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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
홍혜림
Advisor
하승열
Major
자연과학대학 수리과학부
Issue Date
2016-08
Publisher
서울대학교 대학원
Keywords
Cucker-Smale modelcollision-avoiding initial configurationscommunication weightstability
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
URI
https://hdl.handle.net/10371/131509
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Master's Degree_수리과학부)
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