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Details of Grant 

EPSRC Reference: EP/C531531/1
Title: Solvent Models
Principal Investigator: Theil, Dr F
Other Investigators:
Researcher Co-Investigators:
Project Partners:
University of Warwick
Department: Mathematics
Organisation: University of Warwick
Scheme: Springboards Scheme (Pre-FEC)
Starts: 01 October 2005 Ends: 30 September 2006 Value (£): 36,454
EPSRC Research Topic Classifications:
Non-linear Systems Mathematics Numerical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
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Panel History:  
Summary on Grant Application Form
Computer based simulation of molecules has become a corner stone of disciplines like Molecular Biology. The reasor is that on a molecular level even very complex biological or chemical systems can be described by extremely simple mathematical equations which can be approximately solved on modern computers. This precision comes at a huge prize: Even in simple applications the number of degrees of freedom (positions and velocities of the nuclei, distribution of the electric charges exceed easily 1-million with the consequence that it is not possible to simulate over longer time periods than 1 nanosecond (1 billionth of a second). It turns out that most of the degrees of freedom (in particular the solvent molecules) are not doing anything interesting except wriggling around. On this background, it is quite comprehensible that in typical simulations only 1% of the computer time is spent on the object of interest, 99% of the time goes into the simulation of water! If it would be possible to extract the essential degrees of freedom and neglect the irrelevant stochastic motion the number of accessible systems and the size of accessible time intervals could be dramatically increased.In order to bridge the gap between computationally accessible and scientifically relevant scales many ingenious approaches have been suggested. Typically one replaces the discrete (atomistic) solvent by continuum models which are mathematically extremely well understood. In particular, highly efficient methods for computing approximative solutions have been developed over the last 200 years. The downside of continuum theories is that while they are typically unbeatable at describing long range interactions the are necessarily inaccurate at short distances.The aim of the proposal is to provide quantitative links between the world of discrete (atomistic) models and continuum theories. This research will provide(1) A quantitative understanding of the domains of validity of the existing continuum models for solvents. (2) A framework in which allows the systematic derivation of corrections.(3) New improved effective solvent models which describe discreteness effects such as surface relaxation. Without a proper theoretical understanding these corrections cannot be guessed.The potential benefits are big since solvents are universal in the sense that every improvement will influence many different systems. The research will profit practitioners working in Molecular Dynamics since it clarifies error sources in traditional approaches and lead to the new efficient models. Another group of beneficiaries are applied mathematicians. Atomistic models have not received much attention in the mathematical literature due to a lack of challenges and methods. The research will change the situation and initiate new research on discrete equations.
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Organisation Website: http://www.warwick.ac.uk