Fluctuations of radiation from a chaotic laser below threshold

Radiation from a chaotic cavity filled with gain medium is considered. A set of coupled equations describing the photon density and the population of gain medium is proposed and solved. The spectral distribution and fluctuations of the radiation are found. The full noise is a result of a competition between positive correlations of photons with equal frequencies (due to stimulated emission and chaotic scattering) which increase fluctuations, and a suppression due to interaction with a gain medium which leads to negative correlations between photons. The latter effect is responsible for a pronounced suppression of the photonic noise as compared to the linear theory predictions.Comment: 7 pages, 5 figures; expanded version, to appear in Phys. Rev.

Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

Studying surface chemistry of mixed conducting perovskite oxide electrodes with synchrotron-based soft X-rays

A fundamental understanding of the electrochemical reactions and surface chemistry at the solid–gas interface in situ and operando is critical for electrode materials applied in electrochemical and catalytic applications. Here, the surface reactions and surface composition of a model of mixed ionic and electronic conducting (MIEC) perovskite oxide, (La0.8Sr0.2)0.95Cr0.5Fe0.5O3-δ (LSCrF8255), were investigated in situ using synchrotron-based near-ambient pressure (AP) X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine-structure spectroscopy (NEXAFS). The measurements were conducted with a surface temperature of 500 °C under 1 mbar of dry oxygen and water vapor, to reflect the implementation of the materials for oxygen reduction/evolution and H2O electrolysis in the applications such as solid oxide fuel cell (SOFC) and electrolyzers. Our direct experimental results demonstrate that, rather than the transition metal (TM) cations, the surface lattice oxygen is the significant redox active species under both dry oxygen and water vapor environments. It was proven that the electron holes formed in dry oxygen have a strong oxygen character. Meanwhile, a relatively higher concentration of surface oxygen vacancies was observed on the sample measured in water vapor. We further showed that in water vapor, the adsorption and dissociation of H2O onto the perovskite surface were through forming hydroxyl groups. In addition, the concentration of Sr surface species was found to increase over time in dry oxygen due to Sr surface segregation, with the presence of oxygen holes on the surface serving as an additional driving force. Comparatively, less Sr contents were observed on the sample in water vapor, which could be due to the volatility of Sr(OH)2. A secondary phase was also observed, which exhibited an enrichment in B-site cations, particularly in Fe and relatively in Cr, and a deficiency in A-site cation, notably in La and relatively in Sr. The findings and methodology of this study allow for the quantification of surface defect chemistry and surface composition evolution, providing crucial understanding and design guidelines in the electrocatalytic activity and durability of electrodes for efficient conversions of energy and fuels

Comparison of Numerical Simulations and Analytical Theories for Elastic Wave Scattering within Polycrystalline Materials

Understanding the propagation and scattering of ultrasonic waves within polycrystalline materials is relevant to both material characterisation and flaw detection NDE. Validating analytical theories of scattering however has historically been hampered by the difficulty of obtaining sufficiently reliable experimental data where the statistical properties of the grains within the volume of the material are known well enough. Instead, this presentation exploits important recent progress in numerical modelling, which for the first time enables accurate three-dimensional simulations of wave propagation and scattering in polycrystals. The presentation reports work using such a model to compare and validate 3D numerical simulations of wave scattering against existing analytical theories. A wide range of wavenumber to grain size ratios, ka, are considered such that scattering within the Rayleigh, transitional, and stochastic regimes are compared. The numerical calculations are based on an established Voronoi algorithm to generate statistically representative random materials. An explicit Finite Element scheme (Pogo) running on an array of graphics processors is used to solve the time-domain wave propagation problem. It is found that near perfect agreement exists with the generalized second order theories (type of Stanke-Kino) for attenuation coefficient when these theories are implemented with properly fitted second order material statistics

BiOX (X = Cl, Br, I) photocatalysts prepared using NaBiO 3 as the Bi source: Characterization and catalytic performance

The Bismuth oxyhalides, crystalline BiOX (X = Cl, Br, I) were prepared via a facile method, using NaBiO 3 and HX aqueous solutions as the raw materials for the first time. The systematic microstructure and optical property characterizations of the BiOX photocatalysts demonstrated the reliability of this new and facile preparation approach. The photocatalytic activity on the degradation of typical phenolic endocrine disrupting chemicals over BiOX and P25 were evaluated under Xenon-light irradiation and the initial photocatalytic mechanism was discussed based on the band edge potential analysis. © 2009.postprin

Photocatalytic decomposition of 4-t-octylphenol over NaBiO 3 driven by visible light: Catalytic kinetics and corrosion products characterization

