Density of States for a Specified Correlation Function and the Energy Landscape

Abstract

The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are described in terms of the roughness of the energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered systems.

Computer simulations of glasses: the potential energy landscape

“…In particular, the density of states in configuration space near the global minimum is much higher for glassy systems: fragility seems to be associated with a higher density of inherent states, lower activation barriers and higher vibrational frequencies [88]. A mathematical treatment of the density of states demonstrates that there is a strong correlation between ground state degeneracy and the roughness of the PEL [89], which fits well with the general picture that good glass-formers have a rough, highly degenerate PEL with no easily accessible ground state. Doye and Wales [90] draw similarities between the potential energy surfaces and the free energy surface model used by Wolynes et al to describe protein folding [91,92].…”

Stable-phase method for hierarchical annealing in the reconstruction of porous media images

“…Recently, two general approaches [10][11][12][13][14][15][16][17][18][19][20][21][22] based on statistical reconstructions have actively been pursued. The first method is based on the conditioning and truncation of Gaussian random fields [10][11][12][13]: successively passing a normalized uncorrelated random Gaussian field through a linear and then a nonlinear filter to yield the discrete values representing the phases (or states) of the structure.…”

“…This is a drawback, and even more serious, it is difficult to generalize the structures for systems with more than two phases. Another popular stochastic approach to reconstruct the 3D microstructure of a * Corresponding author: hxh@scu.edu.cn porous medium is the simulated annealing (SA) reconstruction algorithm [14][15][16][17][18][19][20][21]. This method was first introduced by Rintoul and Torquato in 1997 [22], which starts with a given, arbitrarily chosen, initial configuration of a random medium and a set of target functions.…”

“…The attractive convergence property of the SA algorithm [14][15][16][17][18][19][20][21][22] is offset rapidly by the high demand for computational resources, particularly for the reconstruction of a large-scale microstructure-very common in porous media. To enhance the rate of convergence, several methods were proposed within the SA reconstruction framework.…”

Reconstruction of heterogeneous materials via stochastic optimization of limited-angle X-ray tomographic projections

“…Our reconstruction procedure is inspired by the stochastic optimization scheme developed by Yeong and Torquato to generate virtual microstructures from prescribed statistical morphological descriptors of the microstructure, i.e., various correlation functions associated with different phases of the material [30][31][32][33]. It works as follows.…”