We invite applications for a three-year postdoctoral research position, funded by the European Research Council Starting Grant awarded to Dr Radek Erban. The successful candidate will work with Dr Erban at the Oxford Centre for Collaborative Applied Mathematics (OCCAM) which is part of the Mathematical Institute, University of Oxford. The salary will be on Oxford's Grade 7 salary scale for academic-related staff (starting salary £28,839-£30,594). This position is available from 1st January 2010 or as soon as possible thereafter.
Project summary: Well-stirred chemical systems are traditionally simulated using deterministic (mean-field) models which are written in terms of ordinary differential equations (ODEs) describing the time evolution of concentrations of chemical species involved. A more detailed description of chemically reacting systems is given by the Gillespie stochastic simulation algorithm (SSA). The behaviour of the Gillespie SSA can be approximated by the chemical Fokker-Planck equation (CFPE), a partial differential equation (PDE) which gives a more detailed description than the mean-field ODEs (including a description of the noise). We will use the N-dimensional CFPE to investigate the differences between stochastic and deterministic models of systems of N chemical species (either by solving the CFPE numerically, or by asymptotic methods). The potential of numerical methods for solving high-dimensional PDEs (which are the subject of current research in numerical mathematics) will be explored for larger values of N. We will also investigate a multiscale method based on the n-dimensional effective Fokker-Planck equation (where n<<N can be detected by newly developed anisotropic diffusion maps). Its coefficients will be estimated by short bursts of appropriately initialized stochastic simulations. We will also investigate the conditions under which the multiscale approaches are accurate and efficient.
Applicants should have a PhD Degree (awarded or submitted at the time of taking up the position) in applied mathematics or related discipline together with familiarity of partial differential equations and experience of scientific computation. Experience with computer implementation and analysis of numerical methods for partial differential equations and background knowledge of modern approaches to multiscale computation is desirable.
Further particulars may be obtained from the Administrative Assistant at the Mathematical Institute, 24-29 St Giles', Oxford, OX1 3LB, email vacancies [-at-] maths [dot] ox [dot] ac [dot] uk and from the link below. Applications should include a Curriculum Vitae, a covering letter explaining your suitability for the position and how you meet the selection criteria, and the names and contact details of two referees. Applications must arrive by noon on Friday 27 November 2009. Ensure that you clearly quote the reference BK/09/032. Candidates should ask their referees to send their references directly to the Administrative Assistant, Mathematical Institute so that they arrive before the closing date. It is the responsibility of candidates to ensure that their references arrive by the closing date. Interviews for this position will be held on Tuesday December 15, 2009 (telephone interviews are possible).
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