Three applications of a bonus relation for gravity amplitudes

Arkani-Hamed et al. have recently shown that all tree-level scattering amplitudes in maximal supergravity exhibit exceptionally soft behavior when two supermomenta are taken to infinity in a particular complex direction, and that this behavior implies new non-trivial relations amongst amplitudes in addition to the well-known on-shell recursion relations. We consider the application of these new ‘bonus relations’ to MHV amplitudes, showing that they can be used quite generally to relate (n−2)!-term formulas typically obtained from recursion relations to (n−3)!-term formulas related to the original BGK conjecture. Specifically we provide (1) a direct proof of a formula presented by Elvang and Freedman, (2) a new formula based on one due to Bedford et al., and (3) an alternate proof of a formula recently obtained by Mason and Skinner. Our results also provide the first direct proof that the conjectured BGK formula, only very recently proven via completely different methods, satisfies the on-shell recursion.     

Radiative charge transfer and radiative association of protons colliding with Na at low energies

Using the fully quantum-mechanical approach, the radiative charge transfer for H⁺ + Na(3s) collisions has been investigated. The charge transfer emission spectra are analyzed at resonant and non-resonant collision energies. The radiative association cross sections, obtained by subtracting the radiative charge transfer part from total radiative decay cross sections calculated by the optical potential method, are presented in the energy range 10⁻⁶-1 eV.     

Integrable structure of melting crystal model with two -parameters

This paper explores integrable structures of a generalized melting crystal model that has two q-parameters q₁,q₂. This model, like the ordinary one with a single q-parameter, is formulated as a model of random plane partitions (or, equivalently, random 3D Young diagrams). The Boltzmann weight contains an infinite number of external potentials that depend on the shape of the diagonal slice of plane partitions. The partition function is thereby a function of an infinite number of coupling constants t₁,t₂,… and an extra one Q. There is a compact expression of this partition function in the language of a 2D complex free fermion system, from which one can see the presence of a quantum torus algebra behind this model. The partition function turns out to be a tau function (times a simple factor) of two integrable structures simultaneously. The first integrable structure is the bigraded Toda hierarchy, which determines the dependence on t₁,t₂,…. This integrable structure emerges when the q-parameters q₁,q₂ take special values. The second integrable structure is a q-difference analogue of the 1D Toda equation. The partition function satisfies thisq-difference equation with respect to Q. Unlike the bigraded Toda hierarchy, this integrable structure exists for any values of q₁,q₂.     

Diffractive performance of square Fresnel zone plates

We analyze the optical behavior of square Fresnel zones plates. A theoretical analysis and numerical simulations based on the Rayleigh-Sommerfeld approach have been developed analyzing properties such as the depth of focus and the intensity of the focus in terms of the number of zones. In addition, an experimental verification has been performed using a Spatial Light Modulator to implement the designed square Fresnel zones plates.     

Synthesis and luminescent properties of europium-activated Ca2SnO4 phosphors by sol-gel method

In this paper, the Ca₂SnO₄:Eu³⁺ phosphor was prepared by low-temperature sol-gel method. The influence of calcined temperature and time on structure of Ca₂SnO₄:Eu³⁺ was investigated by using X-ray powder diffraction (XRD). The experimental results show that the dried gel was crystallized to the pure orthorhombic phase after calcination at 900 °C in air for 6 h. These phosphors have displayed bright red color under a UV source. The richness of the red color has been verified by determining their color coordination from the CIE standard charts, and this red emission has been assigned to ⁵D₀→⁷F₂ electric dipole transition at 616 and 620 nm. The excellent luminescence properties make it possible as a good candidate for plasma display panel (PDP) application.     

