Physical Review E
(Statistical, Nonlinear, and Soft Matter Physics)
Print Issue of June 2001

Phys. Rev. E 63, 066701 (2001) (8 pages)

Full text: PDF (852 kB)

Efficient reconstruction of multiphase morphologies from correlation functions

M. G. Rozman and Marcel Utz
Institute of Materials Science and Department of Physics, University of Connecticut, Storrs, Connecticut 06269
(Received 11 December 2000; published 15 May 2001)

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.

©2001 The American Physical Society


02.70.-c Computational techniques;
61.43.Bn Structural modeling
05.10.Ln Computational methods in statistical physics and nonlinear dynamics
81.07.-b Nanoscale materials and structures

Keywords: heterogeneous medium; two-point correlation functions; reconstruction; stereology; mathematical morphology;

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© 2001 Michael Rozman (
Last modified: May 17, 2001