Phase Transitions in a Kinetic Flocking Model of Cucker-Smale Type

We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a “disordered” to an “ordered” state. This effect is related to recently noticed phenomena for the diffusive Vicsek model. We also carry out numerical simulations of the system and give further details on the phase transition

Structure preserving schemes for mean-field equations of collective behavior

In this paper we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang-Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.Comment: Proceedings of the XVI International Conference on Hyperbolic Problem

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

Young stars and brown dwarfs surrounding Alnilam (eps Ori) and Mintaka (del Ori)

Aims: We look for new regions for the search of substellar objects. Methods: Two circular areas, 45 arcmin-radius each, centred on the young massive star systems Alnilam and Mintaka in the Orion Belt, have been explored. The regions are very young (less than 10 Ma), have low extinction, and are neighbours to sigma Orionis (~3 Ma), a young open cluster very rich in brown dwarfs and planetary-mass objects. We have used Virtual Observatory tools, the astro-photometric Tycho-2, DENIS and 2MASS catalogues, 10 control fields at similar galactic latitudes, and X-ray, mid-infrared and spectroscopic data from the literature. Results: We have compiled exhaustive lists of known young stars and new candidate members in the Ori OB1b association, and of fore- and background sources. A total of 136 stars display features of extreme youth, like early spectral types, lithium in absorption, or mid-infrared flux excess. Other two young brown dwarf and 289 star candidates have been identified from an optical/near-infrared colour-magnitude diagram. We list additional 74 known objects that might belong to the association. This catalogue can serve as an input for characterisation of the stellar and high-mass substellar populations in the Orion Belt. Finally, we have investigated the surface densities and radial distributions of young objects surrounding Alnilam and Mintaka, and compared them with those in the sigma Orionis cluster. We report a new open cluster centred on Mintaka. Conclusions: Both regions can be analogs to the sigma Orionis cluster, but more massive, more extended, slightly older, and less radially concentrated.Comment: Accepted for publication in A&A. It will be published on line in Sect. 14 (Catalogs and data). Tables in Appendix A will soon be available at the CD

Phase transitions in a kinetic flocking model of Cucker--Smale type

We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a “disordered” to an “ordered” state. This effect is related to recently noticed phenomena for the diffusive Vicsek model. We also carry out numerical simulations of the system and give further details on the phase transition