Virginia TechLeung, K. T.2014-04-252014-04-251992-11Leung, K. T., " Trough models: Universality classes, distribution of avalanches, and cluster sizes," Phys. Rev. A 46, 6211 (1992); DOI: http://dx.doi.org/10.1103/PhysRevA.46.62111050-2947http://hdl.handle.net/10919/47682Extensions of the one-dimensional two-state trough model introduced by Carlson, Chayes, Grannan, and Swindle (CCGS) [Phys. Rev. A 42, 2467 (1990)] are considered. In particular, I investigate what kinds of physical processes are relevant to its scaling behavior. Short-range rearrangements of trough positions (slide events), which were neglected by CCGS, are shown to be irrelevant. By a simple modification of the dynamics, however, I obtain universality classes characterized by a single parameter. For trough models in general, including the two-state and the "limited local" sandpile models, asymptotically exact relations between the distribution of trough-trough distances and that of the mass of avalanches are derived. They yield moment relations in agreement with Krug's [J. Stat. Phys. 66, 1635 (1992)]. All results are verified by simulations.en-USIn Copyrightself-organized criticalityArticle - Refereedhttp://journals.aps.org/pra/abstract/10.1103/PhysRevA.46.6211https://doi.org/10.1103/PhysRevA.46.6211