Details of Grant 

EPSRC Reference:	EP/F031807/1
Title:	Anomalous Diffusion in Deterministic Systems
Principal Investigator:	Melbourne, Professor I
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Surrey
Scheme:	Standard Research
Starts:	30 October 2008	Ends:	29 October 2011	Value (£):	297,841
EPSRC Research Topic Classifications:	Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 29 Nov 2007 Mathematics Prioritisation Panel (Science) Announced
Summary on Grant Application Form
Certain gas models (planar periodic Lorentz flows) were introduced as deterministic models for Brownian motion. A statistical law called the almost sure invariance principle (ASIP) makes precise the connection with Brownian motion. Recent work established the ASIP for the Lorentz flow.Brownian motion has a characteristic growth rate of order sqrt t (square root of t ) where t denotes time. Currently, there is a great deal of interest in anomalous diffusion with a different growth rate. The aim of this project is the systematic study of anomalous diffusion (both subdiffusive and superdiffusive) in deterministic systems. In the superdiffusive (fast) case, this means proving the ASIP with Brownian motion replaced by a Levy process. In the subdiffusive (slow) case, we will focus on Sinai diffusion where the growth rate is of order (log t)^2.The results will apply to infinite horizon Lorentz gases and Bunimovich stadia. In addition, there are applications in dynamical systems with symmetry, including spiral waves in excitable media, and travelling waves.
Key Findings
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Potential use in non-academic contexts
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Impacts
Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk Summary Date Materialised
Sectors submitted by the Researcher
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Project URL:
Further Information:
Organisation Website:	http://www.surrey.ac.uk