Matrix differential equations and scalar polynomials satisfying higher order recursions

We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same property. The construction of the correspond- ing family of matrix valued polynomials has been studied in [D1, D2, DV] but the existence of a differential operator having them as common eigen- functions had not been considered This correspondence goes only one way and most matrix valued situations do not arise in this fashion. We illustrate this general construction with a few examples. In the case of some families of scalar valued polynomials introduced in [GH] we take a first look at the algebra of all matrix differential operators that share these common eigenfunctions and uncover a number of phenomena that are new to the matrix valued case

Geometric properties of two-dimensional coarsening with weak disorder

The domain morphology of weakly disordered ferromagnets, quenched from the high-temperature phase to the low-temperature phase, is studied using numerical simulations. We find that the geometrical properties of the coarsening domain structure, e.g., the distributions of hull enclosed areas and domain perimeter lengths, are described by a scaling phenomenology in which the growing domain scale R(t) is the only relevant parameter. Furthermore, the scaling functions have forms identical to those of the corresponding pure system, extending the 'super-universality' property previously noted for the pair correlation function.Comment: 6 pages, 6 figure

Exact results for curvature-driven coarsening in two dimensions

We consider the statistics of the areas enclosed by domain boundaries (`hulls') during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than $A$ has, for large time $t$, the scaling form $N_h(A,t) = 2c/(A+\lambda t)$, demonstrating the validity of dynamical scaling in this system, where $c=1/8\pi\sqrt{3}$ is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of $A/\lambda t$. Identical forms are obtained for coarsening from a critical initial state, but with $c$ replaced by $c/2$.Comment: 4 pages, 4 figure

Curvature-driven coarsening in the two dimensional Potts model

We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the $q$-states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with non-conserved order parameter. We analyze the distribution of hull enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for $q=2$ (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit super-universality properties.Comment: 12 pages, 16 figure

Interatomic Methods for the Dispersion Energy Derived from the Adiabatic Connection Fluctuation-Dissipation Theorem

Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory (DFT) calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on \textit{ad hoc} assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula. Moreover, for a system of quantum harmonic oscillators coupled through a dipole--dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD correlation energy in the random-phase approximation. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy

Dynamic Potential-Ph Diagrams Application to Electrocatalysts for Water Oxidation

The construction and use of "dynamic potential-pH diagrams" (DPPDs), that are intended to extend the usefulness of thermodynamic Pourbaix diagrams to include kinetic considerations is described. As an example, DPPDs are presented for the comparison of electrocatalysts for water oxidation, i.e., the oxygen evolution reaction (OER), an important electrochemical reaction because of its key role in energy conversion devices and biological systems (water electrolyses, photoelectrochemical water splitting, plant photosynthesis). The criteria for obtaining kinetic data are discussed and a 3-D diagram, which shows the heterogeneous electron transfer kinetics of an electrochemical system as a function of pH and applied potential is presented. DPPDs are given for four catalysts: IrO(2), Co(3)O(4), Co(3)O(4) electrodeposited in a phosphate medium (Co-Pi) and Pt, allowing a direct comparison of the activity of different electrode materials over a broad range of experimental conditions (pH, potential, current density). In addition, the experimental setup and the factors affecting the accurate collection and presentation of data (e. g., reference electrode system, correction of ohmic drops, bubble formation) are discussed.Ministry of Education, University and Research PRIN 2008PF9TWZ, 2008N7CYL5Universita degli Studi di MilanoNational Science Foundation CHE-0808927Robert A. Welch Foundation F-0021Center for Electrochemistr

Major shifts at the range edge of marine forests: the combined effects of climate changes and limited dispersal

Global climate change is likely to constrain low latitude range edges across many taxa and habitats. Such is the case for NE Atlantic marine macroalgal forests, important ecosystems whose main structuring species is the annual kelp Saccorhiza polyschides. We coupled ecological niche modelling with simulations of potential dispersal and delayed development stages to infer the major forces shaping range edges and to predict their dynamics. Models indicated that the southern limit is set by high winter temperatures above the physiological tolerance of overwintering microscopic stages and reduced upwelling during recruitment. The best range predictions were achieved assuming low spatial dispersal (5 km) and delayed stages up to two years (temporal dispersal). Reconstructing distributions through time indicated losses of similar to 30% from 1986 to 2014, restricting S. polyschides to upwelling regions at the southern edge. Future predictions further restrict populations to a unique refugium in northwestern Iberia. Losses were dependent on the emissions scenario, with the most drastic one shifting similar to 38% of the current distribution by 2100. Such distributional changes might not be rescued by dispersal in space or time (as shown for the recent past) and are expected to drive major biodiversity loss and changes in ecosystem functioning.Electricity of Portugal (Fundo EDP para a Biodiversidade); FCT - Portuguese Science Foundation [PTDC/MAR-EST/6053/2014, EXTANT-EXCL/AAG-GLO/0661/2012, SFRH/BPD/111003/2015

Formícidos del litoral granadino

The myrmecofauna of the coast of Granada includes 48 species, with a main group of ethiopic origin (33 %), and few holartic species (10 %). Cataglyphis sp. ined. is confirmed as a new species for science. Cardiocondyla mauritanica and Monomorium algiricum are recorded for the first time in the European continent, and Oxyopomyrmex santschii is reported for the second time in the Iberian peninsula. The most numerous biotopes, calcareous and siliceous, contain the same number of species, though the calcareous one is quantitatively richer. Some ant species live strictly at the seaside (Monomorium subopacum),while others tend to live far from the sea (Cremastogaster sordidula).La mirmecofauna de la costa granadina comprende 48 especies, con un componente mayoritario de origen eti6pico en sentido amplio (33 %), siendo 10s elementos holárticos relativamente escasos (10 %). Se confirma a Cataglyphis sp. ined. como nueva especie para la ciencia. Se cita por primera vez a Cardiocondyla mauritanica y a Monomorium algiricum en el continente europeo, asi como a Oxyopomyrmex santschii por segunda vez para la península ibérica. Los biotopos mayoritarios, calizo y siliceo, contienen el mismo número de especies, siendo el primero más rico cuantitativamente. Se distingue entre hormigas estrictamente litorales (Monomorium subopacum) y otras tendentes a alejarse del litoral (Cremastogaster sordidula)

Kibble-Zurek mechanism and infinitely slow annealing through critical points

We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phase ordering systems during an infinitely slow annealing across a second order phase transition. We elucidate the time and cooling rate dependence of the typical growing length and we use it to predict the number of topological defects left over in the symmetry broken phase as a function of time, both close and far from the critical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.Comment: 5 pages, 4 fig