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Seminar on Stochastic Processes, 2000 Anomalously Slow Diffusion and Homogenisation on Infinitely Many Scales
| Content Provider | Semantic Scholar |
|---|---|
| Author | Arous, Gérard Ben |
| Copyright Year | 2000 |
| Abstract | It is now well known that natural Brownian motions on various fractal structures are anomalously slow. In this joint work with Houman Owhadi (EPFL) we try to understand the basic mechanisms of anomalously slow diusion. These mechanisms are well understood for very regular strictly self-similar fractals. The archetypical specic example of a deep problem being the one solved by Barlow and Bass on the Sierpinski Carpet (which is innitely ramied, a codeword for hard to understand rigorously). It appears that the main feature is the existence of an innite number of scales of obstacles (with proper size) for the diusion. We show that this last feature is the key for the possibility of anomalous diusion, in a general context (without any local symetries as those of the Sierpinski Carpet), using the tools of homogenisation. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.utah.edu/~davar/ba.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
