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 a kinetic model for pedestrians, who are assumed toadapt their motion towards a desired direction while avoiding collisions withothers by stepping aside. These minimal microscopic interaction rules lead tocomplex emergent macroscopic phenomena, such as velocity alignment inunidirectional flows and lane or stripe formation in bidirectional flows. Westart by discussing collision avoidance mechanisms at the microscopic scale,then we study the corresponding Boltzmann-type kinetic description and itshydrodynamic mean-field approximation in the grazing collision limit. In thespatially homogeneous case we prove directional alignment under specificconditions on the sidestepping rules for both the collisional and themean-field model. In the spatially inhomogeneous case we illustrate, by meansof various numerical experiments, the rich dynamics that the proposed model isable to reproduce.

Kinetic description of collision avoidance in pedestrian crowds by sidestepping