Voronoi Cell Patterns: theoretical model and applications

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We use our model to describe the Voronoi cell patterns of several systems. Specifically, we study the island nucleation with irreversible attachment, the 1D car parking problem, the formation of second-level administrative divisions, and the pattern formed by the Paris M\'etro stations.Comment: 12 pages, 9 figure

Single Mothers and Poverty in Costa Rica

Despite increasing average real family incomes in Costa Rica in the late 1990s and early 2000s, poverty rates did not fall. In this paper, we argue that during this period economic growth in Costa Rica did not translate into reduced poverty because of changes in family structure and in the labor market, and that these changes had an important gender dimension. Specifically, an increase in the proportion of Costa Rican households headed by single mothers led to an increase in the number of women with children entering the labor force. Many of these mothers, new entrants to the labor force, were unable or unwilling to find full-time work in the high-paying formal sector, and ended up unemployed or working part-time as self-employed workers. These labor market phenomena, in turn, contributed to low incomes for households vulnerable to poverty, especially those households headed by single mothers.wages, Central America, poverty, employment, single mothers, Costa Rica

Competition between supersolid phases and magnetisation plateaux in the frustrated easy-axis antiferromagnet on a triangular lattice

The majority of magnetic materials possess some degree of magnetic anisotropy, either at the level of a single ion, or in the exchange interactions between different magnetic ions. Where these exchange interactions are also frustrated, the competition between them and anisotropy can stabilize a wide variety of new phases in applied magnetic field. Motivated by the hexagonal delafossite 2H-AgNiO 2, we study the Heisenberg antiferromagnet on a layered triangular lattice with competing first- and second-neighbour interactions and single-ion easy-axis anisotropy. Using a combination of classical Monte Carlo simulation, mean-field analysis, and Landau theory, we establish the magnetic phase diagram of this model as a function of temperature and magnetic field for a fixed ratio of exchange interactions, but with values of easy-axis anisotropy D extending from the Heisenberg (D =0) to the Ising (D=&#8734) limits. We uncover a rich variety of different magnetic phases. These include several phases which are magnetic supersolids (in the sense of Matsuda and Tstuneto or Liu and Fisher), one of which may already have been observed in AgNiO 2. We explore how this particular supersolid arises through the closing of a gap in the spin-wave spectrum, and how it competes with rival collinear phases as the easy-axis anisotropy is increased. The finite temperature properties of this phase are found to be different from those of any previously studied magnetic supersolid.Comment: 25 pages; 29 figures; minor revisions; accepted for publication in Phys. Rev.

On the inconsistency of the Malmquist-Luenberger index

Apart from the well-known weaknesses of the standard Malmquist productivity index related to infeasibility and not accounting for slacks, already addressed in the literature, we identify a new and significant drawback of the Malmquist-Luenberger index decomposition that questions its validity as an empirical tool for environmental productivity measurement associated with the production of bad outputs. In particular, we show that the usual interpretation of the technical change component in terms of production frontier shifts can be inconsistent with its numerical value, thereby resulting in an erroneous interpretation of this component that passes on to the index itself. We illustrate this issue with a simple numerical example. Finally, we propose a solution for this inconsistency issue based on incorporating a new postulate for the technology related to the production of bad output

Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications

We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) $P(s)=a s^\beta \exp(-b s^2)$, where $s$ is the CZ area divided by its average value. This approach offers arguably the best method to find the critical nucleus size $i$, since $\beta \approx i + 2$. Various analytical and numerical investigations, which we discuss, show that the simple GWD expression is inadequate in the tails of the distribution, it does account well for the central regime $0.5 < s < 2$, where the data is sufficiently large to be reliably accessible experimentally. We summarize and catalog the many experiments in which this method has been applied.Comment: 6 pages, 3 figures, conference paper for 17th International Conference on Crystal Growth and Epitaxy (ICCGE-17), Warsaw, Poland, Aug. 11-16, 2013, submitted for publication in different forma

A density functional theory for general hard-core lattice gases

We put forward a general procedure to obtain an approximate free energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.Comment: 4 pages, 1 eps figure, uses RevTeX

Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions

Functional central limit theorem; Occupation time fluctuation; Branching particle system; Generalized Wiener process; Critical dimension

An instance of the MIKADO migration model

In this document, we briefly describe the main contribution to the deliverable on experimenting with the implementation of most of the calculi considered in the project. First, we describe how two well known calculi for mobile processes KLAIM and Dπ have been implemented on the top of IMC. We then describe the implementation of the MiKO programming language, an instance of the parametric calculus introduced in the WP1 with the TyCO calculus as the content of the membrane itself. After this, we outline the description of the implementation of the abstract machine for an instance of the Kell Calculus that dedicates particular attention to the proof of its correctness. Our presentation ends with a discussion of the problem of implementing security membranes on the top of an execution platform