Turbulence and shock-waves in crowd dynamics

In this paper, we analyze crowd turbulence from both classical and quantum perspective. We analyze various crowd waves and a collision using crowd macroscopic wave functions. In particular, we will show that nonlinear Schrödinger (NLS) equation is fundamental for quantum turbulence, while its closed-form solutions include shock-waves, solitons, and rogue waves, as well as planar de Broglie’s waves. We start by modeling various crowd flows using classical fluid dynamics, based on Navier–Stokes equations. Then we model turbulent crowd flows using quantum turbulence in Bose–Einstein condensation, based on modified NLS equation.