arXiv subjects

Kent B. Lauritsen

Publications and source records attributed to Kent B. Lauritsen.

3 recordsLinked to original sources

arXiv1997

Directed Percolation with a Wall or Edge

We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface critical phenomena and field theory. The results of previous numerical work for a wall can thus be interpreted in terms of surface exponents satisfying scaling relations generalising those for ordinary directed percolation. New exponents for edge directed percolation are also introduced. They are calculated in mean-field theory and measured numerically in 2+1 dimensions.

cond-mat.stat-mech↗

arXiv1996

Energy avalanches in a rice-pile model

We investigate a one-dimensional rice-pile model. We show that the distribution of dissipated potential energy decays as a power law with an exponent $α=1.53$. The system thus provides a one-dimensional example of self-organized criticality. Different driving conditions are examined in order to allow for comparison with experiments.

cond-mat.stat-mech↗

arXiv1996

Self-organized criticality in a rice-pile model

We present a new model for relaxations in piles of granular material. The relaxations are determined by a stochastic rule which models the effect of friction between the grains. We find power-law distributions for avalanche sizes and lifetimes characterized by the exponents $τ= 1.53 \pm 0.05$ and $y = 1.84 \pm 0.05$, respectively. For the discharge events, we find a characteristic size that scales with the system size as $L^μ$, with $μ= 1.20 \pm 0.05$. We also find that the frequency of the discharge events decrease with the system size as $L^{-μ'}$ with $μ' = 1.20 \pm 0.05$.

cond-mat.stat-mech↗