Percolation of straight slots on a square grid.

This work is devoted to the emergence of a connected network of slots (cracks) on a square grid. Accordingly, extensive Monte Carlo simulations and finite-size scaling analysis have been conducted to study the site percolation of straight slots with length l measured in the number of elementary cells of the grid with the edge size L. A special focus was made on the dependence of the percolation threshold p_{C}(l,L) on the slot length l varying in the range 1≤l≤L-2 for the square grids with edge size in the range 50≤L≤1000. In this way, we found that p_{C}(l,L) strongly decreases with increase of l, whereas the variations of p_{C}(l=const,L) with the variation of ratio l/L are very small. Consequently, we acquire the functional dependencies of the critical filling factor and percolation strength on the slot length. Furthermore, we established that the slot percolation model interpolates between the site percolation on square lattice (l=1) and the continuous percolation of widthless sticks (l→∞) aligned in two orthogonal directions. In this regard, we note that the critical number of widthless sticks per unit area is larger than in the case of randomly oriented sticks. Our estimates for the critical exponents indicate that the slot percolation belongs to the same universality class as standard Bernoulli percolation.

Characterization of hybrid microparticles/Montmorillonite composite with raspberry-like morphology for Atorvastatin controlled release.

In this work, we prepared a novel composite based on hybrid gelatin carriers and montmorillonite clay (MMT) to analyze its viability as controlled drug delivery system. The objective of this research involves the characterization of composites formed by structured lipid-gelatin micro-particles (MP) and MMT clay. This analysis included the evaluation of the composite according to its rheological properties, morphology (SEM), particle size, XRD, FT-IR, and in vitro drug release. The effect of pH in the properties of the composite is evaluated. A novel raspberry-like or armor MP/MMT clay composite is reported, in which the pH has an important effect on the final structure of the composite for ad-hoc drug delivery systems. For pH values below the isoelectric point, we obtained defined morphologies with entrapment efficiencies up to 67%. The pH level controls the MP/MMT composite release mechanism, restringing drug release in the stomach-like environment. Intended for oral administration, these results evidence that the MP/MMT composite represents an attractive alternative for intestinal-colonic controlled drug delivery systems.

Random walk in chemical space of Cantor dust as a paradigm of superdiffusion.

We point out that the chemical space of a totally disconnected Cantor dust K(n) [Symbol: see text E(n) is a compact metric space C(n) with the spectral dimension d(s) = d(ℓ) = n > D, where D and d(ℓ) = n are the fractal and chemical dimensions of K(n), respectively. Hence, we can define a random walk in the chemical space as a Markovian Gaussian process. The mapping of a random walk in C(n) into K(n) [Symbol: see text] E(n) defines the quenched Lévy flight on the Cantor dust with a single step duration independent of the step length. The equations, describing the superdiffusion and diffusion-reaction front propagation ruled by the local quenched Lévy flight on K(n) [Symbol: see text] E(n), are derived. The use of these equations to model superdiffusive phenomena, observed in some physical systems in which propagators decay faster than algebraically, is discussed.