Interactive particle systems with pair-wise interactions: linear (in)stability analysis and simulations

Bachelor thesis (2021)

Authors

Y. Yao Electrical Engineering, Mathematics and Computer Science

Contributors

D. Balagué Guardia Numerical Analysis - EEMCS (supervisor 1)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Yunsong Yao
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Published Date

09-07-2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this project we study the stability of stationary solutions of interactive particle systems with shortrange repulsion and long-range attraction. Firstly we describe the model and discuss ring steady state solutions. We give a comprehensive and detailed proof of Theorem 2.1 done in [2]. This theorem gives the conditions for the (in)stability of stationary ring solutions. Omitting details of the computations, we present Theorem 3.1 in [2] to find the conditions for (un)stable stationary solutions in the situation when the mode is sufficiently large. Having these conditions altogether we find the region of the parameters in which the stationary solutions are stable. Finally, we use a steepest descent method for the simulations of the model. Figures of equilibrium states of the particles corresponding to various families of interaction forces will be shown.

Files

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