Partial Differential Equations in Science and Technology



Partial Differential Equations in Science and Technology
Some data
• IMI established in 2007 to foster
interdisciplinary research involving
• Funding 2009:
• Seeding money from UCM: 90.000 €
• Research grants from participants: 1.000.000 €
Operational structure
Director: Dr. Miguel Ángel Herrero
Secretary: Dr. Antonio Díaz-Cano
Manager: Marta Arregi
Management assistants:
Natividad López, Alba Táboas
Executive Committee
Scientific Programmes Coordinators
Scientific Programmes 2010-2011
Entanglement in Quantum Systems
Coordinator: David Pérez
Pure Interthematic Mathematics Coordinators: Jesús M. Ruiz
Francisco Romero,
Luis Giraldo.
Mathematics in Life and Social Sciences
Coordinator: Miguel A. Herrero.
Modelling and Simulation of Problems in Physics and Engineering Coordinators: J.I. Díaz, Á.M. Ramos, L. Vázquez
Decision and Information Technologies
Coordinator: Miguel A. Gómez‐Villegas.
Coordinator: David Pérez
p(ab | xy )
Main goal: To understand the difference between the correlations
achievable in quantum mechanics with respect to those coming
from classical mechanics.
Applications: communication technologies, complexity theory,
Main goal: to characterize the most intriguing global
quantum phases of nature (topological order, long-range
entanglement, percolation, …) in a local way, via the so
called Tensor Network States.
Main goal: To derive models for the formation of early vasculature in vertebrates using chick embryos as a model. Participants: A. Deutsch (Professor TU Dresden), A. Köhn (Graduate Student, UCM, Madrid), J.M. Pérez‐Pomares (Associate Professor, Universidad de Málaga).
Main goal: To derive and analyse mathematical models for the Blood
Coagulation Cascade in order to improve current antibleeding procedures.
Participants: Academic Partners: J.C. Carballo (Graduate Student, Universidad de la Habana), G. Guria (Professor, National Centre for Haematology, NCH, Moscow), K. Zlobina (Posdoc, NCH, Moscow)
Medical Partners: C. Altisent (MD, Hospital de la Vall d´Hebrò, HVH, Barcelona), E. Arellano (MD, HVH Barcelona) J. C. Souto (MD, Hospital Santa Creu i Sant Pau, HSC Barcelona), P. Fuentes (Ph. D, HSC Barcelona) Main goal: To derive integrated models for optimal radiation delivery which
focus on medical targets and minimize side effects.
Physical Planning
Anatomical data:
location, size, shape
Physical Plan:
HI=1.5-2.5, high DR
Participants: Academic Partners: J.C. López (Graduate Student, UCM).
Medical Partners: L. Nuñez (Ph. D, Hospital Universitario Puerta de Hierro, Madrid)
Main goal: To study mathematical models to describe the evolution of complex populations subject to resource competition under the action of global constraints.
Participants: J. C. Nuño (Universidad Politécnica de Madrid , M. Primicerio (Universitá di Firenze , Italy). MATPUR
Pure Interthematic Mathematics
Jesús Ruiz (UCM), Francisco Romero
(UCM), Luis Giraldo (UCM)
Dynamics and geometry: three approaches
MATPUR aims to be centered around topics that even when included in the realm of pure mathematics, are relevant for applications and for the development of other scientific areas.
Aims of the concentration period
We will carry out a series of activities centered around dynamics and geometry, considered from different perspectives: topological and holomorphic dynamics, foliations and flow quasi‐invariant sets in classical and quantum mechanics.
Dynamics and geometry: three approaches
The activities are being developed with the support of several funding agencies and involve researchers from a number of Spanish and foreign universities.
Topics of the concentration period
Quasi‐invariant sets under the flow of a dynamical systema in classical and quantum mechanics. Organizer: Daniel Azagra (UCM).
Participants include: L. Vega (EHU‐UPV, Spain), F. Macià (UPM, Spain), A. Davini (Rome, Italy), A. Fathi (Lyon, France), R. Pérez Marco (CNRS, France).
Plane dynamics. Organizer: Francisco Romero (UCM).
Participants include: M. Barge (Montana, USA), P. Le Calvez (Paris 13, France), R. Ghrist (Illinois, USA), M. Haendel (CUNY, New York, USA).
Holomorphic foliations and dynamics in complex manifolds. Organizer: Luis Giraldo (UCM).
Participants include: R. Pérez‐Marco (CNRS, France), J.V. Pereira (IMPA, Brazil), J.E. Fornaess (Michigan, USA), S. Cantat (Rennes 1, France), M. Brunella (Bourgogne, France).
Some research lines included and scientists in charge
Differential geometry and systems symmetry (J.M. Ancochea)
Geometry of projective varieties (E. Arrondo)
Algebraic and real analytic geometry (A. Díaz-Cano)
Functional spaces, operators and applications (F. Hernández)
Non-linear functional analysis (J.A. Jaramillo)
Singularity theory and its applications in arithmetics, cryptography,
geometry and topology (I. Luengo)
Shape theory and topological dynamics (F. Romero)
Modelling and Simulation of Problems in
Physics and Engineering
Jesús Ildefonso Díaz (UCM); Ángel M.
