Saddle-node bifurcation to jammed state for quasi-one-dimensional counter-chemotactic flow

Area of Science:

• Physics
• Complex Systems
• Statistical Mechanics

Background:

• Counter-chemotactic particle flows exhibit transitions between free-flow and jammed states.
• A key feature is the spontaneous formation of path-blocking clusters (PBCs) that impede flow.
• The dynamics near the jamming threshold involve occasional PBC collapse and free-flow recovery.

Purpose of the Study:

• To investigate the transition from free-flow to jammed states in quasi-one-dimensional counter-chemotactic particle flows.
• To model the size evolution of path-blocking clusters (PBCs) and their impact on flow flux.
• To identify the underlying mechanism driving the emergence of jammed states.

Main Methods:

• Numerical simulations using a stochastic cellular automata (SCA) model.
• Development of a Langevin equation model to describe PBC size dynamics.
• Analysis of the qualitative characteristics reproduced by the Langevin model compared to the SCA model.

Main Results:

• The time evolution of the PBC size dictates the flux in counter-chemotactic flows.
• A Langevin equation model successfully captures the qualitative behaviors observed in the SCA model.
• The emergence of the jammed state is linked to a saddle-node bifurcation.

Conclusions:

• The transition to a jammed state in quasi-one-dimensional counterflows is driven by a saddle-node bifurcation.
• The developed Langevin model provides a simplified yet effective framework for understanding PBC dynamics.
• Understanding PBC size evolution is crucial for characterizing counter-chemotactic flow behavior.