### Abstract

increases. It is shown, for the first time, that certain characteristics of the bottleneck can be captured by considering only the number of particles in the swarm. Considering the case of a connected communication graph constructed in the hypothesis that each particle is influenced by a fixed number of neighbouring particles, a limit case is determined for which a lower limit to the

Cheeger constant can be derived analytically without the need for extensive algebraic calculations. Results show that as the number of particles increases the Cheeger constant decreases. Although ensuring a minimum number of interactions per particle is sufficient, in theory, to ensure cohesion, the swarm may face fragmentation as more particles are added to the swarm.

Original language | English |
---|---|

Article number | 032903 |

Number of pages | 12 |

Journal | Physical Review E |

Volume | 89 |

DOIs | |

Publication status | Published - 10 Mar 2014 |

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### Keywords

- swarm behaviour
- swarm potential fields
- particle concentration effects

### Cite this

*Physical Review E*,

*89*, [032903]. https://doi.org/10.1103/PhysRevE.89.032903

}

*Physical Review E*, vol. 89, 032903. https://doi.org/10.1103/PhysRevE.89.032903

**Characteristics of swarms on the edge of fragmentation.** / Punzo, Giuliano; Simo, Jules; Bennet, Derek James; Macdonald, Malcolm.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Characteristics of swarms on the edge of fragmentation

AU - Punzo, Giuliano

AU - Simo, Jules

AU - Bennet, Derek James

AU - Macdonald, Malcolm

PY - 2014/3/10

Y1 - 2014/3/10

N2 - Fragmentation of particle swarms into isolated subgroups occurs when interaction forces are weak or restricted. In the restricted case, the swarm experiences the onset of bottlenecks in the graph of interactions that can lead to the fragmentation of the system into subgroups. This work investigates the characteristics of such bottlenecks when the number of particles in the swarmincreases. It is shown, for the first time, that certain characteristics of the bottleneck can be captured by considering only the number of particles in the swarm. Considering the case of a connected communication graph constructed in the hypothesis that each particle is influenced by a fixed number of neighbouring particles, a limit case is determined for which a lower limit to theCheeger constant can be derived analytically without the need for extensive algebraic calculations. Results show that as the number of particles increases the Cheeger constant decreases. Although ensuring a minimum number of interactions per particle is sufficient, in theory, to ensure cohesion, the swarm may face fragmentation as more particles are added to the swarm.

AB - Fragmentation of particle swarms into isolated subgroups occurs when interaction forces are weak or restricted. In the restricted case, the swarm experiences the onset of bottlenecks in the graph of interactions that can lead to the fragmentation of the system into subgroups. This work investigates the characteristics of such bottlenecks when the number of particles in the swarmincreases. It is shown, for the first time, that certain characteristics of the bottleneck can be captured by considering only the number of particles in the swarm. Considering the case of a connected communication graph constructed in the hypothesis that each particle is influenced by a fixed number of neighbouring particles, a limit case is determined for which a lower limit to theCheeger constant can be derived analytically without the need for extensive algebraic calculations. Results show that as the number of particles increases the Cheeger constant decreases. Although ensuring a minimum number of interactions per particle is sufficient, in theory, to ensure cohesion, the swarm may face fragmentation as more particles are added to the swarm.

KW - swarm behaviour

KW - swarm potential fields

KW - particle concentration effects

UR - http://journals.aps.org/pre/pdf/10.1103/PhysRevE.89.032903

U2 - 10.1103/PhysRevE.89.032903

DO - 10.1103/PhysRevE.89.032903

M3 - Article

VL - 89

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

M1 - 032903

ER -