On steady-state preserving spectral methods for homogeneous Boltzmann equations

Francis Filbet, Lorenzo Pareschi, Thomas Rey 
(08/08/2014 CRAS Volume 353, Issue 4, 2015, 309–314, ArXiv:1408.1863)

In this note, we present a general way to construct spectral methods for the collision operator of the Boltzmann equation which preserves exactly the Maxwellian steady-state of the system. We show that the resulting method is able to approximate with spectral accuracy the solution uniformly in time.

Boltzmann type control of opinion consensus through leaders

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella
(06/05/2014 Phil. Trans. R. Soc. A 2014 372 20140138, arXiv:1405.0736)

The study of formations and dynamics of opinions leading to the so called opinion consensus is one of the most important areas in mathematical modeling of social sciences. Following the Boltzmann type control recently introduced in Albi, Herty, Pareschi 2014, we consider a group of opinion leaders which modify their strategy accordingly to an objective functional with the aim to achieve opinion consensus.

Modeling self-organized systems interacting with few individuals: From microscopic to macroscopic dynamics

Giacomo Albi, 
Lorenzo Pareschi

(31/10/2012 Applied Mathematics Letters, 26 (2013), 397-401. arXiv:1210.1172)

In nature self-organized systems as flock of birds, school of fishes or herd of sheeps have to deal with the presence of external agents such as predators or leaders which modify their internal dynamic. Such situations take into account a large number of individuals with their own social behavior which interact with a few number of other individuals acting as external point source forces.

Binary interaction algorithms for the simulation of flocking and swarming dynamics

Giacomo Albi, Lorenzo Pareschi
(04/03/2012 Multiscale Modeling and Simulation 11, (2013), 1-29.  arXiv:1203.0721)

Microscopic models of flocking and swarming takes in account large numbers of interacting individuals. Numerical resolution of large flocks implies huge computational costs. Typically for N interacting individuals we have a cost of O(N²). We tackle the problem numerically by considering approximated binary interaction dynamics described by kinetic equations and simulating such equations by suitable stochastic methods.

Exponential Runge-Kutta methods for stiff kinetic equations

Giacomo Dimarco, Lorenzo Pareschi (7/10/2010 SIAM J. Num. Anal. 49, 2057-2077, 2011, arXiv:1010.1472v1)

We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation operators of BGK type. For Boltzmann type kinetic equations they work uniformly for a wide range of relaxation times and avoid the solution of nonlinear systems of equations even in stiff regimes.

European Researchers' Night 2010

The Researchers' Night is a Europe-wide event bringing together the public at large and researchers once a year on the fourth Friday of September. It offers the opportunity to discover research facilities that are usually not open to public (laboratories, research centres, museum collections ), use the most recent technologies and instruments with the guidance of scientists, participate in experiments, competitions and quizzes, watch demonstrations and simulations, exchange ideas and party with the researchers.