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.