Publications
Detailed Information
Stability of Collision-Avoiding Initial Configurations for Cucker-Smale Model : 쿠커-스매일 모델의 입자들이 충돌을 피하는 초기조건의 안정성
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 하승열 | - |
dc.contributor.author | 홍혜림 | - |
dc.date.accessioned | 2017-07-19T09:01:25Z | - |
dc.date.available | 2017-07-19T09:01:25Z | - |
dc.date.issued | 2016-08 | - |
dc.identifier.other | 000000136298 | - |
dc.identifier.uri | https://hdl.handle.net/10371/131509 | - |
dc.description | 학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 하승열. | - |
dc.description.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. | - |
dc.description.tableofcontents | Chapter 1 Introduction 1
Chapter 2 Preliminaries 3 2.1 Previous Results 3 2.2 Collision-Avoiding Initial Congurations 7 Chapter 3 Main Result 10 3.1 Explicit Initial Congurations when β = 0 10 3.2 The Stability of Collision-Avoiding Initial Congurations when β < 1 12 Chapter 4 Numerical Simulations 20 Chapter 5 Conclusion 27 Bibliography 29 국문 초록 31 | - |
dc.format | application/pdf | - |
dc.format.extent | 4407223 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Cucker-Smale model | - |
dc.subject | collision-avoiding initial configurations | - |
dc.subject | communication weight | - |
dc.subject | stability | - |
dc.subject.ddc | 510 | - |
dc.title | Stability of Collision-Avoiding Initial Configurations for Cucker-Smale Model | - |
dc.title.alternative | 쿠커-스매일 모델의 입자들이 충돌을 피하는 초기조건의 안정성 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | HYERIM HONG | - |
dc.description.degree | Master | - |
dc.citation.pages | 31 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2016-08 | - |
- Appears in Collections:
- Files in This Item:
Item View & Download Count
Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.