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.

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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Assuming square, hexagonal, and random packed arrays of nonoverlapping identical parallel cylindrical voids dispersed in an aluminum matrix, we have calculated numerically the concentration dependence of the transverse Poisson's ratios. It was shown that the transverse Poisson's ratio of the hexagonal and random packed arrays approached 1 upon increasing the concentration of voids while the ratio of the square packed array along the principal continuation directions approached 0. Experimental measurements were carried out on rectangular aluminum bricks with identical cylindrical holes drilled in square and hexagonal packed arrays. Experimental results were in good agreement with numerical predictions. We then demonstrated, based on the numerical and experimental results, that by varying the spatial arrangement of the holes and their volume fraction, one can design and manufacture voided materials with a tailored Poisson's ratio between 0 and 1. In practice, those with a high Poisson's ratio, i.e., close to 1, can be used to amplify the lateral responses of the structures while those with a low one, i.e., close to 0, can largely attenuate the lateral responses and can therefore be used in situations where stringent lateral stability is needed.

Strain solitons have been observed statically in several 2D materials and dynamically in substrate materials using ultrafast laser pulses. The latter case relies on lattice relaxation in response to ultrafast heating in a light-absorbing transducer material, a process which is sensitive to the thermal expansion coefficient. Here we consider an unusual case where the sign of the thermal expansion coefficient is negative, a scenario which is experimentally feasible in light of rapid and recent advances in the discovery of negative thermal expansion materials. We present numerical solutions to a nonlinear differential equation which has been repeatedly demonstrated to quantitatively model experimental data and discuss the salient results using realistic parameters for material linear and nonlinear elasticity. The solitons that emerge from the initial value problem with negative and positive thermal expansion are qualitatively different in several ways. The new case of negative thermal expansion gives rise to a nearly-periodic soliton train with chirped profile and free of an isolated shock front. We suggest this unanticipated result may be realized experimentally and assess the potential for certain applications of this generic effect.