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Documents  70G75 | enregistrements trouvés : 4

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Research schools;Partial Differential Equations;Mathematics in Science and Technology

Emergence is a process by which coherent structures arise through interactions among elementary entities without being directly encoded in these interactions. In this course, we will address some of the key questions of emergence such as the deciphering of the hidden relation between individual behavior and emergent structures. We will start with presenting biologically relevant examples of microscopic individual-based models (IBM). Then, we will develop a systematic coarse-graining approach and derive corresponding coarse-grained models (CGM) using mathematical kinetic theory as the key methodology. We will highlight that novel kinetic theory concepts need to be developed as new mathematical problems arise with emergent systems such as the lack of conservations, the build-up of correlations, or the presence of phase transitions (or bifurcations). Our goal is to show how kinetic theory can be used to provide better understanding of emergence phenomena taking place in a wide variety of biological contexts. Emergence is a process by which coherent structures arise through interactions among elementary entities without being directly encoded in these interactions. In this course, we will address some of the key questions of emergence such as the deciphering of the hidden relation between individual behavior and emergent structures. We will start with presenting biologically relevant examples of microscopic individual-based models (IBM). Then, we ...

70G75 ; 76Zxx ; 74L15 ; 92C10

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- 441 p.
ISBN 978-1-4020-6963-5

NATO science for peace and security series-B

Localisation : Ouvrage RdC (Hami)

système dynamique hamiltonien # mécanique des particules # forme normale Birkhoff pour EDP # méthode variationnelle # hydrodynamique eulerienne # invariant adiabatique # équation Navier-Stokes # équation Schrödinger non linéaire

37-06 ; 70-06 ; 70H11 ; 70G75

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- xx; 299 p.
ISBN 978-0-8218-9138-4

Student mathematical library , 0069

Localisation : Collection 1er étage

équation d'Euler-Lagrange # Hamilton # Jacobi # Maupertuis # systèmes Hamiltoniens # calcul des variations # théorie du contrôle

34-XX ; 37-XX ; 49-XX ; 70-XX ; 00A07 ; 70-01 ; 70Bxx ; 70MXX ; 70G75 ; 49S05 ; 49J40 ; 97M50 ; 00A79

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- x; 298 p.
ISBN 978-1-4704-1495-5

Student mathematical library , 0072

Localisation : Collection 1er étage

calcul de variations # brachistochrone # surface minimale # première variation # géodésique # contrainte # seconde variation # minimum faible # minimum fort

49-01 ; 00A05 ; 00A06 ; 00A69 ; 49J35 ; 49J40 ; 49S05 ; 97M50 ; 70G75

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