Multi-cluster flocking of the thermodynamic Cucker-Smale model with a unit-speed constraint under a singular kernel

Shenglun Yan; Wanqian Zhang; Weiyuan Zou; Shenglun Yan; Wanqian Zhang; Weiyuan Zou

doi:10.3934/nhm.2024024

Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 547-568. doi: 10.3934/nhm.2024024

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Theory article

Multi-cluster flocking of the thermodynamic Cucker-Smale model with a unit-speed constraint under a singular kernel

College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, P. R. China

Received: 18 April 2024 Revised: 28 May 2024 Accepted: 30 May 2024 Published: 04 June 2024

This paper presents several sufficient frameworks for multi-cluster flocking of the thermodynamic Cucker-Smale model with a unit-speed constraint (in short, TCSUS) under a singular kernel. By providing precise estimates and deriving the dissipative structure of TCSUS, it was proved that under specific well-prepared conditions for particle positions and fully separated initial velocities, multi-cluster flocking occurs in the TCSUS system under a strong singular kernel. Furthermore, the velocities and temperatures converge to the average final data for each cluster group.
- Cucker-Smale Model,
- thermodynamic,
- unit-speed,
- singular kernel,
- multi-cluster flocking,
- convergence value
Citation: Shenglun Yan, Wanqian Zhang, Weiyuan Zou. Multi-cluster flocking of the thermodynamic Cucker-Smale model with a unit-speed constraint under a singular kernel[J]. Networks and Heterogeneous Media, 2024, 19(2): 547-568. doi: 10.3934/nhm.2024024

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Abstract

This paper presents several sufficient frameworks for multi-cluster flocking of the thermodynamic Cucker-Smale model with a unit-speed constraint (in short, TCSUS) under a singular kernel. By providing precise estimates and deriving the dissipative structure of TCSUS, it was proved that under specific well-prepared conditions for particle positions and fully separated initial velocities, multi-cluster flocking occurs in the TCSUS system under a strong singular kernel. Furthermore, the velocities and temperatures converge to the average final data for each cluster group.

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