MODySIM. MODELISATION AND SIMULATION OF SOME PROBLEMS OF PHYSICS AND ENGINEERING.

The aims of our research program are related to the basic philosophy of MODELISATION and SIMULATION. This orientation is the Point 9.1 between the Prioritary Research Lines designed by the IV PRICIT program for Spatial Sciences, Physics and Mathematics, it is also an Strategic Research Line of Universidad Complutense de Madrid and it is a frequent thema in the Framework Programs of the UE and the NSF of the USA.

Most of the models considered are given by nonlineal EDPs and sometimes by stochastics equations. The joint of the two UCM Research Groups collaborating in our program and their rich staff (with researchers from other departments of the UCM, other Universities in the neighborhood of Madrid the and CSIC) allow to attack a big set of complex problems that will otherwise hardly be reachable without this cooperation.

A first set of aims deals with mathematical intrinsic techniques like the modelisation of complex systems through homogenization of nonlinear EDPs, average process in nonlinear EDPs, decomposition methods for Numerical Analysis, Neuronal Networks in nonlinear EDPs, stochastic equations, fractional equations... The importance is obvious because these techniques are generic tools that may find unexpected future applications.

A second block of aims is the application of the previous techniques to the above mentioned Prioritary Research Lines for Spatial Sciences, Physics and Mathematics; for example, Modelisation and Simulation of the Earth Climate System and Modelisation and Simulation of Elementary Particles and High Energy Physics.

The last block searchs the application of our techniques to problems from other Prioritary Research lines. It deals with Modelisation and Simulation for Food technologies and for Medical Images and their procesing.

Thus, the wide range of application goes from advance topics of basic science (like Elementary Particles or Earth Sciences) to new technological fields with high sociological consequences (like Nuclear Fusion, Food Technologies or Medical Images). Please note that not all these topics have been considered by other new and near institutions or projects like Consolider Mathematica, IMDEA Mathematics or ICM.

The researchers team involved in the project come mainly from the Applied Mathematics Department of the UCM but, as above mentioned, there are as well researchers from other departments of the UCM, other Universities in the neighborhood of Madrid and from the CSIC. In some sense, to the research experience of the Applied Mathematics Department of the UCM one should add the solid contacts with researchers from the UPM (specially the prestigous research group of Amable Liñan) and other contacts with the National Institute of Metereology, Ciemat, Institute of Coolness, Institute of Astronomy and Geodesy (UCM and CSIC), "La Paz" Hospital, Medical Image Analysys and Biometrics Lab of the Universidad Rey Juan Carlos, Astrobiology Institute (NASA-INTA), INRIA (France), IMA (USA), OXford Mathematics Institute and the Center for Computational Science and Engineering of the University of California at Davis.

The contact with different industries like “GEC ALSTHON ACB”, “Esteban Espuña S.A.”, “Helados y postres, S.A. (Helados Miko)” y “Advanced Dynamics, S.A.” allow us to test our models, what plays a crucial role in our research activity.

Key words: Modelisation, Numeric Simulation, Inverse problems, Finite Elements Method, Climatology, Nuclear fusion, Freezing, High Preasure, Image Processing, Lubrication, Fractional Equations and Stochastic Equations.