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It is shown how to reconstruct the stacking sequence from the pairwise correlation functions between layers in close-packed structures. First, of theoretical interest, the analytical formulation and solution of the problem are presented when the exact pairwise correlation counts are known. In the second part, the practical problem is approached. A simulated annealing procedure is developed to solve the problem using as initial guess approximate solutions from previous treatments. The robustness of the procedure is tested with synthetic data, followed by an experimental example. The developed approach performs robustly over different synthetic and experimental data, comparing favorably with the reported methods.

This is the second contribution in a series of papers dealing with dynamical models in equilibrium theories of polytypism. A Hamiltonian introduced by Ahmad & Khan [Phys. Status Solidi B(2000),218, 425–430] avoids the unphysical assignment of interaction terms to fictitious entities given by spins in the Hägg coding of the stacking arrangement. In this paper an analysis of polytype generation and disorder in close-packed structures is made for such a Hamiltonian. Results are compared with a previous analysis using the Ising model. Computational mechanics is the framework under which the analysis is performed. The competing effects of disorder and structure, as given by entropy density and excess entropy, respectively, are discussed. It is argued that the Ahmad & Khan model is simpler and predicts a larger set of polytypes than previous treatments.

The correlated biased random walk with latency in one and two dimensions is discussed with regard to the portion of irreducible random movement and structured movement. It is shown how a quantitative analysis can be carried out by using computational mechanics. The stochastic matrix for both dynamics are reported. Latency introduces new states in the finite state machine description of the system in both dimensions, allowing for a full nearest neighbor coordination in the two dimensional case. Complexity analysis is used to characterize the movement, independently of the set of control parameters, making it suitable for the discussion of other random walk models. The complexity map of the system dynamics is reported for the two dimensional case.

International audience; Extrinsic faulting has been discussed previously within the so-called difference method and random walk calculation. In this contribution it is revisited under the framework of computational mechanics, which allows expressions to be derived for the statistical complexity, entropy density and excess entropy as a function of faulting probability. The approach allows one to compare the disordering process of an extrinsic fault with other faulting types. The "-machine description of the faulting mechanics is presented. Several useful analytical expressions such as probability of consecutive symbols in the Hä gg coding are presented, as well as hexagonality. The analytical expression for the pairwise correlation function of the layers is derived and compared with results previously reported. The effect of faulting on the interference function is discussed in relation to the diffraction pattern.

The stacking problem is approached by computational mechanics, using an Ising next nearest neighbor model. Computational mechanics allows to treat the stacking arrangement as an information processing system in the light of a symbol generating process. A general method for solving the stochastic matrix of the random Gibbs field is presented, and then applied to the problem at hand. The corresponding phase diagram is then discussed in terms of the underlying $\epsilon$-machine, or optimal finite state machine, describing statistically the system. The occurrence of higher order polytypes at the borders of the phase diagram is also analyzed. Discussion of the applicability of the model to real system such as ZnS and Cobalt is done. The method derived is directly generalizable to any one dimensional model with finite range interaction.

The use of Hilbert curves to visualize massive vector of data is revisited following previous authors. The Hilbert curve mapping preserves locality and makes meaningful representation of the data. We call such visualization as Hilbert plots. The combination of a Hilbert plot with its Fourier transform allows to identify patterns in the underlying data sequence. The use of different granularity representation also allows to identify periodic intervals within the data. Data from different sources are presented: periodic, aperiodic, logistic map and 1/2-Ising model. A real data example from the study of heartbeat data is also discussed., Accepted at Computer Physics Communications