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Updated: Jul 6, 2026
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Published on: May 23, 2020
Singularities and symmetry breaking in swarms
Wei Li1, Hai-Tao Zhang, Michael Zhi Qiang Chen
1Department of Automation, Shanghai Jiao Tong University, Shanghai, PR China.
Summary
The directional alignment rule (DAR) in self-propelled particle systems creates inherent singularities. These singularities, not long-range interactions, drive collective motion and symmetry breaking in swarms.
Area of Science:
- Complex systems
- Statistical physics
- Collective behavior
Background:
- Self-propelled particle systems often self-organize into ordered states from symmetric configurations.
- The directional alignment rule (DAR) is widely believed to be the primary driver of collective motion due to effective long-range interactions.
Purpose of the Study:
- To investigate unperceived singularities within the DAR.
- To elucidate the fundamental role of these singularities and topological connectivity in emergent collective behavior.
- To understand the mechanism behind spontaneous symmetry breaking in swarms.
Main Methods:
- Analysis of self-propelled particle systems governed by the directional alignment rule (DAR).
- Identification and characterization of inherent singularities within the DAR framework.
- Examination of symmetry-breaking effects and topological connectivity during system evolution.
Main Results:
- The DAR harbors unperceived, inherent singularities.
- Singularity-induced symmetry breaking and topological connectivity are fundamental to collective behavior.
- Weakening or eliminating singularities causes a sharp transition from coherent motion to isotropic dispersion.
Conclusions:
- Collective motion in self-propelled particle systems is fundamentally driven by singularities within the DAR, not solely by long-range interactions.
- Spontaneous symmetry breaking leading to coherent motion is intrinsically linked to these singularities.
- Understanding these singularities is key to comprehending the fundamental mechanisms of collective dynamics.
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