A note on fractional stochastic convergence

We show that a class of non-stationary stochastic processes exhibiting long-range dependence satisfies one definition of time series convergence proposed in the literature. We also show explicitly the relationship between two time series concepts convergence proposed in the literature. Furthermore, we assess income per capita convergence for a sample OECD of economies using time series based tests. When we allow income shocks to exhibit long-range dependence, generalizing previous specifications, we find ample evidence of pairwise convergence among OECD economies. This finding is contrary to the literature that uses unit roots and cointegration tests.

Phase Separation and the Dual Nature of the Electronic Structure in Cuprates

The dual nature of the electronic structure of stripes in $La_{2-x}Sr_xCuO_4$ was characterized by experimental observations, mainly by ARPES, of nodal spectral weight together with the straight segments near antinodal regions. We present here an attempt to understand this dual behavior in terms of the competition of order and disorder, by applying the phase separation theory of Cahn-Hilliard (CH) to the high pseudogap temperature, which is very large in the far underdoping region and vanishs near the doping level p=0.2. The spinodal phase separation predictions together with the Bogoliubov-deGennes (BdG) superconducting theory provides several interesting insights. For instance, we find that the disorder enhances the local superconducting gap which scales with the leading edge shift and that, upon doping, the size of the hole-rich stripes increases, yielding to the system their metallic properties.Comment: revised version, 4 pages and 3 fig

Numerical Study of the Cahn-Hilliard Equation in One, Two and Three Dimensions

The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it numerically increases with the dimensionality and therefore, there are several published numerical studies in one dimension (1D), dealing with different approaches, and much fewer in two dimensions (2D). In three dimensions (3D) there are very few publications, usually concentrate in some specific result without the details of the used numerical scheme. We present here a stable and fast conservative finite difference scheme to solve the Cahn-Hilliard with two improvements: a splitting potential into a implicit and explicit in time part and a the use of free boundary conditions. We show that gradient stability is achieved in one, two and three dimensions with large time marching steps than normal methods.Comment: 20 pages with 12 figs. Accepted in the Physica