2000/06/29 by Herbert Levine, Wouter‐Jan Rappel, Wouter-Jan Rappel +1 · 11 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Boundary value problem #Classical mechanics #Computer science #Diffusion and Search Dynamics #Focus (optics) #Mechanics #Micro and Nano Robotics #Modular Robots and Swarm Intelligence #Optics #Periodic boundary conditions #Physics #Quantum mechanics #Self-organization #Simple (philosophy) #Statistical physics #Vortex #cond-mat.dis-nn #cond-mat.soft
paper · pdf · doi:10.1103/physreve.63.017101
4 pages, 5 figures
arxiv created 2000/06/29 · openalex publication_date 2000/12/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions. In one-dimension, the self-organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges. In two-dimensions, we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions, even in the absence of a confining boundary. Furthermore, we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent.