The purpose of this research is to investigate properties of diffusion processes
in porous media. Porous media are modelled by random Sierpinski carpets,
each carpet is constructed by mixing two different generators with the same
linear size. Diffusion on porous media is studied by performing random
walks on random Sierpinski carpets and is characterized by the random walk
dimension $d_w$.
In the first part of this work we study $d_w$ as a function of the ratio of constituents
in a mixture. The simulation results show that the resulting $d_w$ can
be the same as, higher or lower than $d_w$ of carpets made by a single constituent
generator. In the second part, we discuss the influence of static external
fields on the behavior of diffusion. The biased random walk is used to model
these phenomena and we report on many simulations with different field
strengths and field directions. The results show that one structural feature
of Sierpinski carpets called traps can have a strong influence on the observed
diffusion properties. In the third part, we investigate the effect of diffusion
under the influence of external fields which change direction back and forth
after a certain duration. The results show a strong dependence on the period
of oscillation, the field strength and structural properties of the carpet.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-201000205 |
| Date | 08 March 2010 |
| Creators | Ngoc Anh, Do Hoang |
| Contributors | TU Chemnitz, Fakultät für Naturwissenschaften, Prof. Dr. Karl Heinz Hoffmann, Prof. Dr. Guenter Radons, Prof. Dr. Karl Heinz Hoffmann, Prof. Dr. Guenter Radons, Prof. Dr. Karl Heinz Hoffmann |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, text/plain, application/zip |
| Rights | Dokument ist für Print on Demand freigegeben |
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