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Uncertainty quantification for kinetic models in socio-economic and life sciences
Kinetic equations play a major rule in modeling large systems of interacting
particles. Recently the legacy of classical kinetic theory found novel
applications in socio-economic and life sciences, where processes characterized
by large groups of agents exhibit spontaneous emergence of social structures.
Well-known examples are the formation of clusters in opinion dynamics, the
appearance of inequalities in wealth distributions, flocking and milling
behaviors in swarming models, synchronization phenomena in biological systems
and lane formation in pedestrian traffic. The construction of kinetic models
describing the above processes, however, has to face the difficulty of the lack
of fundamental principles since physical forces are replaced by empirical
social forces. These empirical forces are typically constructed with the aim to
reproduce qualitatively the observed system behaviors, like the emergence of
social structures, and are at best known in terms of statistical information of
the modeling parameters. For this reason the presence of random inputs
characterizing the parameters uncertainty should be considered as an essential
feature in the modeling process. In this survey we introduce several examples
of such kinetic models, that are mathematically described by nonlinear Vlasov
and Fokker--Planck equations, and present different numerical approaches for
uncertainty quantification which preserve the main features of the kinetic
solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic
Equations
A statistical mechanics framework for the large-scale structure of turbulent von K{\'a}rm{\'a}n flows
In the present paper, recent experimental results on large scale coherent
steady states observed in experimental von K{\'a}rm{\'a}n flows are revisited
from a statistical mechanics perspective. The latter is rooted on two levels of
description. We first argue that the coherent steady states may be described as
the equilibrium states of well-chosen lattice models, that can be used to
define global properties of von K{\'a}rm{\'a}n flows, such as their
temperatures. The equilibrium description is then enlarged, in order to
reinterpret a series of results about the stability of those steady states,
their susceptibility to symmetry breaking, in the light of a deep analogy with
the statistical theory of Ferromagnetism. We call this analogy
"Ferro-Turbulence
Job Search Mechanism and Individual Behaviour.
This paper modelles job search mechanism at individual level by a determinstic-stochastic approach in a economy with perfect competion and rational agents. Each single unit, firm or worker, is analyzed over time; aggregate dynamics comes directly from the micro-structure of the economy. We show that the unemployment as well as vacancy rate converge in the long run to an ergodic distribution whose average value lies on the Beverdige curve. Transitional paths are not-monotone and depending on initial conditions. The micro-model is exploited to assess the relationship between job search and social networks (neighborhood effects); results show that, when the network is endogenous, such spillovers affect both transitional paths and steady state in several way, not last in a negative way.job-search, human capital, local effects
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