2005/01/04 by Darryl D. Holm, Vakhtang Putkaradze · 86 citations
Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Diffusion #Dimension (graph theory) #Mathematical Biology Tumor Growth #Mathematics #Particle (ecology) #Physics #Quantum mechanics #Slime Mold and Myxomycetes Research #Statistical physics #Stochastic processes and statistical mechanics #nlin.PS #nlin.SI
paper · pdf · doi:10.1103/physrevlett.95.226106
published in Physical Review Letters 95(22), 226106 (American Physical Society) · 4 pages, 2 figures
arxiv created 2005/01/04 · openalex publication_date 2005/11/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
New model equations are derived for dynamics of aggregation of finite-size particles. The differences from standard Debye-Hückel and Keller-Segel models are that the mobility of particles depends on the configuration of their neighbors and linear diffusion acts on locally averaged particle density. The evolution of collapsed states in these models reduces exactly to finite-dimensional dynamics of interacting particle clumps. Simulations show these collapsed (clumped) states emerge from smooth initial conditions, even in one spatial dimension. Extensions to two and three dimensions are also discussed.