Percolation model for structural phase transitions in Li1−x_{1-x}Hx_xIO3_3 mixed crystals

A percolation model is proposed to explain the structural phase transitions found in Li$_{1-x}$H$_x$IO$_3$ mixed crystals as a function of the concentration parameter $x$. The percolation thresholds are obtained from Monte Carlo simulations on the specific lattices occupied by lithium atoms and hydrogen bonds. The theoretical results strongly suggest that percolating lithium vacancies and hydrogen bonds are indeed responsible for the solid solution observed in the experimental range $0.22 < x < 0.36$.Comment: 4 pages, 2 figure

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

Fraction of uninfected walkers in the one-dimensional Potts model

The dynamics of the one-dimensional q-state Potts model, in the zero temperature limit, can be formulated through the motion of random walkers which either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is investigated numerically and found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial exponent \phi(q). Our study is extended to include the coupled diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) \sim t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi}, where \phi \simeq 1.13 when infection occurs between like particles only, and \phi \simeq 1.93 when we also include cross-species contamination.Comment: Expanded introduction with more discussion of related wor

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

Preparation, structural, dielectric and magnetic properties of LaFeO3-PbTiO3 solid solutions

Solid solutions of (1-x)LaFeO3-(x)PbTiO3 (0<x<1) have been prepared by conventional solid-state reaction. These complex perovskites have been studied by means of X-ray (XRPD) and neutron powder (NPD) diffraction, complemented with dielectric, magnetic, heat capacity and M\"ossbauer measurements. Complete solubility in the perovskite series was demonstrated. The NPD and XRPD patterns were successfully refined as orthorhombic (x \leq 0.7) and tetragonal (x \geq 0.8). A composition-driven phase transformation occurs within the interval 0.7<x<0.8. The samples with x<0.5 showed evidence of long-range magnetic ordering with an G-type antiferromagnetic arrangement of the magnetic moments of the Fe3+ cations in the B-site with propagation vector k = (0,0,0). Based on the obtained experimental data, a combined structural and magnetic phase diagram has been constructed. The factors governing the structural, dielectric and magnetic properties of (1-x) LaFeO3 - (x)PbTiO3 solid solutions are discussed, as well as their possible multiferroicity.Comment: 33 pages, 15 figure

Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation

In this chapter, we will describe, in a tutorial style, recent work on the use of fluid approximation techniques in the context of stochastic model checking. We will discuss the theoretical background and the algorithms working out an example. This approach is designed for population models, in which a (large) number of individual agents interact, which give rise to continuous time Markov chain (CTMC) models with a very large state space. We then focus on properties of individual agents in the system, specified by Continuous Stochastic Logic (CSL) formulae, and use fluid approximation techniques (specifically, the so called fast simulation) to check those properties. We will show that verification of such CSL formulae reduces to the computation of reachability probabilities in a special kind of time-inhomogeneous CTMC with a small state space, in which both the rates and the structure of the CTMC can change (discontinuously) with time. In this tutorial, we will discuss only briefly the theoretical issues behind the approach, like the decidability of the method and the consistency of the approximation scheme

Powder second harmonic generation efficiencies of saccharide materials

Saccharide materials are potential candidates for frequency conversion applications. In addition to being chiral, which ensures crystallization in a space group necessary for three-wave mixing processes, they generally possess useful physical and optical properties. We have examined the powder second harmonic generation efficiencies of both saturated saccharides and sugars with simple polar π-functionalities. Powder efficiencies of up to 5 times that of sucrose were observed for simple saturated sugars, whereas values of 18 times sucrose (or 0.45 x urea) were observed for unsaturated saccharide derivatives. We have noted that for both classes of material, there is a tendency for more efficient nonlinear compounds to reside in a monoclinic rather than an orthorhombic space group. We have also noted that there appears to be a correlation between the phase-matching potential and the crystal symmetry. In addition, two promising saccharide materials have been identified for frequency conversion applications, based on their powder second-harmonic generation efficiencies, their phase-matching capabilities, and their UV transparency. © 1993 American Chemical Society