DESIGN AND OPTIMISATION OF NON-LOCAL DIFFUSE MODELS APPLIED TO BIOENGINEERING (Q3149649)
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Project Q3149649 in Spain
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | DESIGN AND OPTIMISATION OF NON-LOCAL DIFFUSE MODELS APPLIED TO BIOENGINEERING |
Project Q3149649 in Spain |
Statements
23,716.0 Euro
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29,645.0 Euro
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80.0 percent
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1 January 2018
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31 December 2021
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UNIVERSIDAD DE CASTILLA-LA MANCHA
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45168
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EL OBJETIVO ES EL ESTUDIO DE LA MODELIZACION DE FENOMENOS RELACIONADOS CON LA DIFUSION DENTRO DEL CONTEXTO GENERAL DE LA BIOINGENIERIA. EL PUNTO DE PARTIDA ES EL PLANTEAMIENTO NO LOCAL DE LAS ECUACIONES DE DIFUSION Y LA INCORPORACION A ESTAS DE DIFERENTES TERMINOS AL OBJETO DE CONTROLAR DE FORMA OPTIMA UN SISTEMA BIOLOGICO. LA JUSTIFICACION FISICA DEL PLANTEAMIENTO DE LAS ECUACIONES, LA INCORPORACION DE CONTROLES, COEFICIENTES O FUNCIONES QUE ACTUARAN NORMALMENTE EN LA FRONTERA DEL DOMINIO, Y LA ADECUACION DE UN FUNCIONAL COSTE A UN OBJETIVO CONCRETO, SON LOS ELEMENTOS QUE CONFORMARAN NUESTRO PROBLEMA DE CONTROL. LA DEPENDENCIA CONTINUA DE PARAMETROS O UN ESTUDIO CUALITATIVO COMPLETO DE LAS ECUACIONES DE ESTADO, ASI COMO UNA METODOLOGIA NUMERICA EN LA RESOLUCION DE LAS MISMAS SERAN IMPRESCINDIBLES PARA HACER VIABLE NUESTRO ESTUDIO. DE MANERA PARALELA Y DENTRO DEL MARCO NO LOCAL, DIRIGIEREMOS GRAN PARTE DE NUESTROS ESFUERZOS A LA MODELIZACION DE LOS DISTINTOS TIPOS DE DIFUSION, PRESTANDO ESPECIAL ATENCION A LAS SITUACIONES DE DIFUSION ANOMALA O TURBULENTA. SE ENSAYARAN NUMERICAMENTE VARIOS MODELOS, USANDO PARA ELLO DISTINTOS TIPOS DE COEFICIENTES. ESTO SE HARA CON EL OBJETO DE REPRODUCIR LOS RESULTADOS YA CONOCIDOS Y QUE FUERON OBTENIDOS A TRAVES DE LOS COMPLEJOS SISTEMAS CLASICOS DE ECUACIONES EN DERIVADAS PARCIALES._x000D_ _x000D_ EL AREA GENERICA EN EL QUE ENCUADRAR ESTA INVESTIGACION ES EL DE LA MODELIZACION Y OPTIMIZACION MATEMATICA DE SISTEMAS GOBERNADOS POR ECUACIONES DE DIFUSION. LOS ELEMENTOS QUE MOTIVAN ESTA INVESTIGACION SON LA MODELIZACION NO LOCAL Y EL ANALISIS DE PROBLEMAS DE CONTROL OPTIMO EN DICHO CONTEXTO. EN LO QUE CONCIERNE A LA ECUACION DE ESTADO, SE PRETENDE MODELIZAR DISTINTOS TIPOS DE DIFUSION, HACIENDO PARA ELLO USO DE DISTINTOS NUCLEOS Y DISTINTOS TIPOS DE COEFICIENTES DE DIFUSION. A SU VEZ, SE INTRODUCEN DISTINTOS CONTROLES EXTERNOS AL OBJETO DE CONTROLAR LA DINAMICA DEL SISTEMA, SE DEFINE UN COSTE NO LOCAL, EN GENERAL, Y SE ESTUDIA EL PROBLEMA DE CONTROL OBTENIDO. _x000D_ EL FIN PRACTICO ES CIMENTAR DE MANERA RIGUROSA LA MODELIZACION DE SISTEMAS DE ECUACIONES QUE DESCRIBAN LOS MECANISMOS DE TRANSPORTE DE MASA. LA APUESTA O HITO FINAL PODRIA RESUMIRSE COMO LA EFICIENCIA DE UN MODELO NO LOCAL DIFUSIVO Y EL CONTROL DEL MISMO PARA LA MODELIZACION DE UN SISTEMA COMPLEJO, COMO EL QUE SE ESTABLECE POR EJEMPLO CON EL TRANSPORTE DE FARMACOS EN EL INTERIOR DE UN SISTEMAS BIOLOGICO. (Spanish)
