|Modeling, Analysis, Control and Simulation in Science and Engineering|
|QPHASE: Classifying quantum phases of nature via PEPS|
|Sound Technologies for Reliable, Open, New Generation Software|
|DEC-HUMLOG: Decision Aid Models and Humanitarian Logistics|
|Studies of Mars|
|Non-linear and Geometric Functional Analysis|
|Game Theory and Applications|
|INVEDUMAT: Research in Mathematical Education at University Level|
|Non-specific interdisciplinary activities|
Most of the models the group is dealing with are given by nonlinear partial differential equations PDEs (purely deterministic or, sometimes, involving some stochastic terms).
A first set of aims of this Program deals with mathematical intrinsic techniques like the modelisation of complex systems through many different techniques: nonlinear analysis, homogenization of nonlinear PDEs, averaged process in nonlinear PDEs, decomposition methods for Numerical Analysis, stochastic equations, integro-differential equations, fractional equations, etc. These techniques are very powerful and generic tools that may find unexpected future applications.
Among the second block of aims consists of the application of the previous techniques to some of the above mentioned Prioritary Research Lines in the Regional, National and International calls such as, for example, Modelisation and Simulation of the Earth Climate System, Modelisation and Simulation of Elementary Particles and High Energy Physics. Applications to many other fields as, for instance, Chemical Engineering, Genetics or Economics are also regarded as future goals.
The last block of searches is the application of our techniques to problems Modelling and Simulation for Food Technologies, Medical Images and their processing.
Thus, the wide range of application goes from advance topics of the basic science (like Elementary Particles or Earth Sciences) to new technological fields with high sociological consequences (like Nuclear Fusion, Food Technologies, Animal Health or Medical Images).
Aims of the program:
Researchers: J. Ildefonso Díaz Díaz (Full Professor, Fac. Math. UCM)
Ángel M. Ramos del Olmo (Associate Professor, Fac. Math.UCM)
Gregorio Díaz Díaz (Full Profesor, Fac. Math.UCM)
Sixto Álvarez Contreras (Associate Professor, Fac. Chemistry UCM)
J. Antonio Infante del Río (Associate Professor, Fac. Math.UCM)
Benjamín Ivorra (Asistant Teacher, Fac. Math.UCM)
José Mª Rey Cabezas (Associate Professor, Fac. Chemistry.UCM)
Emmanuele Schiavi (Associate Professor, URJC)
José M. Vegas Montaner (Full Profesor, UCM)
External collaborators: H. Brezis (Rurgers University, USA), Roland Glowinski (University of Houston, USA), J.M. Rakotoson (Iniv. Poitiers), J. Hernández (Univ. Autónoma de Madrid), C, Cázquez (Univ. a Coruña), A. Fowler (Limerik Univ., Ireland), E. Sánchez-Palencia (Univ. Pierre et Marie Curie), S. N. Antontsev (Univ. Lisboa), P. Begout (Univ. Toulouse), Susana Gómez Gómez (Universidad Nacional Autónoma de México), Alain Rapaport and Jérôme Harmand (Institut National de Recherche en Agronomie, France) Profs. Hector Ramírez Cabrera and Pedro Gajardo (Universidad de Chile), several research groups from CSIC (National Council for Scientific Research) and INTA (National Institute for Aerospace Technology), Companies: Esteban Espuña, S.A. and NC Hyperbaric, Criovac,