Slow relaxation due to optimization and restructuring: Solution on a hierarchical lattice

Details Slow relaxation due to optimization and restructuring: Solution on a hierarchical lattice Slow relaxation due to optimization and restructuring: Solution on a hierarchical lattice

2002-09-09

arxiv.org/abs/cond-mat/0209211v2

Physics

Condensed Matter

Statistical Mechanics

11 pages, 7 figures revtex, submitted to PRE see also: cond-mat/0209209

Scientific paper

Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other models of statistical phyics are discussed. We investigate our model on a hierarchical lattice which allows an exact asymptotic renormalization treatment. A surprisingly close analogy is observed between the simulation results on the regular and the hierarchical lattices. The dynamics is characterized by the breakdown of ergodicity, by unusual system size effects in the development of the average density as well as by the age distribution, the latter showing multifractal properties.

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