The study of toppling on permutations with an extra labeled chip was initiated by the first author D. Hathcock and P. Tetali (arXiv:2010.11236), where added in middle. We extend this to all possible locations $p$ as well values $r$ give a complete characterization which topple identity. Further, we classify are outcomes process generality, call resultant permutations. Resultant turn out be cert...

The stability analysis of rock slopes is a complex task for the geotechnical engineers due to the complex nature of the rock mass in a tropical climate that often has discontinuities in several forms, and consequently, in several types of slope failures. In this work, a rock mass classification scheme is followed in a tropical environment using the Rock Mass Rating (RMR) and Geological St...

We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd ðkÞ k ; through the Bak–Tang–Wiesenfeld sandpile model. The threshold height of a node i is set to be k 1 Z i with 0pZo1: We obtain the exponents for the avalanche size and the duration distributions analytically as a function of g and Z by using the branching process approach. The analytic solutio...

The sand pile model was introduced by Bak, Tang and Wiesenfeld (see [BTW88]) in the context of selforganized criticality. Since then, there has been a lot of work on this model and related models, especially from the graph-theoretical point of view (see, e.g., [ALSSTW89, GK93, GMP]). In the classical model, designed by Brylawski for another purpose (see [Bry73]), a sand pile is a decreasing seq...

OBJECTIVE To assess outcomes of trauma caused by television sets falling onto children. METHODS Retrospective review of medical charts of 183 children aged 7 years and younger hospitalized for injuries caused by falling television sets. Descriptive statistics were applied. DATA SOURCES Phase 2 (1988-1995) and phase 3 (1995-1999) of the National Pediatric Trauma Registry. OUTCOME MEASURES ...

The Southwell Topple is a spectacular example of toppling failure on the southeastern coastline Isle Portland, south coast England. Types mass movements, which occur around almost entire Portland and include some other much smaller but well-known topples, vary depending local geological topographical contexts. ‘Southwell Landslide’ 1734 (i.e. Topple) differs in most respects from all others, no...

We study the nature of statistical correlations that develop between systems of interacting self-organized critical automata (sandpiles). Numerical and analytical findings are presented describing the emergence of "synchronization" between sandpiles and the dependency of this synchronization on factors such as variations in coupling strength, toppling rule probabilities, symmetric versus asymme...

We study critical properties of the continuous Abelian sandpile model with anisotropies in toppling rules that produce ordered patterns on it. Also, we consider the continuous directed sandpile model perturbed by a weak quenched randomness, study critical behavior of the model using perturbative conformal field theory, and show that the model has a random fixed point.