| EPSRC Reference: |
EP/M002896/1 |
| Title: |
Random Fractals |
| Principal Investigator: |
Belyaev, Dr D |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
EPSRC Fellowship |
| Starts: |
01 October 2014 |
Ends: |
30 September 2019 |
Value (£): |
847,723
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Statistics & Appl. Probability |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
The proposed research is in Pure Mathematics, namely on the border of Complex Analysis, Probability, and Mathematical Physics. I will mostly study random fractal structures and use them to study important models of Statistical Physics. Fractals are self-similar structures that look the same at all places and on all scales. They appear everywhere in nature, notable examples are Romanesco broccoli, shorelines, lightnings, and sea shells. They also appear in many models of statistical physics that describe such phenomena as magnetism, flow of fluid through porous matter, spread of epidemics, robustness of networks and many others. One of the fundamental parameters of fractal structures is the dimension. Roughly speaking it describes the growth rate of the fractal structures. For example a straight interval of diameter N, which is made of the particles of unit size, contains N particles. We say that the interval has dimension 1. The square of size N contains N squared particles and has dimension 2. The characteristic property of fractal structures is that the structure of size N contains approximately N^d particles where 1
Except fractals that appear from physics lattice models, similar fractals are important in various areas of pure mathematics. A notable example is the area of mathematics which is called Complex Analysis. It turned out that the objects that maximize various quantities of interest must be of fractal nature. It turned out that it is very difficult to study these fractals since we don't have a good description of their structure. Here randomness comes into play in a seemingly paradoxical way: we introduce artificial randomness to simplify computations.
The proposed research will develop novel methods to study and describe growing random structures and apply these methods to fractals that appear in Analysis, Probability, and Mathematical Physics.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ox.ac.uk |