Benedetto Piccoli
Transport equation with nonlocal velocity in Wasserstein spaces: existence, uniqueness and numerical schemes.
Wed, 06/15/2011 - 15:01 — SomNambulAuthors: Benedetto Piccoli, Francesco Rossi
Subjects: Analysis of PDEs
AbstractMotivated by pedestrian modelling, we study evolution of measures in the
Wasserstein space. In particular, we consider the Cauchy problem for a
transport equation, where the velocity field depends on the measure itself. We
prove existence and uniqueness of the solution under Lipschitzianity of the
velocity with respect to the Wasserstein distance. We also deal with numerical
schemes for this problem. We prove convergence of a Lagrangian scheme to the
solution, when the discretization parameters approach zero.Multiscale modeling of granular flows with application to crowd dynamics.
Fri, 06/04/2010 - 15:01 — SomNambulAuthors: Emiliano Cristiani, Benedetto Piccoli, Andrea Tosin
Subjects: Mathematical Physics
AbstractIn this paper a new multiscale modeling technique is proposed. It relies on a
recently introduced measure-theoretic approach, which allows to manage the
microscopic and the macroscopic scale under a unique framework. In the
resulting coupled model the two scales coexist and share information. This
allows to perform numerical simulations in which the trajectories and the
density of the particles affect each other. Crowd dynamics is the motivating
application throughout the paper.Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints.
Mon, 10/26/2009 - 14:11 — SomNambulAuthors: Emiliano Cristiani, Benedetto Piccoli, Andrea Tosin
Subjects: Mathematical Physics
AbstractThis paper is concerned with mathematical modeling of intelligent systems,
such as human crowds and animal groups. In particular, the focus is on the
emergence of different self-organized patterns from non-locality and anisotropy
of the interactions among individuals. A mathematical technique by
time-evolving measures is introduced to deal with both macroscopic and
microscopic scales within a unified modeling framework. Then self-organization
issues are investigated and numerically reproduced at the proper scale,
according to the kind of agents under consideration.Effects of anisotropic interactions on the structure of animal groups.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Emiliano Cristiani, Paolo Frasca, Benedetto Piccoli
Subjects: Dynamical Systems
AbstractThis paper proposes an agent-based model which reproduces different
structures of animal groups. The shape and structure of the group is the effect
of simple interaction rules among individuals: each animal deploys himself
depending on a limited number of neighboring group mates. The proposed model is
shown to produce clustered formations, as well as lines and V-like formations.
The key factors which trigger the onset of different patterns are argued to be
the relative strength of attraction and repulsion forces, and most important,
the anisotropy in their application.Effects of anisotropic interactions on the structure of animal groups.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Emiliano Cristiani, Paolo Frasca, Benedetto Piccoli
Subjects: Dynamical Systems
AbstractThis paper proposes an agent-based model which reproduces different
structures of animal groups. The shape and structure of the group is the effect
of simple interaction rules among individuals: each animal deploys himself
depending on a limited number of neighboring group mates. The proposed model is
shown to produce clustered formations, as well as lines and V-like formations.
The key factors which trigger the onset of different patterns are argued to be
the relative strength of attraction and repulsion forces, and most important,
the anisotropy in their application.
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