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Critical bottleneck size for jamless particle flows in two dimensions.

Takumi Masuda1, Katsuhiro Nishinari1, Andreas Schadschneider2

  • 1Department of Aeronautics and Astronautics, Faculty of Engineering, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

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Summary

We developed a simple model for particle flow blockages, revealing oscillations and a critical size for continuous flow. Jamming probability follows a Gompertz function, matching simulation results.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Arching phenomena at bottlenecks are common in granular materials and traffic flow.
  • Understanding the microscopic origins of jamming is crucial for predicting flow behavior.

Purpose of the Study:

  • To propose a simple microscopic model for arching phenomena at bottlenecks.
  • To investigate the dynamics of particle flow and jamming.
  • To identify critical parameters governing continuous flow.

Main Methods:

  • A one-dimensional stochastic cellular automaton on a semicircular geometry was used.
  • The model simulates particle dynamics in front of a bottleneck.
  • Analytical approximations and numerical simulations were employed.

Main Results:

  • The model reproduces oscillation phenomena caused by arch formation and collapse.
  • A critical bottleneck size for continuous particle flow was predicted.
  • Jamming probability dependence on system size was approximated by the Gompertz function.

Conclusions:

  • The proposed microscopic model effectively captures arching phenomena and jamming dynamics.
  • The model provides insights into critical conditions for particle flow at bottlenecks.
  • Analytical predictions align well with simulation outcomes.