Editeur
mijec
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Rapports de stage
The expected long time behavior of a solution of the spatially homogeneous Boltzmann equation seems to leave little room for imagination: if the initial datum has finite kinetic energy then as time t goes to the solution should converge to a Maxwellian distri bution In I thought about two related but seemingly more original problems One was the possibility to keep the energy finite but let time go to instead of then the asymptotic behavior looks a priori unclear but what is more there is good reason to suspect that there is no solution at all The other was to relax the assumption of finite energy and try to construct self similar solutions which would capture the asymptotic be havior of solutions with infinite energy and would play the role of the stable stationary laws in classical probability theory In a preliminary investigation it looked very reasonable to consider these problems in the simple setting of the spatially homogeneous Boltzmann equation with Maxwellian collision kernel
6 pages
English
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Etudes supérieures
DANIEL LÉVINE Université de Paris Sorbonne UFR d'Art et d'Archéologie rue Michelet Paris Courriel Daniel sorbonne fr Professeur l'Université de Paris Sorbonne titulaire de la chaire d'archéologie des civilisations de l'Amérique préhispanique Conseiller scientifique pour l'archéologie et les Instituts Français de Recherche l'Etranger au ministère de la recherche Direction de la Recherche SHS depuis Chargé de mission au cabinet du ministre délégué au tourisme de septembre Directeur adjoint de l'École Doctorale d'Archéologie et d'Histoire de l'Art de l'Université de Paris Sorbonne Co directeur du CRAP EA Centre de Recherche sur l'Amérique Préhispanique Équipe d'Accueil commune l'Université de Paris Sorbonne et l'École des Hautes Études en Sciences Sociales Membre de l'Unité Mixte de Recherche du CNRS Institut d'archéométrie Diplômes Licence maîtrise diplôme de l'Ecole Nationale des Langues
3 pages
Français
Documents
Rapports de stage
The morphology of built up landscapes in Wallonia Belgium a classification using fractal indices Abstract The spatial pattern of built up areas within a NUTS European region Wallonia in Belgium is analysed using fractal indices Methodologically this paper illustrates the usefulness of fractal indices in measuring built up morphologies and also shows that clustering techniques have to be adapted for the non Euclidean nature of the fractal measurements An expectation maximisation algorithm EM combined with a Bayesian information criterion BIC is used Empirically we show that fractal indices partition the region into sub areas that do not correspond to “natural landscapes” but result from the history of urbanisation Urban sprawl seems to affect most communes even the remotest villages: traditional compact ribbon etc villages are transformed into more complex and heterogeneous shapes These indices seem to be useful for characterising and understanding the built landscapes as well as for modelling and planning urban realities Keywords: fractal dimension built up geometry pattern analysis peri urbanisation Belgium
44 pages
English
