Testing predictions of macroscopic binary diffusion coefficients using lattice models with site heterogeneity

Quantitatively predicting mass transport rates for chemical mixtures in porous materials is important in applications of materials such as adsorbents, membranes, and catalysts. Because directly assessing mixture transport experimentally is challenging, theoretical models that can predict mixture diffusion coefficients using Only single-component information would have many uses. One such model was proposed by Skoulidas, Sholl, and Krishna (Langmuir, 2003, 19, 7977), and applications of this model to a variety of chemical mixtures in nanoporous materials have yielded promising results. In this paper, the accuracy of this model for predicting mixture diffusion coefficients in materials that exhibit a heterogeneous distribution of local binding energies is examined. To examine this issue, single-component and binary mixture diffusion coefficients are computed using kinetic Monte Carlo for a two-dimensional lattice model over a wide range of lattice occupancies and compositions. The approach suggested by Skoulidas, Sholl, and Krishna is found to be accurate in situations where the spatial distribution of binding site energies is relatively homogeneous, but is considerably less accurate for strongly heterogeneous energy distributions.

Energy level statistics for models of coupled single-mode Bose-Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.

Solution of the dual reflection equation for A(n-1)((1)) solid-on-solid model

We obtain a diagonal solution of the dual reflection equation for the elliptic A(n-1)((1)) solid-on-solid model. The isomorphism between the solutions of the reflection equation and its dual is studied. (C) 2004 American Institute of Physics.

Central elements of the elliptic Zn monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo. (c) 2004 Elsevier B.V. All rights reserved.

A parallel implementation of the lattice solid model for the simulation of rock mechanics and earthquake dynamics

The Lattice Solid Model has been used successfully as a virtual laboratory to simulate fracturing of rocks, the dynamics of faults, earthquakes and gouge processes. However, results from those simulations show that in order to make the next step towards more realistic experiments it will be necessary to use models containing a significantly larger number of particles than current models. Thus, those simulations will require a greatly increased amount of computational resources. Whereas the computing power provided by single processors can be expected to increase according to Moore's law, i.e., to double every 18-24 months, parallel computers can provide significantly larger computing power today. In order to make this computing power available for the simulation of the microphysics of earthquakes, a parallel version of the Lattice Solid Model has been implemented. Benchmarks using large models with several millions of particles have shown that the parallel implementation of the Lattice Solid Model can achieve a high parallel-efficiency of about 80% for large numbers of processors on different computer architectures.

Parallel 3D Simulation of a Fault Gouge using the Lattice Solid Model

Despite the insight gained from 2-D particle models, and given that the dynamics of crustal faults occur in 3-D space, the question remains, how do the 3-D fault gouge dynamics differ from those in 2-D? Traditionally, 2-D modeling has been preferred over 3-D simulations because of the computational cost of solving 3-D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3-D fault micro-mechanics and to advance understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2-D and 3-D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3-D models undergo significant out-of-plane motion during shear. The 3-D models also exhibit a higher mean macroscopic friction than the 2-D models for varying values of interparticle friction. 2-D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3-D models are shown to also display accelerating energy release, and good fits of power law time-to-failure functions to the cumulative energy release are obtained.