Uncertainty Quantification in Control Problems for Flocking Models

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella 
(5/3/2015 preprint arXiv:1503.00548)

In this paper the optimal control of flocking models with random inputs is investigated from a numerical point of view. The effect of uncertainty in the interaction parameters is studied for a Cucker-Smale type model using a generalized polynomial chaos (gPC) approach. Numerical evidence of threshold effects in the alignment dynamic due to the random parameters is given.

Numerical methods for plasma physics in collisional regimes

Giacomo Dimarco, Qin Li, Lorenzo Pareschi, Bokai Yan (01/01/2015 Journal of Plasma Physics, 2015, pp. 305810106, hal-01110369)

We consider the development of accurate and efficient numerical methods for the solution of the Vlasov-Landau equation describing a collisional plasma. The methods combine a Lagrangian approach for the Vlasov solver with a fast spectral method for the solution of the Landau operator. To this goal new modified spectral methods for the Landau integral which are capable to capture correctly the Maxwellian steady state are introduced.

Numerical methods for kinetic equations

Giacomo Dimarco, Lorenzo Pareschi
(01/05/2014 Acta Numerica 23, 2014 pp. 369-520, hal-00986714)

In this survey we consider the development and the mathematical analysis of numerical methods for kinetic partial differential equations. Kinetic equations represent a way of describing the time evolution of a system consisting of a large number of particles. Due to the high number of dimensions and their intrinsic physical properties, the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.

Interacting Multiagent Systems. Kinetic equations and Monte Carlo methods

Lorenzo Pareschi, Giuseppe Toscani
Oxford University Press
392 pages,  2013

The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as sociology and economics. Applied mathematics is concerned with the construction, analysis and interpretation of mathematical models that can shed light on significant problems of the natural sciences as well as our daily lives.