2002/05/31 by R. C. Ball, E. Somfai, Ellák Somfai · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #cond-mat.stat-mech #nanoparticles nucleation surface interactions
paper · pdf · doi:10.1103/physrevlett.89.135503
published as Phys. Rev. Lett. 89, 135503 (2002) · 4 pages, 3 figures, submitted to PRL
arxiv created 2002/05/31 · openalex publication_date 2002/09/04 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We expand upon a new theoretical framework for diffusion-limited aggregation and associated dielectric breakdown models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these models interrelate when the ultraviolet cut-off strategy is changed, the analogy with turbulence, and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is discussed. We find angular resonances relatable to the cone angle theory, and we are led to predict a new screening transition in the DBM at large eta.