Showing papers by "Anders Malthe-Sørenssen published in 1999"
TL;DR: In this paper, the authors have analyzed several fracture patterns around the Skafta cauldron on Iceland and demonstrated that an understanding of sampling biases allows a scaling relation L ∝ Aβ to be established and the exponent β to be determined.
Abstract: During drainage of subglacial lakes the surface of the glacier subsides and fractures, generating a homogeneous, circular fracture pattern on the rim of the resulting depression. We have analyzed several fracture patterns around the Skafta cauldron on Iceland. A regular fracture spacing was observed on the cauldron rim, indicating that the region was subjected to a uniform strain. In this region, standard image analysis techniques were applied to find the lengths L and open areas A of the fractures. We demonstrate that an understanding of sampling biases allows a scaling relation L ∝ Aβ to be established and the exponent β to be determined. This relation provides a quantitative characterization of interactions between fractures in the population. The value of β is higher for that observed for laboratory experiments on clay, but the uncertainties do not rule out a universal behavior, which applies to ice, rock, and all other solids. The size distribution of fractures did not display a similarly simple crossover behavior, and a power law scaling relation could not be established without a better understanding of the crossovers for large fractures. We introduce a simple simulation model that reproduces the most important visual and statistical properties of the glacier fracture pattern. The direct comparison validates the use of the model to simulate geological fracturing processes.
16 citations
TL;DR: In this article, the surface geometry and dynamics in a slowly driven pile of rice are studied for two types of rice, a long-grained rice that displays power-law distributed avalanches and a rounder rice with a characteristic avalanche size.
Abstract: The surface geometry and dynamics in a one-dimensional, slowly driven pile of rice are studied for two types of rice, a long-grained rice that displays power-law distributed avalanches and a rounder rice with a characteristic avalanche size. The surface fluctuations are proportional to a power of the system size with exponents x 0.2 6 0.1, for both types of rice. The time correlation functions for the mass and height of the pile are characterized by a crossover time that is proportional to a power of the system size. The scaling behavior is similar for both types of rice, but the correlation time is much larger for the long-grained rice.
10 citations
TL;DR: In this paper, a sandpile model with dynamically varying critical heights is studied in one dimension, and the average transit time of a grain through the model is proportional to the system size, but the distribution of transit times has a power-law tail.
Abstract: A sandpile model with dynamically varying critical heights is studied in one dimension. The model displays self-organized critical behavior with an avalanche exponent τ=1.35±0.02, which correspond to the value found from a mean-field argument. The time evolution of the mass and height of the pile is characterized by a time-correlation function with a crossover time that increases systematically with system time. The average transit time of a grain through the model is proportional to the system size, but the distribution of transit times has a power-law tail. A modified model, which includes non-local interactions from force propagation within the pile, belongs to the same universality class, although the distribution of transit times changes significantly.