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EPSRC Reference: EP/D025842/1
Title: Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena
Principal Investigator: Gorban, Professor A
Other Investigators:
Stuart, Professor A Theodoropoulos, Professor C
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: University of Leicester
Scheme: Mathematics Small Grant PreFEC
Starts: 08 August 2005 Ends: 07 January 2006 Value (£): 4,650
EPSRC Research Topic Classifications:
Continuum Mechanics Non-linear Systems Mathematics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
The problem of model reduction is one of the central problems in multiscale modelling that has recently attracted much attention from the research community across a number of disciplines ranging from applied mathematics to physics, biology and engineering. It has many different aspects and many versions of problem statements and solution methodologies have been created to answer the recent challenges of natural sciences and engineering, from fluid dynamics and chemical engineering to system biology. Coarse-graining theories and computational approaches are becoming a subject of intense research efforts. Such methods provide an effective route for constructing multi-scale models, in other words models which computationally couple phenomena occurring at different scales (macroscopic and microscopic ones). Special efforts are needed to collect the results obtained for different specific problems in different directions into an entire complete toolbox that can be used for model reduction and coarse-graining purposes.The main mission of the Workshop is to create a meeting point between researchers from a wide range o disciplines where knowledge about model reduction and coarse-graining for multiscale phenomena will be constructed, obtained and advanced through the dissemination of particular research efforts and achievements.The theme of the workshop is deliberately broad in scope and aims to promote a vigorous exchange of new ideas and fresh methodological perspectives in the increasingly important area of model reduction and coarse graining for multiscale phenomena through a number of dissemination approaches ranging from formal plenary and regular presentations to informal open-ended discussions. The main thematic areas of the workshop in theoretical and computational approaches are:1. Invariance and model reduction: 1.1. Invariant manifolds for ODE and PDE, 1.2. Perturbation theory and application for model reduction, 1.3. Geometric singular perturbations;2. Coarse-graining approaches: 2.1. Microscopic dynamics and macrodynamics extraction, 2.2. Renormalisation group method, 2.3. Turbulence modelling and subgrids approximations;3. Accuracy estimation and post-processing algorithms.Specific areas of study represented in the workshop include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, particulate systems, nonlinear dynamics, nonlinear control, and nonlinear estimation.The Workshop will constitute a step in collecting and advancing the knowledge generated on model reduction and coarse-graining for multiscale phenomena construction through the dissemination of research results and efforts. This new synthesis will be presented in the published Workshop materials and in the future work and publications of the participants. As a future perspective we envisage the formation of a new discipline in applied mathematics education, along with the preparation of a relevant textbook.
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Organisation Website: http://www.le.ac.uk