A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms
By F. Peruani, A. Deutsch, M. Baer. 2008
134 citations recorded by the source corpus.
Abstract.A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of ferromagnetic (F) and liquid-crystal (LC) alignment. In both cases, MFA yields a second order phase transition for a critical noise strength and a scaling exponent of 1/2 for the respective order parameters. We find that the critical noise amplitude ηc at which orientational order emerges in the LC case is smaller than in the F-alignment case, i.e. ηLCC<ηFC. A comparison with simulations of individual-based models with F- resp. LC-alignment shows that the predictions about the critical behavior and the qualitative relation between the respective critical noise amplitudes are correct.
Subfields: Genetics, Global and Planetary Change, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/f21b2346b812022df03c3d8ef6c4ae149454e979
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In Global and Planetary Change
In Molecular Biology
Citations in the corpus
- Tuned, driven, and active soft matter (2015, unknown): “Other variants of the Vicsek model, such as polar particles of apolar alignment interactions [383, 391, 393, 394, 405] or nematic particles that randomly reverse their migration”
- Physics of microswimmers—single particle motion and collective behavior: a review (2014, background): “…in a system of self-propelled point particles has led to numerous analytical (Baskaran and Marchetti, 2009; Bertin et al., 2009; Golestanian, 2009; Peruani et al., 2008; Ramaswamy et al., 2003; Simha and Ramaswamy, 2002; Toner and Tu, 1995; Toner et al., 2005b) as well as computational (Aldana et…”
- Hydrodynamics of soft active matter (2013, background): “Numerical simulations of self-propelled hard rods have also been carried out by Kraikivski, Lipowsky, and Kierfeld (2006), Peruani, Deutsch, and Bär (2006, 2008), and Yang, Marceau, and Gompper (2010) and have revealed a rich behavior.”
- Active Brownian particles (2012, methodology): “A similar result can be also obtained for self-propelled particles with constant velocity [267], corresponding to the limit α, β → ∞ with α/β = v(2) 0 = const.”