The transition from fracton to phonon states in a Sierpinski triangle lattice

Lattice dynamics of a Sierpinski triangle submitted to different levels of disorder was studied via atomistic Green’s functions. It was found that there is a critical level of disorder that separates two regions of thermal transport. The first is characterized by a fast destruction of fracton states and the formation of spatially extended phonon states. The second region is characterized by a transition from extended to localized phonon states as predicted by the Anderson model.     

Drying of solids with irregular geometry: numerical study and application using a three-dimensional model

This article proposes a numerical solution for the diffusion equation applied to solids with arbitrary geometry using non-orthogonal structured grids for the boundary condition of the first kind. A transient three-dimensional mathematical formulation written in boundary fitted coordinates and numerical formalism to discretize the diffusion equation by using the finite volume method, including numerical analysis of the computational solution are presented. To validate the proposed solution, the results obtained in this work were compared with well-known numerical solution available in literature and good agreement was observed. In order to verify the potential of the proposed numerical solution, it was applied to describe mass transfer inside ceramic roof tiles during drying. For that, it was used experimental data of the drying kinetics at the following temperatures: 55.6; 69.7; 82.7 and 98.6 °C. An optimization technique using experimental dataset has been presented to estimation of transport properties. The obtained statistical indicators enable to conclude that the numerical solution satisfactorily describes the drying processes.     

Niobium oxide solid catalyst: esterification of fatty acids and modeling for biodiesel production

Biodiesel can be obtained from fatty acid raw materials through esterification. The reactivity of lauric, palmitic, stearic, oleic, and linoleic fatty acids with methanol using powdered niobic acid as a heterogeneous catalyst was investigated in this work, both experimentally (in a batch reactor) and theoretically. A 2³ experimental design was used, with methanol/fatty acid molar ratio, catalyst concentration, and temperature as main factors. An empirical model demonstrated that temperature is the most important variable. Fourteen heterogeneous and 56 homogeneous‐like kinetic models were tested. A homogeneous‐like model considering zero order for all species and inhibition by water was the most adequate for experiments without catalyst. A homogeneous‐like model considering a second‐order reaction in relation to the fatty acid and no water inhibition was the most adequate for niobic acid catalyzed reaction. Molecular modeling confirmed the experimental results showing that the reactivity is directly related to the increase of unsaturated bonds and the reduction of carbon chain length. The polarity of the fatty acid is determinant in the reactivity. At the molecular level, reaction occurs between the HOMO orbital of methanol and LUMO orbitals of fatty acids and reactivity is higher when the energy difference between these orbitals is lower. Copyright © 2010 John Wiley & Sons, Ltd.     

Characterisation of foxing stains in eighteenth to nineteenth century drawings using non-destructive techniques

The reddish-brown, brown or yellowish stains of circular or irregular shape known as foxing spots have been fully described in conservation literature but still, this phenomenon does not find any scientific agreement since many hypotheses have been raised concerning their origin. In this work a contribution to foxing definition not only focussed on its appearance but also reported on its chemical information. For this purpose foxing stains present in drawings from two Portuguese artists dated from the eighteenth to nineteenth centuries were observed under ultra-violet light and optical microscope and analysed by three non-invasive spectroscopy techniques. The observations carried out on the stains provided information on their surface morphology. The use of energy-dispersive X-ray fluorescence revealed a variation on the elemental content between foxing and paper region. Although the results from X-ray diffraction analysis showed no signs of cellulose degradation in foxing stains, Fourier-transformed infrared analysis revealed the presence of oxide groups. Both the information on the chemical nature and surface morphology of the stains achieved in this study will contribute to increase foxing formation information and develop future protocols for conservation purposes.     

Tunable L-band erbium-doped fibre ring laser by means of induced cavity loss using a fibre taper

In this paper, we present a continuous-wave tunable fibre ring laser operating in the L-band. A bi-directional pumped L-band erbium-doped fibre amplifier provides gain to the loop. Tunability is achieved by bending a single-mode fibre taper using a micrometer drive, controlling in this way the spectral cavity losses. Laser emission is achieved between 1587 and 1606 nm, and low variation of the output laser power is observed over all the tuning range. PACS 42.55.Wd; 42.60.Da     

Isotopic Liftings of Clifford Algebras and Applications in Elementary Particle Mass Matrices

Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.     

Enhanced Photocatalytic Activity of MIL‐125 by Post‐Synthetic Modification with CrIII and Ag Nanoparticles

NH₂‐MIL‐125, [Ti₈O₈(OH)₄(bdc‐NH₂)₆] (bdc^2?=1,4‐benzene dicarboxylate) is a highly porous metal–organic framework (MOF) that has a band gap lying within the ultraviolet region at about 2.6 eV. The band gap may be reduced by a suitable post‐synthetic modification of the nanochannels using conventional organic chemistry methods. Here, it is shown that the photocatalytic activity of NH₂‐MIL‐125 in the degradation of methylene blue under visible light is remarkably augmented by post‐synthetic modification with acetylacetone followed by Cr^III complexation. The latter metal ion extends the absorption from the ultraviolet to the visible light region (band gap 2.21 eV). The photogenerated holes migrate from the MOF’s valence band to the Cr^III valence band, promoting the separation of holes and electrons and increasing the recombination time. Moreover, it is shown that the MOF’s photocatalytic activity is also much improved by doping with Ag nanoparticles, formed in situ by the reduction of Ag⁺ with the acetylacetonate pendant groups (the resulting MOF band gap is 2.09 eV). Presumably, the Ag nanoparticles are able to accept the MOF’s photogenerated electrons, thus avoiding electron–hole recombination. Both, the Cr‐ and Ag‐bearing materials are stable under photocatalytic conditions. These findings open new avenues for improving the photocatalytic activity of MOFs.     

Cleft extensions of a family of braided Hopf algebras

We introduce a family of braided Hopf algebras that (in characteristic zero) generalizes the rank 1 Hopf algebras introduced by Krop and Radford and we study its cleft extensions.     

High-performance hydrogen production and oxidation electrodes with hydrogenase supported on metallic single-wall carbon nanotube networks

We studied the electrocatalytic activity of an [FeFe]-hydrogenase from Clostridium acetobutylicum (CaH2ase) immobilized on single-wall carbon nanotube (SWNT) networks. SWNT networks were prepared on carbon cloth by ultrasonic spraying of suspensions with predetermined ratios of metallic and semiconducting nanotubes. Current densities for both proton reduction and hydrogen oxidation electrocatalytic activities were at least 1 order of magnitude higher when hydrogenase was immobilized onto SWNT networks with high metallic tube (m-SWNT) content in comparison to hydrogenase supported on networks with low metallic tube content or when SWNTs were absent. We conclude that the increase in electrocatalytic activities in the presence of SWNTs was mainly due to the m-SWNT fraction and can be attributed to (i) substantial increases in the active electrode surface area, and (ii) improved electronic coupling between CaH2ase redox-active sites and the electrode surface.