Model of charge transfer collisions between C60 and slow ions.

A semiclassical model describing the charge transfer collisions of C60 fullerene with different slow ions has been developed to analyze available observations. These data reveal multiple Breit-Wigner-like peaks in the cross sections, with subsequent peaks of reactive cross sections decreasing in magnitude. Calculations of charge transfer probabilities, quasi-resonant cross sections, and cross sections for reactive collisions have been performed using semiempirical interaction potentials between fullerenes and ion projectiles. All computations have been carried out with realistic wave functions for C60's valence electrons derived from the simplified jellium model. The quality of these electron wave functions has been successfully verified by comparing theoretical calculations and experimental data on the small angle cross sections of resonant C60+C60 + collisions. Using the semiempirical potentials to describe resonant scattering phenomena in C60 collisions with ions and Landau-Zener charge transfer theory, we calculated theoretical cross sections for various C60 charge transfer and fragmentation reactions which agree with experiments.

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.

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.