Ramos (UCM); Luis Vázquez (UCM)
Exploration of Mars
Fractional Calculus and Applications
Fronts and Interfaces in Science and Technology
High Pressure Processes and Food Engineering
Mathematical modeling in Animal Health
Partial Differential Equations in Science and Technology
Partial Differential Equations in Science and Technology (J.I. Díaz)
Universidad Complutense de Madrid (Applied Mathematics and Astronomy and Geodesy)
Universidad Politécnica de Madrid (ETS Arquitectura)
Universidad Autónoma de Madrid (Mathematics)
Universidad Rey Juan Carlos (Applied Mathematics, Medical Images Institute)
Fronts and Interfaces in Science and Technology (FIRST)
Initial Training Networks of the European Commission (Grant Agreement Number 238702), SEVENTH FRAMEWORK PROGRAMME, PEOPLE Work Programme 2008 ”, from January 1, 2010 to December 31, 2013. Coordinator: J.I. Díaz, UCM
Partial Differential Equations in Science and Technology (J.I. Díaz)
Some research topics
1. Models on Natural Resources (Climatology, Glaciology and Geodesy). • Coupling between climate (models of energy balance with a deep ocean) and the dynamics of polar icecaps (in Glaciology).
• Socio‐economic aspects of environmental management,
• Gravity determination (Problem of Backus) in Geodesy
• Non‐deterministic climate models (volcanoes). • Formation of river basins. • Plant community patches as localized solutions of a reaction‐diffusion system (desertification process in southern Spain: a World Coordination
Center for the study of desertification is established in Almeria).
Partial Differential Equations in Science and Technology (J.I. Díaz)
2. Problems arising in Elasticity. • Structures like thin shells and homogenization (Torroja roof of the Hipódromo de la Zarzuela)
• Singular perturbation problems leading to complexification phenomena arising in certain types of thin elastic shells (unusual solution to the limit problem: it is outside the area of distributions). • Coulomb dry friction and their properties. • Best column (according Euler), • Deformation of the Earth strata by the gravity and magma actions (appearing in Geodynamics)
• Viscoelastic materials with memory
High Pressure Processes and Food Engineering (A.M. Ramos)
The aim of the project is to develop mathematical models to simulate high pressure processes, mainly in the Food Engineering sector, where a new emerging technology, based on hydrostatic high pressure, is being used in order to extend food shelf life, preserving organoleptic (flavour, colour, etc...) and nutritional properties. Aims
Modelling the effects of temperature and Hydrostatic High pressure on microorganisms and enzymes.
Solving related inverse problems
Numerical simulation
Optimization and control of processes
Research Groups at UCM (PI: V. García Baonza; A. Rey); Institute of Refrigeration (CSIC) PI: P. Dimas Sanz Martínez; Institution Nacional de Técnica Aeroespacial (INTA) PI: O. Prieto; Institute of Material Science of Madrid (CSIC). PI: J. Sánchez; companies: Esteban Espuña, S.A.; NC Hyperbaric.
Mathematical modelling in Animal Health (A.M. Ramos)
The project aims at developing models able to simulate the evolution of epidemics in Farm animals. For instance we consider the case of Classical Swine Fever Virus (CSFV). Topics
Modelling the evolution of epidemics in Farm animals. Solving related inverse problems. Optimization and control of processes. Development of software for decision making tasks in Government agencies. Network
Research Group MOMAT (PI: J.I. Díaz; A. M. Ramos); Spanish National project MTM2008‐04621/MTM (PI: A.M. Ramos)
Research Group in the Animal Health Department in School of Chemistry at Universidad Complutense de Madrid. PI: José Manuel Sánchez‐Vizcaíno; Spanish Ministry of Agriculture, Fishing and Food (MAPA), PI: Lucio Carbajo Goñi (General Subdirector of Animal Health) Mars MetNet (Meteorological Network) Precursor Mission
Mission Director
Dr. Héctor Guerrero Padrón
Mission Scientific Director
Prof. Luis Vázquez Martínez
Mars MetNet Precursor Mission (L. Vázquez)
We are participating in the first mission to Mars with Spanish flag (Scientific Director: Prof. Luis Vázquez), Meiga‐(Mars Environmental Instrumentation for Ground and Atmosphere) Mars‐MetNet (Meteorological Network) Precursor Mission.
It is a joint mission with Russia and Finland, and will be launched in 2011. Its aim is to place a meteorological station over the surface of Mars. The program is to place in Mars 16 meteorological stations.
Fractional Calculus (L.Vázquez)
Framework The framework of the project is to carry out analytical and numerical basic studies of fractional systems. On the other hand, we consider the application of such systems to technological environments as the
materials with shape memory
Aims of the program
To study the transition from parabolic to hyperbolic behaviour using fractional derivative.
To analysis the symmetries associated to fractional differential
Numerical schemes associated to fractional differential equations.
Applications of fractional models in different scientific and technological contexts
Information and Decision Technologies
Miguel Ángel Gómez-Villegas
Research topics
Game theory
Bayesian methods
Problems related to preferences representation
Software design
Fuzzy decision methods
Algorithmic Complexity Some research lines
and scientists in charge
Computer algebra in artificial intelligence (E. Roanes, UCM)
Formal Analysis and Design of Software Systems, FADoSS (N. Martí, UCM) z
Game theory and applications (J. Tejada, UCM)
Bayesian methods (M.A. Gómez‐Villegas, UCM)
Decision Aid Systems (J. Montero, UCM)
Some research lines
and scientists in charge
Mathematical models to assisst in decision making in natural disasters (B. Vitoriano, UCM)
WSO‐UV World Space Observatory – Ultraviolet (Europe – Russia research project) (A.I. Gómez de Castro, UCM)
DESAFÍOS: High quality software development (N. Martí, UCM) z
Aid decision systems under linguistic uncertainty (J. Montero, UCM)