English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we study the macroscopic behavior of the inertial spin (IS)model. This model has been recently proposed to describe the collectivedynamics of flocks of birds, and its main feature is the presence of anauxiliary dynamical variable, a sort of internal spin, which conveys theinteraction among the birds with the effect of better describing the turning offlocks. After discussing the geometrical and mechanical properties of the ISmodel, we show that, in the case of constant interaction among the birds, itsmean-field limit is described by a non-linear Fokker-Planck equation, whoseequilibria are fully characterized. Finally, in the case of non-constantinteractions, we derive the kinetic equation for the mean-field limit of themodel in the absence of thermal noise, and explore its macroscopic behavior byanalyzing the mono-kinetic solutions.

Some aspects of the inertial spin model for flocks and related kinetic equations