PORTALE DELLA DIDATTICA

Ricerca CERCA
  KEYWORD

Mean field dynamical models over large scale networks

keywords GRAPH, HYDRODYNAMIC LIMIT, INTERACTING AGENTS

Reference persons FABIO FAGNANI

Research Groups Analisi e controllo di sistemi dinamici

Thesis type THEORETICAL AND SIMULATION

Description Socio-economic, financial or infrastructural (electric grids, transportation) networks represent some of the most challenging and exciting multi-disciplinary scientific areas of these decades. They are of large scale, with a complex dynamical behavior emerging from the interconnection of relatively simple units. The presence of nonlinearities and stochastic effects, as well the complexity of the topology of interconnections make their analysis a formidable task and is catalyzing the energies of a large number of scientists with expertise ranging from economics, theoretical engineering, to mathematics and physics.

A successful approach to study such systems is the so-called mean-field approximation. It amounts to assume that each unit interacts with the rest of the network in a homogeneous 'average' way. This leads to an 'Eulerian point of view' analogous to the one undertaken in fluid dynamics: instead of following the evolution of each single unit, we describe the system through the evolution of a probability measure which takes into consideration the fraction of the population sharing a certain state. Moreover, we can perform the so-called hydrodynamic limit wich consists in taking the limit when the number of units N goes to infinity. Goal of this thesis is to study some specific mean field models.

See also  http://calvino.polito.it/~fagnani/topics%20PhD.html

Required skills graphs, probability, basic calculus, differential equations, Matlab


Deadline 27/06/2014      PROPONI LA TUA CANDIDATURA