AIDS, Economic Growth and the HIPC Initiative in Honduras

AIDS, Heavily indebted poor countries, Economic growth, Foreign capital flows

Phase behavior of hard-core lattice gases: A Fundamental Measure approach

We use an extension of fundamental measure theory to lattice hard-core fluids to study the phase diagram of two different systems. First, two-dimensional parallel hard squares with edge-length $\sigma=2$ in a simple square lattice. This system is equivalent to the lattice gas with first and second neighbor exclusion in the same lattice, and has the peculiarity that its close packing is degenerated (the system orders in sliding columns). A comparison with other theories is discussed. Second, a three-dimensional binary mixture of parallel hard cubes with $\sigma_{\rm{L}}=6$ and $\sigma_{\rm{S}}=2$. Previous simulations of this model only focused on fluid phases. Thanks to the simplicity introduced by the discrete nature of the lattice we have been able to map out the complete phase diagram (both uniform and nonuniform phases) through a free minimization of the free energy functional, so the structure of the ordered phases is obtained as a result. A zoo of entropy-driven phase transitions is found: one-, two- and three-dimensional positional ordering, as well as fluid-ordered phase and solid-solid demixings.Comment: 14 pages, 16 figure

General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions

We examine critically the issue of phase transitions in one-dimensional systems with short range interactions. We begin by reviewing in detail the most famous non-existence result, namely van Hove's theorem, emphasizing its hypothesis and subsequently its limited range of applicability. To further underscore this point, we present several examples of one-dimensional short ranged models that exhibit true, thermodynamic phase transitions, with increasing level of complexity and closeness to reality. Thus having made clear the necessity for a result broader than van Hove's theorem, we set out to prove such a general non-existence theorem, widening largely the class of models known to be free of phase transitions. The theorem is presented from a rigorous mathematical point of view although examples of the framework corresponding to usual physical systems are given along the way. We close the paper with a discussion in more physical terms of the implications of this non-existence theorem.Comment: Short comment on possible generalization to wider classes of systems added; accepted for publication in Journal of Statistical Physic

Neutral networks of genotypes: Evolution behind the curtain

Our understanding of the evolutionary process has gone a long way since the publication, 150 years ago, of "On the origin of species" by Charles R. Darwin. The XXth Century witnessed great efforts to embrace replication, mutation, and selection within the framework of a formal theory, able eventually to predict the dynamics and fate of evolving populations. However, a large body of empirical evidence collected over the last decades strongly suggests that some of the assumptions of those classical models necessitate a deep revision. The viability of organisms is not dependent on a unique and optimal genotype. The discovery of huge sets of genotypes (or neutral networks) yielding the same phenotype --in the last term the same organism--, reveals that, most likely, very different functional solutions can be found, accessed and fixed in a population through a low-cost exploration of the space of genomes. The 'evolution behind the curtain' may be the answer to some of the current puzzles that evolutionary theory faces, like the fast speciation process that is observed in the fossil record after very long stasis periods.Comment: 7 pages, 7 color figures, uses a modification of pnastwo.cls called pnastwo-modified.cls (included

Fundamental measure theory for mixtures of parallel hard cubes. II. Phase behavior of the one-component fluid and of the binary mixture

A previously developed fundamental measure fucntional [J. Chem. Phys. vol.107, 6379 (1997)] is used to study the phase behavior of a system of parallel hard cubes. The single-component fluid exhibits a continuous transition to a solid with an anomalously large density of vacancies. The binary mixture has a demixing transition for edge-length ratios below 0.1. Freezing in this mixture reveals that at least the phase rich in large cubes lies in the region where the uniform fluid is unstable, hence suggesting a fluid-solid phase separation. A method is develop to study very asymmetric binary mixtures by taking the limit of zero size ratio (scaling the density and fugacity of the solvent as appropriate) in the semi-grand ensemble where the chemical potential of the solvent is fixed. With this procedure the mixture is exactly mapped onto a one-component fluid of parallel adhesive hard cubes. At any density and solvent fugacity the large cubes are shown to collapse into a close-packed solid. Nevertheless the phase diagram contains a large metastability region with fluid and solid phases. Upon introduction of a slight polydispersity in the large cubes the system shows the typical phase diagram of a fluid with an isostructural solid-solid transition (with the exception of a continuous freezing). Consequences about the phase behavior of binary mixtures of hard core particles are then drawn.Comment: 14 pages, 6 eps figures, uses revtex, amstex, epsfig, and multicol style file

Phase diagrams of Zwanzig models: The effect of polydispersity

The first goal of this article is to study the validity of the Zwanzig model for liquid crystals to predict transitions to inhomogeneous phases (like smectic and columnar) and the way polydispersity affects these transitions. The second goal is to analyze the extension of the Zwanzig model to a binary mixture of rods and plates. The mixture is symmetric in that all particles have equal volume and length-to-breadth ratio, $\kappa$. The phase diagram containing the homogeneous phases as well as the spinodals of the transitions to inhomogeneous phases is determined for the cases $\kappa=5$ and 15 in order to compare with previous results obtained in the Onsager approximation. We then study the effect of polydispersity on these phase diagrams, emphasizing the enhancement of the stability of the biaxial nematic phase it induces.Comment: 11 pages, 12 figure

Cross-diffusion systems for image processing: II. The nonlinear case

In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a numerical point of view, a computational study of the performance of the models is carried out, suggesting their diversity and potentialities to treat image filtering problems. The present paper is a continuation of a previous work of the same authors, devoted to linear cross-diffusion models. \keywords{Cross-diffusion \and Complex diffusion \and Image restoration