2003/05/31 by M. Wilkinson, Michael Wilkinson, B. Mehlig · 4 citations
Engineering · Physics and Astronomy · #Quantum chaos and dynamical systems #Sports Dynamics and Biomechanics #Theoretical and Computational Physics #cond-mat.dis-nn #nlin.CD
paper · pdf · doi:10.1103/physreve.68.040101
published as Phys. Rev. E 68, 040101 (2003) · 4 pages, 3 figures; revised version, as published
openalex publication_date 2003/10/23 · arxiv created 2003/10/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the motion of a system of particles subjected to a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition; the particle trajectories coalesce. We analyze this transition by mapping it to a Kramers problem which we solve exactly. In the limit of weak random force we characterize the dynamics by computing the rate at which caustics are crossed, and the statistics of the particle density in the coalescing phase. Last but not least we describe possible realizations of the effect, ranging from trajectories of raindrops on perspex surfaces to animal migration patterns.