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Fluctuating nonlinear hydrodynamics of flocking
Phys. Rev. E 97, 032607 – Published 23 March, 2018
DOI: https://doi.org/10.1103/PhysRevE.97.032607
Abstract
Starting from a microscopic model, the continuum field theoretic description of the dynamics of a system of active ingredients or “particles” is presented. The equations of motion for the respective collective densities of mass and momentum follow exactly from that of a single element in the flock. The single-particle dynamics has noise and anomalous momentum dependence in its frictional terms. The equations for the collective densities are averaged over a local equilibrium distribution to obtain the corresponding coarse grained equations of fluctuating nonlinear hydrodynamics (FNH). The latter are the equations used frequently for describing active systems on the basis of intuitive arguments. The transport coefficients which appear in the macroscopic FNH equations are determined in terms of the parameters of the microscopic dynamics.
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References (27)
- M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Rev. Mod. Phys. 85, 1143 (2013).
- C. Bechinger, R. Di Leonardo, H. Lőwen, C. Reichhardt, G. Volpe, and G. Volpe, Rev. Mod. Phys. 88, 045006 (2016).
- D. N. Zuberav, V. Morozov, and G. Röpke, Statistical Mechanics of Non-equilibrium Processes (Akademie Verlag, Berlin, 1997), Vol. 2.
- J.-P. Boon and S. Yip, Molecular Hydrodynamics (Dover, New York, 1991).
- S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (Dover, New York, 1984).
- D. Forster, D. R. Nelson, and M. J. Stephen, Phys. Rev. A 16, 732 (1977).
- M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986).
- J. Toner and Y. Tu, Phys. Rev. Lett. 75, 4326 (1995); Phys. Rev. E 58, 4828 (1998).
- G. F. Mazenko, Nonequilibrium Statistical Mechanics (Wiley-VCH, New York, 2006).
- S. P. Das, Statistical Physics of Liquids at Freezing and Beyond (Cambridge University Press, Cambridge, UK, 2011).
- D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).
- R. A. Simha and S. Ramaswamy, Phys. Rev. Lett. 89, 058101 (2002).
- J. Toner, Y.-H. Tu, and S. Ramaswamy, Ann. Phys. 318, 170 (2005).
- T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995).
- E. Bertin, M. Droz, and G. Grégoire, Phys. Rev. E 74, 022101 (2006).
- N. Kumar, S. Ramaswamy, and A. K. Sood, Phys. Rev. Lett. 106, 118001 (2011).
- F. Thűroff, C. A. Weber, and E. Frey, Phys. Rev. Lett. 111, 190601 (2013).
- S. P. Das and A. Yoshimori, Phys. Rev. E 88, 043008 (2013).
- A. Cavagnaa, A. Cimarelli, I. Giardina, G. Parisi, R. Santagatib, F. Stefaninib, and M. Vialea, PNAS 107, 11865 (2010).
- S. P. Das and J. W. Dufty, Phys. Rev. A 46, 6371 (1992).
- S. P. Das and G. F. Mazenko, Phys. Rev. A 34, 2265 (1986); Phys. Rev. E 79, 021504 (2009).
- E. Bertin, H. Chatè, F. Ginelli, S. Mishra, A. Peshkov, and S. Ramaswamy, New J. Phys. 15, 085032 (2013).
- C. Yao-li, M. R. D'Orsognab, D. Marthalerc, A. L. Bertozzia, L. S. Chayesb, Phys. D (Amsterdam, Neth.) 232, 33 (2007).
- A. Peshkov, S. Ngo, E. Bertin, H. Chaté, and F. Ginelli, Phys. Rev. Lett. 109, 098101 (2012).
- A. Peshkov, I. S. Aranson, E. Bertin, H. Chaté, and F. Ginelli, Phys. Rev. Lett. 109, 268701 (2012).
- J. Toner, Phys. Rev. E 86, 031918 (2012).
- P. Résibois and M. de Leener, Classical Kinetic Theory of Fluids (Wiley Interscience, New York, 1977).
