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  5. Tricritical points in a Vicsek model of self-propelled particles with bounded confidence
 
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Tricritical points in a Vicsek model of self-propelled particles with bounded confidence

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Author(s)
Romensky, Maksym 
Lobaskin, Vladimir 
Ihle, Thomas 
Uri
http://hdl.handle.net/10197/8422
Date Issued
24 December 2014
Date Available
06T16:12:41Z April 2017
Abstract
We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard Vicsek model with a bounded-confidence collision rule: a given particle only aligns to neighbors who have directions quite similar to its own. Neighbors whose directions deviate more than a fixed restriction angle α are ignored. The collective dynamics of this system is studied by agent-based simulations and kinetic mean-field theory. We demonstrate that the reduction of the restriction angle leads to a critical noise amplitude decreasing monotonically with that angle, turning into a power law with exponent 3/2 for small angles. Moreover, for small system sizes we show that upon decreasing the restriction angle, the kind of the transition to polar collective motion changes from continuous to discontinuous. Thus, an apparent tricritical point with different scaling laws is identified and calculated analytically. We investigate the shifting and vanishing of this point due to the formation of density bands as the system size is increased. Agent-based simulations in small systems with large particle velocities show excellent agreement with the kinetic theory predictions. We also find that at very small interaction angles, the polar ordered phase becomes unstable with respect to the apolar phase. We derive analytical expressions for the dependence of the threshold noise on the restriction angle. We show that the mean-field kinetic theory also permits stationary nematic states below a restriction angle of 0.681 π. We calculate the critical noise, at which the disordered state bifurcates to a nematic state, and find that it is always smaller than the threshold noise for the transition from disorder to polar order. The disordered-nematic transition features two tricritical points: At low and high restriction angle, the transition is discontinuous but continuous at intermediate α. We generalize our results to systems that show fragmentation into more than two groups and obtain scaling laws for the transition lines and the corresponding tricritical points. A numerical method to evaluate the nonlinear Fredholm integral equation for the stationary distribution function is also presented. This method is shown to give excellent agreement with agent-based simulations, even in strongly ordered systems at noise values close to zero.
Sponsorship
Irish Research Council for Science, Engineering and Technology
Type of Material
Journal Article
Publisher
American Physical Society
Journal
Physical Review E
Volume
90
Issue
6
Copyright (Published Version)
2014 American Physical Society
Keywords
  • Self-propelled partic...

  • Swarming

  • Vicsek model

DOI
10.1103/PhysRevE.90.063315
Web versions
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.063315
Language
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
Owning collection
Physics Research Collection
Scopus© citations
31
Acquisition Date
Jan 28, 2023
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