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Self-Organized Criticality by Henrik Jeldtoft Jensen

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5

The Search for a Formalism

5.1 Introduction

Self-organized criticality was introduced in 1987 by Bak, Tang, and Wiesenfeld (BTW), who employed some appealing yet heuristic handwaving arguments. To substantiate the hypothesis, computer simulations of a simple algorithm − inspired by the avalanches induced when one plays with a pile of sand − were presented. Substantial analytic understanding was lacking for some time. Soon, however, standard mathematical tools were being applied to the new set of models. Statistical mechanics traditionally makes use of a combination of approaches, one of which consists of defining models that have a structure that allows an exact calculation of specific quantities. The art is to formulate a model of the right ...

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