Swarming Models with Local Alignment Effects

Explore phase transitions driven by noise in swarming models with local alignment effects in this 31-minute lecture from the Hausdorff Junior Trimester Program on Kinetic Theory. Delve into the kinetic localized Cucker-Smale model for particle evolution in phase space, examining its convergence towards the Vicsek-Fokker-Planck equation. Investigate how noise intensity affects solution behavior, including bifurcation diagrams and the emergence of multiple solutions at low noise levels. Learn about applications in mathematical physics and large interacting particle systems in life and social sciences. Discover connections to synchronization and consensus models, and examine hydrodynamic limits leading to Self-Organized Hydrodynamics. Gain insights into cutting-edge research on kinetic equations, phase transitions, and collective behavior modeling.