Leading birds by their beaks: the response of flocks to external perturbations

Nikos Kyriakopoulos; Francesco Ginelli; John Toner

doi:10.1088/1367-2630/18/7/073039

Leading birds by their beaks: the response of flocks to external perturbations

Nikos Kyriakopoulos, Francesco Ginelli, John Toner

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Abstract

We study the asymptotic response of polar ordered active fluids ("flocks") to small external aligning fields h. The longitudinal susceptibility χ∥ diverges, in the thermodynamic limit, like h−ν as h→0. In finite systems of linear size L, χ∥ saturates to a value ∼Lγ. The universal exponents ν and γ depend only on the spatial dimensionality d, and are related to the dynamical exponent z and the "roughness exponent" α characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain ν=2/3, γ=4/5 in d=2 and ν=1/4, γ=2/5 in d=3. These values are confirmed by our simulations.

Original language	English
Article number	073039
Pages (from-to)	1-14
Number of pages	14
Journal	New Journal of Physics
Volume	18
DOIs	https://doi.org/10.1088/1367-2630/18/7/073039
Publication status	Published - 20 Jul 2016

Keywords

active matter
flocking
response theory
emergent behavior
renormalization group

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Leading birds by their beaks: the response of flocks to external perturbations
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Francesco Ginelli
- School of Natural & Computing Sciences, Physics - Honorary Senior Lecturer
Person: Honorary

Cite this

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title = "Leading birds by their beaks: the response of flocks to external perturbations",

abstract = "We study the asymptotic response of polar ordered active fluids ({"}flocks{"}) to small external aligning fields h. The longitudinal susceptibility χ∥ diverges, in the thermodynamic limit, like h−ν as h→0. In finite systems of linear size L, χ∥ saturates to a value ∼Lγ. The universal exponents ν and γ depend only on the spatial dimensionality d, and are related to the dynamical exponent z and the {"}roughness exponent{"} α characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain ν=2/3, γ=4/5 in d=2 and ν=1/4, γ=2/5 in d=3. These values are confirmed by our simulations.",

keywords = "active matter, flocking, response theory, emergent behavior, renormalization group",

author = "Nikos Kyriakopoulos and Francesco Ginelli and John Toner",

note = "Acknowledgments We have benefited from discussions with H Chat{\'e} and A Cavagna. We acknowledge support from the Marie Curie Career Integration Grant (CIG) PCIG13-GA-2013-618399. JT also acknowledges support from the SUPA distinguished visitor program and from the National Science Foundation through awards # EF-1137815 and 1006171, and thanks the University of Aberdeen for their hospitality while this work was underway. FG acknowledges support from EPSRC First Grant EP/K018450/1.",

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AU - Kyriakopoulos, Nikos

AU - Ginelli, Francesco

AU - Toner, John

N1 - Acknowledgments We have benefited from discussions with H Chaté and A Cavagna. We acknowledge support from the Marie Curie Career Integration Grant (CIG) PCIG13-GA-2013-618399. JT also acknowledges support from the SUPA distinguished visitor program and from the National Science Foundation through awards # EF-1137815 and 1006171, and thanks the University of Aberdeen for their hospitality while this work was underway. FG acknowledges support from EPSRC First Grant EP/K018450/1.

PY - 2016/7/20

Y1 - 2016/7/20

N2 - We study the asymptotic response of polar ordered active fluids ("flocks") to small external aligning fields h. The longitudinal susceptibility χ∥ diverges, in the thermodynamic limit, like h−ν as h→0. In finite systems of linear size L, χ∥ saturates to a value ∼Lγ. The universal exponents ν and γ depend only on the spatial dimensionality d, and are related to the dynamical exponent z and the "roughness exponent" α characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain ν=2/3, γ=4/5 in d=2 and ν=1/4, γ=2/5 in d=3. These values are confirmed by our simulations.

AB - We study the asymptotic response of polar ordered active fluids ("flocks") to small external aligning fields h. The longitudinal susceptibility χ∥ diverges, in the thermodynamic limit, like h−ν as h→0. In finite systems of linear size L, χ∥ saturates to a value ∼Lγ. The universal exponents ν and γ depend only on the spatial dimensionality d, and are related to the dynamical exponent z and the "roughness exponent" α characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain ν=2/3, γ=4/5 in d=2 and ν=1/4, γ=2/5 in d=3. These values are confirmed by our simulations.

KW - active matter

KW - flocking

KW - response theory

KW - emergent behavior

KW - renormalization group

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