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 ${\chi }_{{}_{\parallel }}$ diverges, in the thermodynamic limit, like $h^{-\nu }$ as $h\to 0$. In finite systems of linear size $L$, ${\chi }_{{}_{\parallel }}$ saturates to a value $\sim L^{\gamma }$. The universal exponents $\nu$ and $\gamma$ depend only on the spatial dimensionality $d$, and are related to the dynamical exponent $z$ and the "roughness exponent" $\alpha$ characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain $\nu =2/3$, $\gamma =4/5$ in $d=2$ and $\nu =1/4$, $\gamma =2/5$ in $d=3$. These values are confirmed by our simulations.

arXiv comment20 pages, 3 figures, accepted for publication in New Journal of Physics

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• Sounds and hydrodynamics of polar active fluids
• Quantitative Assessment of the Toner and Tu Theory of Polar Flocks
• Hydrodynamic Theory of Flocking in the Presence of Quenched Disorder
• Scale-free behavioral cascades and effective leadership in schooling fish
• Flowing active liquids in a pipe: Hysteretic response of polar flocks to external fields
• Signatures of irreversibility in microscopic models of flocking
• Linear response to leadership, effective temperature and decision making in flocks
• Spatio-temporal correlations in models of collective motion ruled by different dynamical laws
• Equilibrium to off-equilibrium crossover in homogeneous active matter
• Designing circle Swimmers: Principles and strategies
• Polarization and dynamic phases of aligning active matter in periodic obstacle arrays
• Renormalization group study of marginal ferromagnetism
• Field-controlled interfacial transport and pinning in an active spin system
• The Inertial Spin Model of flocking with position-dependent forces