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Stability of Collision-Avoiding Initial Configurations for Cucker-Smale Model : 쿠커-스매일 모델의 입자들이 충돌을 피하는 초기조건의 안정성
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- Authors
- Advisor
- 하승열
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2016-08
- Publisher
- 서울대학교 대학원
- Keywords
- Cucker-Smale model ; collision-avoiding initial configurations ; communication weight ; stability
- Description
- 학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 하승열.
- Abstract
- In this thesis, we present the explicit calculation of collision-avoiding initial configurations for multi-particle Cucker-Smale system when the communi- cation weight ψ equals to 1. Between the two types of ψ: ψ_1(r) = r^(−β) and ψ_2(r) = (1 + r^2)^(−β/2) for r ≥ 0, we consider the latter. It is known that the particles form a flocking behavior when β ∈ [0, 1]. We extend the result to the case when β ∈ (0, 1), i.e., ψ ̸= 1 . We show that ψ is stable against the perturbation of β, i.e. the collision-avoiding initial positions and velocities surprisingly do not change much.
- Language
- English
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