Linear response of vibrated granular systems to sudden changes in the vibration intensity

The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the evolution of the system. The existence of a critical time separating regimes of ``anomalous'' and ``normal'' responses is predicted. A simple model fitting into the general framework is analyzed in the detail. The relationship between this work and previous studies is discussed.Comment: 10 pages, 6 figures; fixed errata, updtated reference

Ground-state energy and entropy of the two-dimensional Edwards-Anderson spin-glass model with different bond distributions

We study the two-dimensional Edwards-Anderson spin-glass model using a parallel tempering Monte Carlo algorithm. The ground-state energy and entropy are calculated for different bond distributions. In particular, the entropy is obtained by using a thermodynamic integration technique and an appropriate reference state, which is determined with the method of high-temperature expansion. This strategy provide accurate values of this quantity for finite-size lattices. By extrapolating to the thermodynamic limit, the ground-state energy and entropy of the different versions of the spin-glass model are determined.Comment: 18 pages, 5 figure

Reversible Random Sequential Adsorption of Dimers on a Triangular Lattice

We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly confirm the importance of two-particle events in the simple two-dimensional triangular lattice. For the two-dimensional triangular lattice with the nearest neighbors excluded, the observed dynamics are consistent with this picture. The two-dimensional simulations were motivated by measurements of Ca++ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.Comment: 9 pages, 10 figure

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

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.Comment: 11 pages, 7 figures revtex, submitted to PRE see also: cond-mat/020920

Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter \Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperature-like parameter \eta(\Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favourably with a range of known experimental behaviour. This includes the logarithmic densification and power spectrum of fluctuations under constant \eta, the annealing curve when \eta is varied cyclically in time, and memory effects observed for a discontinuous shift in \eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.Comment: 2 references added; some figure labels tweaked. To appear in PR