Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene

Crystalline membranes at finite temperatures have an anomalous behavior of the bending rigidity that makes them more rigid in the long wavelength limit. This issue is particularly relevant for applications of graphene in nano- and micro-electromechanical systems. We calculate numerically the height-height correlation function $G(q)$ of crystalline two-dimensional membranes, determining the renormalized bending rigidity, in the range of wavevectors $q$ from $10^{-7}$ \AA$^{-1}$ till 10 \AA$^{-1}$ in the self-consistent screening approximation (SCSA). For parameters appropriate to graphene, the calculated correlation function agrees reasonably with the results of atomistic Monte Carlo simulations for this material within the range of $q$ from $10^{-2}$ \AA$^{-1}$ till 1 \AA$^{-1}$. In the limit $q\rightarrow 0$ our data for the exponent $\eta$ of the renormalized bending rigidity $\kappa_R(q)\propto q^{-\eta}$ is compatible with the previously known analytical results for the SCSA $\eta\simeq 0.82$. However, this limit appears to be reached only for $q<10^{-5}$ \AA$^{-1}$ whereas at intermediate $q$ the behavior of $G(q)$ cannot be described by a single exponent.Comment: 5 pages, 4 figure

Thermodynamics of quantum crystalline membranes

We investigate the thermodynamic properties and the lattice stability of two-dimensional crystalline membranes, such as graphene and related compounds, in the low temperature quantum regime $T\rightarrow0$. A key role is played by the anharmonic coupling between in-plane and out-of plane lattice modes that, in the quantum limit, has very different consequences than in the classical regime. The role of retardation, namely of the frequency dependence, in the effective anharmonic interactions turns out to be crucial in the quantum regime. We identify a crossover temperature, $T^{*}$, between classical and quantum regimes, which is $\sim 70 - 90$ K for graphene. Below $T^{*}$, the heat capacity and thermal expansion coefficient decrease as power laws with decreasing temperature, tending to zero for $T\rightarrow0$ as required by the third law of thermodynamics.Comment: 13 pages, 1 figur

On some fixed point theorems under (α,ψ,ϕ) -contractivity conditions in metric spaces endowed with transitive binary relations

After the appearance of Nieto and Rodríguez-López’s theorem, the branch of fixed point theory devoted to the setting of partially ordered metric spaces have attracted much attention in the last years, especially when coupled, tripled, quadrupled and, in general, multidimensional fixed points are studied. Almost all papers in this direction have been forced to present two results assuming two different hypotheses: the involved mapping should be continuous or the metric framework should be regular. Both conditions seem to be different in nature because one of them refers to the mapping and the other one is assumed on the ambient space. In this paper, we unify such different conditions in a unique one. By introducing the notion of continuity of a mapping from a metric space into itself depending on a function α, which is the case that covers the partially ordered setting, we extend some very recent theorems involving control functions that only must be lower/upper semi-continuous from the right. Finally, we use metric spaces endowed with transitive binary relations rather than partial orders.This article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah. N Shahzad acknowledges with thanks DSR for financial support. A-F Roldán-López-de-Hierro is grateful to the Department of Quantitative Methods for Economics and Business of the University of Granada. The same author has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE

Diagnóstico radiológico de la fractura de la apófisis coronoides medial del cúbito en el perro

En este trabajo se describen los signos radiológicos de la fractura de la apófisis coronoides medial del cúbito (FAC)en 22 perros de diferentes razas cuyas edades estaban comprendidas entre los 5 meses y los 8 años. En todos los casos se realizaron radiografías de ambos codos en las proyecciones craneolateral- caudomedial, mediolateral, mediolateral flexionada y craneocaudal. Las proyecciones craneolateral-caudomedial, y mediolateral resultaron las más valiosas desde un punto de vista diagnóstico mientras que las dos restantes aportaron una información complementaria.The radiological signs of fragmented medial corono id process (FCP) were described in 22 dogs of different breeds with an age ranged from 5 months to 8 years oId. A study of both elbows was performed in all dogs by means of craneolateral-caudomedial, mediolateral, flexed mediolateral and craneocaudal views. The craneolateral-caudomedial and mediolateral views resulted more diagnostic than the remaining ones which only showed ancillary information to the disease

Síntesis y caracterización del nitruro ternario de titanio y vanadio (TixV1-xN)

En el presente trabajo se aborda la síntesis del nitruro ternario de titanio y vanadio por reducción carbotérmica de una mezcla de óxidos o bien por nitruración directa de la mezcla de metales, en todo el rango de composiciones empleando el método de análisis térmico a velocidad controlada (ATVC). La caracterización de los productos obtenidos se ha llevado a cabo mediante difracción de rayos-X y microscopia electrónica. El empleo de la técnica EELS ha mostrado su capacidad para la cuantificación de este tipo de materiales, así como la utilización de la técnica espectroscópica XAS nos ha servido para corroborar los datos obtenidos a partir de los diagramas de difracción de rayos-X sobre distancias de enlace, número de coordinación y grado de desorden, esto último no detectado por las otras técnicas usadas en la caracterización de los productos. Los valores de microdureza registrados para las muestras sintetizadas se encuentran dentro del rango de valores reportados para este tipo de materiales.Peer reviewe

Strain balanced quantum posts

Quantum posts are assembled by epitaxial growth of closely spaced quantum dot layers, modulating the composition of a semiconductor alloy, typically InGaAs. In contrast with most self-assembled nanostructures, the height of quantum posts can be controlled with nanometer precision, up to a maximum value limited by the accumulated stress due to the lattice mismatch. Here we present a strain compensation technique based on the controlled incorporation of phosphorous, which substantially increases the maximum attainable quantum post height. The luminescence from the resulting nanostructures presents giant linear polarization anisotropy.Comment: Submitted to Applied Physics Letters (7th March 2011). 4 pages, 4 figure