Thermodynamic aproach to particle size distribution in granular media

The study of particulate systems is of great interest in many fields of science and technology. Soil, sediments, powders, granular materials, colloidal and particulate suspensions are examples of systems involving many size particles. For those systems, the statistical description of the particle size distribution (PSD), that is, the mathematical distribution that defines the relative amounts of particles present, sorted according to size, is a crutial issue. The PSD can be important in understanding soil hydraulic properties, the geological origin or sediments or the physical and chemical properties of granular materials and ceramics, among others

Chiral Topological Superconductors Enhanced by Long-Range Interactions

We study the phase diagram and edge states of a two-dimensional p-wave superconductor with long-range hopping and pairing amplitudes. New topological phases and quasiparticles different from the usual short-range model are obtained. When both hopping and pairing terms decay with the same exponent, one of the topological chiral phases with propagating Majorana edge states gets significantly enhanced by long-range couplings. On the other hand, when the long-range pairing amplitude decays more slowly than the hopping, we discover new topological phases where propagating Majorana fermions at each edge pair nonlocally and become gapped even in the thermodynamic limit. Remarkably, these nonlocal edge states are still robust, remain separated from the bulk, and are localized at both edges at the same time. The inclusion of long-range effects is potentially applicable to recent experiments with magnetic impurities and islands in 2D superconductors.Comment: 5 pages, 3 figures. Close to published versio

A Fractal Interaction Model for Winding Paths through Complex Distributions: Application to Soil Drainage Networks

Water interacts with soil through pore channels putting mineral constituents and pollutants into solution. The irregularity of pore boundaries and the heterogeneity of distribution of soil minerals and contaminants are, among others, two factors influencing that interaction and, consequently, the leaching of chemicals and the dispersion of solute throughout the soil. This paper deals with the interaction of irregular winding dragging paths through soil complex distributions. A mathematical modelling of the interplay between multifractal distributions of mineral/pollutants in soil and fractal pore networks is presented. A Ho¨lder path is used as a model of soil pore network and a multifractal measure as a model of soil complex distribution, obtaining a mathematical result which shows that the Ho¨lder exponent of the path and the entropy dimension of the distribution may be used to quantify such interplay. Practical interpretation and potential applications of the above result in the context of soil are discussed. Since estimates of the value of both parameters can be obtained from field and laboratory data, hopefully this mathematical modelling might prove useful in the study of solute dispersion processes in soil

Localization and oscillations of Majorana fermions in a two-dimensional electron gas coupled with dd-wave superconductors

We study the localization and oscillation properties of the Majorana fermions that arise in a two-dimensional electron gas (2DEG) with spin-orbit coupling (SOC) and a Zeeman field coupled with a d-wave superconductor. Despite the angular dependence of the d-wave pairing, localization and oscillation properties are found to be similar to the ones seen in conventional s-wave superconductors. In addition, we study a microscopic lattice version of the previous system that can be characterized by a topological invariant. We derive its real space representation that involves nearest and next-to-nearest-neighbors pairing. Finally, we show that the emerging chiral Majorana fermions are indeed robust against static disorder. This analysis has potential applications to quantum simulations and experiments in high-$T_c$ superconductors.Comment: revtex4 file, color figure

Quantum Error Correction with the Semion Code

We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string operators that implement the basic logical operations for information processing. Physically, the new open string operators provide a detailed microscopic description of the creation of semions at their endpoints. Remarkably, topological properties of the string operators are determined using fundamental properties of the Hamiltonian, namely the fact that it is composed of commuting local terms squaring to the identity. In all, the semion code is a topological code that, unlike previously studied topological codes, it is of non-CSS type and fits into the stabilizer formalism. This is in sharp contrast with previous attempts yielding non-commutative codes.Comment: REVTeX 4 file, color figure

Graphic study and geovisualization of the old windmills of La Mancha (Spain)

In Spain, one can find geographical diversity and unique sites of great significance and cultural heritage. Many of the nation’s treasured places, however, have deteriorated or have even disappeared. What is left, then, should be studied and documented both graphically and infographically. It is important to preserve and document Spain’s unique locations, especially those related to vernacular heritage, to transhumance and visual impact assessment in many national infrastructures projects. Windmills are important examples of agro-industrial heritage and are sometimes found in the beds of streams and rivers but can also be found high in the hills. Their presence is constant throughout the Iberian Peninsula. These mills are no longer in use due to technological advances and the emergence of new grinding systems. The aim of this study was to present a specific methodology for the documentation of windmills, to create a graphical representation using computer graphics, as well as to disseminate knowledge of this agro-industrial heritage. This research has integrated graphic materials, including freehand sketches, photographs, digital orthophotos, computer graphics and multimedia in the creation of a specific methodology based on cutting-edge technology such as a digital photogrammetric workstation (DPW), global navigation satellite systems (GNSS), computer-aided design (CAD) and computer animation