2006/12/12 by Eric J. Hildebrand, Eric Hildebrand, Michael A. Buice +1 · 57 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #BBGKY hierarchy #Computation #Correlation function (quantum field theory) #Distribution function #Function (biology) #Hierarchy #Kinetic energy #Kinetic theory #Kuramoto model #Mathematics #Nonlinear Dynamics and Pattern Formation #Order (exchange) #Physics #Quantum mechanics #Slime Mold and Myxomycetes Research #Statistical physics #Synchronization (alternating current) #Theoretical and Computational Physics #Theoretical physics #Topology (electrical circuits) #nlin.CD #nlin.CG #physics.bio-ph
paper · pdf · doi:10.1103/physrevlett.98.054101
published in Physical Review Letters 98(5), 054101 (American Physical Society)
arxiv created 2006/12/12 · openalex publication_date 2007/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is analogous to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the kinetic theory of plasmas and gases. To calculate the lowest order system size effect, we truncate this hierarchy at second order and solve the resulting closed equations for the two-oscillator correlation function around the incoherent state. We use this correlation function to compute the fluctuations of the order parameter, including the effect of transients, and compare this computation with numerical simulations.