Energy-Variation Analysis and Orbit-Complexity Quantification

In state-recurrence analysis, recurrences are considered either in the space that constitutes of the observed quantities, or in an embedding space that is manufactured by time-delayed variables. An alternative approach is proposed here. In the so-called energy-variation analysis, the complexity of an orbit is quantified in terms of the statistics of the constant-speed geodesic condition. Energy-variation analysis requires significantly less operations than state-recurrence analysis, in particular, for multivariate time-series, while numerical experiments demonstrate that the resulting energy-recurrence matrix encodes information that is sufficient for quantifying the complexity of orbits.

Formation of two edge dislocations in a grain due to interface disclination dipoles

The formation of a dipole of edge dislocations inside one grain separated from the adjacent grains by two interfaces in which are lying disclination dipoles (one in each interface) has been theoretically investigated from an energy variation calculation. Critical grain sizes associated with the formation of the edge dislocation dipole have been determined as well as an activation energy. The effects of the inclination angle of the gliding plane of the dislocations and the characteristic parameters of the disclination dipoles have been finally analyzed.