2017/10/31 by Oleg Alekseev · 2 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Brownian motion #Chaotic #Classical mechanics #Computer science #Cutoff #Instability #Laplace operator #Mathematical analysis #Mathematics #Mechanics #Microscale chemistry #Physics #Quantum mechanics #Regularization (linguistics) #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Viscous liquid #cond-mat.stat-mech #hep-th #math-ph #math.MP #nlin.PS
paper · pdf · doi:10.1103/physreve.100.012129
published in Physical review. E 100(1), 012129 (American Physical Society) · 4 pages, 2 figures; v2: exposition improved
arxiv created 2018/05/22 · openalex publication_date 2019/07/22 · arxiv updated 2019/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A systematic analytic treatment of local fluctuations in the regularized Laplacian growth problem is given. The interface dynamics is stabilized by a short-distance cutoff ℏ preventing the cusps production in a finite time. The regularization mechanism results in the violation of the incompressibility condition of the viscous fluid on a microscale in the vicinity of the moving interface, thus producing local fluctuations of pressure. Dissipation of fluctuations with time is described by universal Dyson Brownian motion, which reduces to the complex viscous Burgers equation in the hydrodynamic approximation. Because of the intrinsic instability of the interface dynamics, tiny fluctuations of pressure generate universal complex patterns with well developed fjords and fingers in a long time asymptotic.