The photocatalytic decomposition of 4-t-octylphenol (4-t-OP) by NaBiO 3 photocatalyst and the catalyst stability in aqueous solution were investigated systematically for the first time. The results showed that some parameters such as catalyst dosage, initial 4-t-OP concentration and pH value of the solution had great effects on the photocatalytic activity. The NaBiO 3 photocatalyst maintained considerable catalytic performance under visible light (λ > 400 nm) irradiation and exhibited a higher photocatalytic activity compared to the commercialized photocatalyst P25. In addition, the corrosion products of NaBiO 3 catalyst under acid condition (HCl aqueous solution contained) were characterized by X-ray diffraction (XRD), transmittance electronic microscopy (TEM), selected area electron diffraction (SAED), X-ray photoelectron spectroscopy (XPS) and UV-vis transmittance spectrum analysis. The results showed that NaBiO 3 was unstable under the acidic condition and the catalyst could convert into Bi 3+-containing compounds such as Bi 2O 3, etc. The experiment demonstrates that NaBiO 3 can be corroded to nano-sized BiOCl crystal in the presence of hydrogen chloride, the band gap of which was estimated to be 3.28 eV by Tauc's approach. © 2009 Elsevier B.V. All rights reserved.postprin

First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures

We investigate the equation of state and elastic properties of hcp iron at high pressures and high temperatures using first principles linear response linear-muffin-tin-orbital method in the generalized-gradient approximation. We calculate the Helmholtz free energy as a function of volume, temperature, and volume-conserving strains, including the electronic excitation contributions from band structures and lattice vibrational contributions from quasi-harmonic lattice dynamics. We perform detailed investigations on the behavior of elastic moduli and equation of state properties as functions of temperature and pressure, including the pressure-volume equation of state, bulk modulus, the thermal expansion coefficient, the Gruneisen ratio, and the shock Hugoniot. Detailed comparison has been made with available experimental measurements and theoretical predictions.Comment: 33 pages, 12 figure

A Contour Integral Representation for the Dual Five-Point Function and a Symmetry of the Genus Four Surface in R6

The invention of the "dual resonance model" N-point functions BN motivated the development of current string theory. The simplest of these models, the four-point function B4, is the classical Euler Beta function. Many standard methods of complex analysis in a single variable have been applied to elucidate the properties of the Euler Beta function, leading, for example, to analytic continuation formulas such as the contour-integral representation obtained by Pochhammer in 1890. Here we explore the geometry underlying the dual five-point function B5, the simplest generalization of the Euler Beta function. Analyzing the B5 integrand leads to a polyhedral structure for the five-crosscap surface, embedded in RP5, that has 12 pentagonal faces and a symmetry group of order 120 in PGL(6). We find a Pochhammer-like representation for B5 that is a contour integral along a surface of genus five. The symmetric embedding of the five-crosscap surface in RP5 is doubly covered by a symmetric embedding of the surface of genus four in R6 that has a polyhedral structure with 24 pentagonal faces and a symmetry group of order 240 in O(6). The methods appear generalizable to all N, and the resulting structures seem to be related to associahedra in arbitrary dimensions.Comment: 43 pages and 44 figure

Solute clustering and precipitation in an Al–Cu–Mg–Ag–Si model alloy

Solute clustering and precipitation in an Al–Cu–Mg–Ag–Si model alloy has been investigated by atom probe tomography (APT) as well as high-angle annular dark-field (HAADF) imaging and electron energy loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM). Nine types of solute clusters (Cu, Ag, Mg–Cu, Mg–Ag, Mg–Cu–Si, Mg–Ag–Si, Mg–Ag–Cu, Cu–Ag–Si and MgAgCuSi) were observed by APT in both the as-quenched alloy and after ageing the alloy at 180 °C for 1 h. Three types of precipitates (Ω (AlCuMgAg), θ (Al2Cu) and Mg2Si) were observed by APT and HAADF-STEM after further ageing at 180 °C for 24 h and 100 h. We propose that MgAgCu and MgAgCuSi clusters are likely to be responsible for the formation of the Ω (AlCuMgAg) phase. Furthermore, we also suggest that the θ (Al2Cu) phase forms from Cu clusters and the Mg2Si phase forms from the decomposition of MgAgSi and MgAgCuSi clusters by losing Ag to Ω phase growth. Many early binary clusters (Mg–Cu, Mg–Ag) do not seem to undergo a significant further growth during ageing; these are more likely to be transformed into complex ternary and quaternary clusters and be subsequently consumed during the growth of large clusters/precipitates. Furthermore, it is proposed that the plate-like Ω (AlCuMgAg) precipitates evolve continuously from the MgAgCu and MgAgCuSi clusters, rather than via heterogeneous nucleation on their precursors (i.e. MgAgCu and MgAgCuSi clusters). More interestingly, even after ageing at 180 °C for 100 h, the Ω (AlCuMgAg) precipitates remain coherent with the α-Al matrix, indicating that these precipitates have a high thermal stability. This can mainly be attributed to the presence of a single Mg–Ag-rich monolayer observed at the interface between the Ω precipitate and the α-Al matrix, significantly improving the coarsening resistance of the Ω (AlCuMgAg) precipitates. Our results thus reveal links between a variety of solute clusters and the different types of precipitates in the Al–Cu–Mg–Ag–Si model alloy. Such information can in the future be used to control the precipitation by tailoring solute clustering