2012/03/04 by Giacomo Albi, Lorenzo Pareschi, Albi, Giacomo +1 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Binary number #Biological Physics (physics.bio-ph) #Complex Network Analysis Techniques #Computational Physics (physics.comp-ph) #Computer science #Diffusion and Search Dynamics #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Flocking (texture) #Geometry #Mathematical optimization #Mathematics #Numerical Analysis (math.NA) #Opinion Dynamics and Social Influence #Physics #Quantitative Methods (q-bio.QM) #Scaling #Statistical physics #Statistics #Stochastic simulation #Swarming (honey bee)
paper · pdf · doi:10.48550/arxiv.1203.0721
openalex publication_date 2012/03/04 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Microscopic models of flocking and swarming takes in account large numbers of\ninteracting individ- uals. Numerical resolution of large flocks implies huge\ncomputational costs. Typically for N interacting individuals we have a cost\nof O(N2). We tackle the problem numerically by considering approximated\nbinary interaction dynamics described by kinetic equations and simulating such\nequations by suitable stochastic methods. This approach permits to compute\napproximate solutions as functions of a small scaling parameter \ε\nat a reduced complexity of O(N) operations. Several numerical results show the\nefficiency of the algorithms proposed.\n