ABCD matrix formalism for propagation of Gaussian beam through left-handed material slab system

We apply a simple ABCD matrix formalism to investigate beam propagation in left-handed material (LHM) slab systems. Firstly, we derive the expressions for the matrix elements for a single LHM slab. Based on the ABCD matrix, we obtain the field distributions both inside and outside the LHM slab, and the conditions for focusing and phase compensation of the Gaussian beam. Secondly, the derived ABCD law is applied to analyze the propagation properties of Gaussian beams through various cascaded LHM slab systems. The corresponding focusing and phase compensation conditions of the Gaussian beam are also obtained. Our theoretic formalism may be applied as a compact and effective tool for the research of light beam propagation in complex LHM slab systems, since it avoids the complicated integral operation.     

Spectral analysis of Pr-, Sm- and Dy-doped transparent GeO2-BaO-TiO2 glass ceramics

In this paper, we present the photoluminescence properties of Pr³⁺-, Sm³⁺- and Dy³⁺-doped germanate glasses and glass ceramics. From the X-ray diffraction measurement, the host glass structure was determined. These glasses have shown strong absorption bands in the near-infrared (NIR) region. Compared to Pr³⁺-, Sm³⁺- and Dy³⁺-doped glasses, their respective glass ceramics have shown stronger emissions due to the Ba₂TiGe₂O₈ crystalline phase. For Pr³⁺-doped glass and glass ceramic, emission bands centered at 530 nm (³P₀→³H₅), 614 nm (³P₀→³H₆), 647 nm (³P₀→³F₂) and 686 nm (³P₀→³F₃) have been observed with 485 nm (³H₄→³P₀) excitation wavelength. Of them, 647 nm (³P₀→³F₂) has shown bright red emission. Emission bands of ⁴G_5/2→⁶H_5/2 (565 nm), ⁴G_5/2→⁶H_7/2 (602 nm) and ⁴G_5/2→⁶H_9/2 (648 nm) for the Sm³⁺:glass and glass ceramic, with excitation at ⁶H_5/2→⁴F_7/2 (405 nm) have been recorded. Of them, ⁴G_5/2→⁶H_7/2 (602 nm) has shown a bright orange emission. With regard to the Dy³⁺:glass and glass ceramic, a bright fluorescent yellow emission at 577 nm (⁴F_9/2→⁶H_13/2) has been observed, apart from ⁴F_9/2→⁶H_11/2 (667 nm) emission transition with an excitation at 454 nm (⁶H_15/2→⁴I_15/2) wavelength. The stimulated emission cross-sections of all the emission bands of Pr³⁺, Sm³⁺ and Dy³⁺:glasses and glass ceramics have been computed based on their measured full-width at half-maxima (FWHM, Δ<em>λem>) and lifetimes (<em>τem>_m).     

Photocatalytic property of TiO2 thin films sputtered-deposited on unheated substrates

TiO₂ films deposited on unheated substrates of alumina silicate glass by rf. (13.56 MHz) magnetron sputtering in the mixture of O₂ and Ar gases have been studied with X-ray diffraction (XRD), Atomic Force Microscopy (AFM) and optical spectroscopy. Structural and optical properties of TiO₂ films deposited at different O₂ concentrations and total pressures have been analyzed. Photocatalytic properties of TiO₂ films were characterized by following the degradation of methylene blue molecules under UV irradiation. It was found that the rate of methylene blue decomposition strongly depends on morphology and crystallinity of the deposited films, namely on the content of the anatase phase and on the size of the anatase grains. The best photocatalytic activity was found on TiO₂ films consisting of pure anatase phase with the size of grains of about 450 Å. With the help of those films a thin film reactor for water purification has been designed and tested.     

Nanoepitaxy on quasicrystal surfaces

In film growth on quasicrystalline surfaces, the epitaxy-imposed ordering cannot compete with the stable bulk phases of thick films due to absence of translational order in the structure of the substrate. Energetically, this renders the formation of crystalline domains in the native structure of the film material more favorable, while their global orientation is prescribed by the quasicrystalline order. We present experimental results on the dissociative chemisorption of oxygen at the decagonal surface of Al₇₀Co₁₅Ni₁₅ as well as molecular-dynamics simulations of the diffusion of adatoms on the surface of the partially covered substrate.