title: Keeping speed and distance for aligned motion.
abstract: The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space and time we find that if two particles arrive symmetrically in a plane at a large angle, then (i) radial repulsion and (ii) linear self-propelling toward a fixed preferred speed are sufficient for them to depart at a smaller angle. For this local gain of momentum explicit velocity alignment is not necessary, nor are adhesion or attraction, inelasticity or anisotropy of the particles, or nonlinear drag. With many particles obeying these microscopic rules of motion we find that their spatial confinement to a square with periodic boundaries (which is an indirect form of attraction) leads to stable macroscopic ordering. As a function of the strength of added noise we see--at finite system sizes--a critical slowing down close to the order-disorder boundary and a discontinuous transition. After varying the density of particles at constant system size and varying the size of the system with constant particle density we predict that in the infinite system size (or density) limit the hysteresis loop disappears and the transition becomes continuous. We note that animals, humans, drones, etc., tend to move asynchronously and are often more responsive to motion than positions. Thus, for them velocity-based continuous models can provide higher precision than coordinate-based models. An additional characteristic and realistic feature of the model is that convergence to the ordered state is fastest at a finite density, which is in contrast to models applying (discontinuous) explicit velocity alignments and discretized time. To summarize, we find that the investigated model can provide a minimal description of flocking.
authors: MTA-ELTE Statistical and Biological Physics Research Group (Hungarian Academy of Sciences), Pázmány Péter sétány 1A, Budapest 1117, Hungary and Regional Knowledge Center, ELTE Faculty of Sciences, Irányi Dániel u. 4., Székesfehérvár 8000, Hungary.
authors: Illés J
authors: IJ
authors: Farkas
authors: Department of Biological Physics, Eötvös University, Pázmány Péter sétány 1A, Budapest 1117, Hungary.
authors: Jeromos
authors: J
authors: Kun
authors: Department of Computer Science and Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China.
authors: Yi
authors: Y
authors: Jin
authors: Department of Computer Science and Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China and State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing 100191, China.
authors: Gaoqi
authors: G
authors: He
authors: School of Information Engineering, Zhengzhou University, 100 Science Avenue, Zhengzhou 450001, China.
authors: Mingliang
authors: M
authors: Xu
mesh_terms: D008962:Models, Theoretical; D009038:Motion; D013997:Time Factors