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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. |
