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Title: A continuous-time persistent random walk model for flocking
Authors: Escaff, Daniel
Toral, Raul
VAN DEN BROECK, Christian 
Lindenberg, Katja
Issue Date: 2018
Source: CHAOS, 28(7) (Art N° 075507)
Abstract: A classical random walker is characterized by a random position and velocity. This sort of random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a walker represents an inanimate particle driven by environmental fluctuations. On the other hand, there are many examples of so-called "persistent random walkers," including self-propelled particles that are able to move with almost constant speed while randomly changing their direction of motion. Examples include living entities (ranging from flagellated unicellular organisms to complex animals such as birds and fish), as well as synthetic materials. Here we discuss such persistent non-interacting random walkers as a model for active particles. We also present a model that includes interactions among particles, leading to a transition to flocking, that is, to a net flux where the majority of the particles move in the same direction. Moreover, the model exhibits secondary transitions that lead to clustering and more complex spatially structured states of flocking. We analyze all these transitions in terms of bifurcations using a number of mean field strategies (all to all interaction and advection-reaction equations for the spatially structured states), and compare these results with direct numerical simulations of ensembles of these interacting active particles. Published by AIP Publishing.
Notes: [Escaff, Daniel] Univ Andes, Fac Ingn & Ciencias Aplicadas, Complex Syst Grp, Santiago 12455, Chile. [Toral, Raul] Univ Illes Balears, CSIC, IFISC, Palma de Mallorca 07122, Spain. [Van den Broeck, Christian] Hasselt Univ, B-3500 Hasselt, Belgium. [Van den Broeck, Christian] Stellenbosch Inst Adv Studies, ZA-7602 Matieland, South Africa. [Lindenberg, Katja] Univ Calif San Diego, Dept Chem & Biochem, La Jolla, CA 92093 USA. [Lindenberg, Katja] Univ Calif San Diego, BioCircuits Inst, La Jolla, CA 92093 USA.
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ISSN: 1054-1500
e-ISSN: 1089-7682
DOI: 10.1063/1.5027734
ISI #: 000440606100037
Category: A1
Type: Journal Contribution
Validations: ecoom 2019
Appears in Collections:Research publications

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