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THE OBJECTIVE OF THIS PROJECT IS THE MATHEMATICAL MODELING AND THE STUDY OF DIFFUSION-RELATED PHENOMENA WITHIN THE CONTEXT OF BIO-ENGINEERING. OUR STARTING POINT IS THE NON-LOCAL FORMULATION OF DIFFUSION EQUATIONS; IN THIS FRAMEWORK, WE PROPOSE VARIATIONS OF THE CLASSICAL EQUATIONS AIMED TO PROVIDE AN OPTIMAL CONTROL OVER A BIOLOGICAL SYSTEM. TO ACHIEVE THIS, WE WILL CONSIDER EQUATIONS WHICH INCLUDE ADDITIONAL TERMS IN THE FORM OF CONTROLS, COEFFICIENTS OR FUNCTIONS ACTING ON THE BOUNDARY OF THE DOMAIN, AS WELL AS APPROPRIATE COST FUNCTIONALS. IN DOING THIS, WE WILL PAY SPECIAL ATTENTION TO SUPPLY AN ADEQUATE JUSTIFICATION FROM THE PHYSICS PERSPECTIVE. WE WILL NEED A COMPLETE STUDY OF THE QUALITATIVE PROPERTIES OF THE SYSTEMS THAT WE STUDY, AS WELL AS AN ANALYSIS OF THE CONTINUOUS DEPENDENCE OF THE PARAMETERS INVOLVED, TOGETHER WITH THE WELL-POSEDNESS OF THE MODELS AND THE DEVELOPMENT OF NUMERICAL SCHEMES TO SOLVE THEM. AT THE SAME TIME, AND WITHIN THE NON-LOCAL FRAMEWORK, WE WILL FOCUS ON THE MODELING OF PROCESSES ASSOCIATED WITH DIFFERENT KINDS OF DIFFUSION, PUTTING SPECIAL EMPHASIS ON THOSE SITUATIONS WHERE ANOMALOUS DIFFUSION OR TURBULENCE IS INVOLVED. ONCE THE DIFFERENT MODELS ARE FORMULATED, WE WILL STUDY NUMERICALLY THE BEHAVIOR OF THEIR SOLUTIONS AND HOW DO THEY DEPEND ON THE AFOREMENTIONED COEFFICIENTS AND CONTROLS, VERIFYING THAT WE ARE ABLE TO ACCURATELY REPRODUCE LONG ESTABLISHED RESULTS. _x000D_ THE RESEARCH TO BE PERFORMED IN THE CONTEXT OF THIS PROJECT BELONGS TO THE GENERAL AREA OF MATHEMATICAL MODELING AND OPTIMIZATION OF SYSTEMS GOVERNED BY DIFFUSION EQUATIONS. THIS RESEARCH IS MOTIVATED BY THE INTEREST IN THE NON-LOCAL MODELING AND THE ANALYSIS OF OPTIMA CONTROL PROBLEMS THAT ARISE IN THIS CONTEXT. CONCERNING THE STATE EQUATION, WE WILL MODEL THE DIFFERENT TYPES OF DIFFUSION THROUGH THE USE OF DIFFERENT INTERACTION KERNELS AND DIFFUSION COEFFICIENTS. IN TURN, AND WITH THE AIM OF CONTROLLING THE DYNAMICS OF THE SYSTEM, WE WILL PROPOSE THE USE OF DIFFERENT EXTERNAL CONTROLS AND NON-LOCAL COST FUNCTIONS, AND STUDY THE ASSOCIATED OPTIMAL CONTROL PROBLEM._x000D_ FROM THE PRACTICAL POINT OF VIEW, OUR GOAL IS TO STRENGTHEN THE HABIT OF RIGOROUS MATHEMATICAL MODELING OF THE MECHANISMS OF MASS TRANSPORTATION. WE WANT TO FORMULATE A NON-LOCAL DIFFUSIVE EQUATION AND AN ASSOCIATED CONTROL IN ORDER TO EFFICIENTLY MODEL A COMPLEX SYSTEM, SUCH AS THE TRANSPORT OF DRUGS INSIDE A BIOLOGICAL SYSTEM. (English)
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Toledo
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Identifiers
MTM2017-87912-P
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