L’appel à projet:
Projet IMPULSION retenu dans le cadre de l’appel à projet 2018-2019 de l’I-Site FUTURE
The team is composed of researchers from different disciplines who share a common interest in multifractal analysis, and who want to improve the reliability and the scope of existing methods as well as to develop new ones to tackle specific issues related to their disciplines. Geographers and urban planners (LVMT, TheMA, Louvain, Groningen) have a long record in urban patterns analysis with fractal dimensions, as well as in using fractal geometry to support new urban planning concepts. The teams in LAMA (UPE), the Physics Dept. of ENS Lyon, the IRIT Laboratory in Toulouse and the Math. Dept. of Université de Clermont-Ferrand have developed theoretical and applied methods for fractal and multifractal analysis and have a long record of collaborations. Researchers in electrical engineering (G2elab) will provide their long-lasting expertise in multiscale modelling, analysis and optimal planning of power grids. The Hydrology Meteorology and Complexity (HM&Co) of ENPC will bring its expertise on theoretical multifractals applied across a large diversity of disciplines, with a focus on urban ones. EMGCU (IFSTTAR) brings its expertise on the modelling of dissipative and damaging effects in materials and structures, as well as in signal processing, mechanical and acoustic wave propagation and inverse problems in civil engineering.
Résumé du projet:
De nombreux problèmes urbains sont nettement multi-échelle, tant dans leurs dimensions techniques que dans leur mise en œuvre. Les fractales et l’analyse multi-fractale sont des approches qui ont prouvé leur pertinence pour analyser les systèmes urbains, ainsi que pour les optimiser. Cependant, l’analyse multifractale appliquée aux systèmes urbains soulève des problèmes, dont certains sont étudiés en ce moment par les mathématiciens. Ce projet a pour objectif de développer des boîtes à outils pour aider à résoudre ces problèmes, à savoir l’analyse mutlifractale sur des supports lacunaires, et l’analyse multifractale multivariée.
Abstract
Many urban problems are clearly across scales and multi-scale. Related to urban configuration and functionality, these challenges are either concerning a methodological-technical aspects or application. Since the early 1960s fractals and multifractals as multiscale approaches have proven an increasing interest to analyse urban systems as well as to optimize urban properties. However, application of multifractal analysis to urban systems raises some problems, some of which are currently investigated by mathematicians. This project aims at developing toolboxes to solve these issues namely multifractal analysis on lacunar supports and multivariate multifractal analysis.
Partenaires
Coordinateurs scientifiques du projet : Olivier Bonin, Laboratoire ville Mobilité Transport, LVMT, UMR ENPC, IFSTTAR, UPEM et Stéphane Jaffard, Laboratoire d’analyses et de mathématiques appliquées , LAMA UMR CNRS UPEC UPEM
Les personnels de recherche du projet : Gilles Vuidel, Corentin Regrain, Pierre Frankhauser (ThéMA), Stéphane Roux et Janka Lengyel (ENS Lyon), Olivier Bonin (LVMT) Stéphane Jaffard (LAMA)