Efficient reconstruction of multiphase morphologies from correlation functions

Abstract

A highly efficient algorithm for the reconstruction of microstructures of heterogeneous media from spatial correlation functions is presented. Since many experimental techniques yield two-point correlation functions, the restoration of heterogeneous structures, such as composites, porous materials, microemulsions, ceramics, or polymer blends, is an inverse problem of fundamental importance. Similar to previously proposed algorithms, the new method relies on Monte Carlo optimization, representing the microstructure on a discrete grid. An efficient way to update the correlation functions after local changes to the structure is introduced. In addition, the rate of convergence is substantially enhanced by selective Monte Carlo moves at interfaces. Speedups over prior methods of more than two orders of magnitude are thus achieved. Moreover, an improved minimization protocol leads to additional gains. The algorithm is ideally suited for implementation on parallel computers. The increase in efficiency brings new classes of problems within the realm of the tractable, notably those involving several different structural length scales and/or components.

Necessary and sufficient conditions for the two-point phase probability function of two-phase random media

“…These results complement computational algorithms such as stochastic optimization (Yeong & Torquato 1998;Cule & Torquato 1999;Rozman & Utz 2001, 2002Sheehan & Torquato 2001), which have been used for the same purpose.…”

“…In principle, S 2 can be inferred from a given random material by using small-angle scattering data (Guinier et al 1955;Torquato 2002); however, the required inversion is susceptible to numerical errors. To overcome this difficulty, different techniques have been proposed in the literature for constructing random media with a predetermined S 2 , including stochastic optimization (Yeong & Torquato 1998;Cule & Torquato 1999;Sheehan & Torquato 2001;Rozman & Utz 2001, 2002 and Gaussian random field models (Roberts 1997;Nott & Rydén 1999;Nott & Wilson 2000;Quintanilla & Jones 2007;.…”

Frozen-State Hierarchical Annealing

“…Traditional uses of annealing methods [31,36,37,46] have tended to regard the first two factors, φ and N , as relatively fixed: the first is determined by the choice of energy model, while the second is determined by the image size, leaving the third factor -the number of iterations -as the only area where significant reductions are feasible. Consequently, much of the literature on simulated annealing methods has focused on ways to accelerate the computations by reducing the number of iterations needed to achieve satisfactory results [1,26,35].…”

Statistical methods for mechanical characterization of randomly reinforced media

“…This approached was mathematically developed in further works. Its limitations relate to inconsistency when processing more than two-phase media and Gaussian character of field requirement (Rozman and Utz 2001).…”