School of Mathematical Sciences

Pattern formation in nonlinear systems with asymmetrically coupled elements: Peristaltic waves in pedestrian dynamics in corridors menu

Pattern formation in nonlinear systems with asymmetrically coupled elements: Peristaltic waves in pedestrian dynamics in corridors

Speaker: 
Yuri B. Gaididei (Bogolyubov Institute for Theoretical Physics, Kiev)
Date/Time: 
Tue, 17/05/2016 - 16:00
Room: 
103
Seminar series: 

Many physical systems can be described by particle models. The interaction between these particles is often modeled by forces, which typ- ically depend on the inter-particle distance, e.g., gravitational attraction in celestial me- chanics, Coulomb forces between charged par- ticles or swarming models of self-propelled par- ticles. In most physical systems Newtons third law of actio-reactio is valid. However, when considering a larger class of interacting par- ticle models, it might be crucial to introduce an asymmetry into the interaction terms, such that the forces not only depend on the dis- tance, but also on direction. Examples are found in pedestrian models, where pedestrians typically pay more attention to people in front than behind, or in traffic dynamics, where dri- vers on highways are assumed to adjust their speed according to the distance to the preced- ing car. Motivated by traffic and pedestrian models, it seems valuable to study particle sys- tems with asymmetric interaction where New- tons third law is invalid. Here general parti- cle models with symmetric and asymmetric re- pulsion are studied and investigated for finite- range and exponential interaction in straight corridors and annulus. In the symmetric case transitions from one-to multi-lane (zig-zag) be- havior including multi-stability are observed for varying particle density and for a varying curvature with fixed density. When the asym- metry of the interaction is taken into account a new “bubble”-like pattern arises when the dis- tance between lanes becomes spatially mod- ulated and changes periodically in time, i.e. peristaltic motion emerges. We find the tran- sition from the zig-zag state to the peristaltic state to be characterized by a Hopf bifurcation.