M G Rozman | PubMed Health

PubMed2002

Uniqueness of reconstruction of multiphase morphologies from two-point correlation functions.

The restoration of the spatial structure of heterogeneous media, such as composites, porous materials, microemulsions, ceramics, or polymer blends from two-point correlation functions, is a problem of relevance to several areas of science. In this contribution we revisit the question of the uniqueness of the restoration problem. We present numerical evidence that periodic, piecewise uniform structures with smooth boundaries are completely specified by their two-point correlation functions, up to a translation and, in some cases, inversion. We discuss the physical relevance of the results.

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PubMed2001

Efficient reconstruction of multiphase morphologies from correlation functions.

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.

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