Reconstruction of the dissipation coefficient in lattice models

Variants of the 2-D cellular model introduced by Olami, Feder, and Christensen (an analogue of the Burridge-Knopoff spring-block model) are examined. The influx of energy into each cell from the outside occurs at a constant rate. When the energy in a cell exceeds a certain threshold, the cell is “ruptured;” i.e., part of its energy, defined by the coefficient D, dissipates while the remainder is redistributed among the adjacent cells. The model is used to construct a catalog of clusters of ruptured cells. A method is proposed for estimating the dissipation coefficient D from the recurrence plot for a truncated catalog. In the range 0 ≤ D ≤ 0.35, D is estimated accurate to 0.01. The accuracy is improved with increasing lattice size.