thand of carpets made by a single constitu-went generator. In the second part, we discuss the influence of static externalfields on the behavior of diffusion.