We present some analytical results for the stochastic sandpile model studied earlier by Manna. In this model, the operators corresponding to particle addition at different sites commute. The eigenvalues of operators satisfy a system of coupled polynomial equations. For an L×L square, we...

This article is based on a talk given by one of us (EVI) at the conference “StatPhys-Taipei-1997”. It overviews the exact results in the theory of the sandpile model and discusses briefly the yet unsolved problem of calculation of avalanche distribution exponents. The key ingredients include...

We study the spin-1 Ising model with non-local constraints imposed by the Bak–Tang–Wiesenfeld sandpile model of self-organized criticality (SOC). The model is constructed as if the sandpile is being built on a (honeycomb) lattice with Ising interactions. In this way we combine two models...

Universality and scaling for systems driven to criticality by a tuning parameter has been well studied. However, there are very few corresponding studies for the models of self-organized criticality, e.g., the Bak, Tang, and Wiesenfeld (BTW) sandpile model. It is well known that every avalanche...

We study the distributions of dissipative and nondissipative avalanches separately in the stochastic Zhang (SP-Z) sandpile in two dimension. We find that dissipative and nondissipative avalanches obey simple power laws and do not have the logarithmic correction, while the avalanche distributions...

Self-organized criticality is a hypothesis used to explain the origin of 1/f noise and other scaling behaviors. Despite being proposed nearly 30 years ago, no consensus exists as to its exact definition or mathematical mechanism(s). Recently, a model for 1/f noise was proposed based on a family...

We develop a parsimonious model of the interbank payment system. The model incorporates an endogenous instruction arrival process, a scale-free topology of payments between banks, a fixed total liquidity which limits banks’ capacity to process arriving instructions, and a global market that...

We perform extensive simulations of the sandpile model on a Sierpinski gasket. Critical exponents for waves and avalanches are determined. We extend the existing theory of waves to the present case. This leads to an exact value for the exponent τw which describes the distribution of wave sizes:...

Reduction in b-values before a large earthquake is a very popular topic for discussion. This study proposes an alternative sandpile model being able to demonstrate reduction in scaling exponents before large events through adaptable long-range connections. The distant connection between two...

Avalanche or cascade failure is ubiquitous. We first classify the cascading phenomena into two categories: the cascading disasters which result in large-scale functional failures and the cascading events that do not lead to disasters. We elucidate that two important factors, the increasing...