A. Klar

N. K. Mahato, A. Klar, S. Tiwari

In this paper we present numerical simulations of a macroscopic vision-based model [1] derived from microscopic situation rules described in [2]. This model describes an approach to collision avoidance between pedestrians by taking decisions of turning or slowing down based on basic interaction rules, where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the bearing angle and of the time-to-interaction. A meshfree particle method is used to solve the equations of the model. Several numerical cases are considered to compare this model with models established in the field, for example, social force model coupled to an Eikonal equation [3]. Particular emphasis is put on the comparison of evacuation and computation times. References 1. Degond P., Appert-Rolland C., Pettere J., Theraulaz G., Vision-based macroscopic pedestrian models, Kinetic and Related models, AIMs 6(4), 809-839 (2013) 2. Ondrej J., Pettere J., Olivier A.H., Donikian S., A synthetic-vision based steering approach for crowd simulation, ACM Transactions on Graphics, 29(4), Article 123 (2010) 3. Etikyala R., Gottlich S., Klar A., Tiwari S., Particle methods for pedestrian flow models: From microscopic to nonlocal continuum models, Mathematical Models and Methods in Applied Sciences, 20(12), 2503-2523 (2014)

J. A. Carrillo, A. Klar, A. Roth

We show that double mills are more stable than single mills under stochastic perturbations in swarming dynamic models with basic attraction-repulsion mechanisms. In order to analyse accurately this fact, we will present a numerical technique for solving kinetic mean field equations for swarming dynamics. Numerical solutions of these equations for different sets of parameters will be presented and compared to microscopic and macroscopic results. As a consequence, we numerically observe a phase transition diagram in term of the stochastic noise going from single to double mill for small stochasticity fading gradually to disordered states when the noise strength gets larger. This bifurcation diagram at the inhomogeneous kinetic level is shown by carefully computing the distribution function in velocity space.