First-principles study of the structural, elastic, electronic, optical, and vibrational properties of intermetallic Pd2Ga

The structural, elastic, electronic, optical, and vibrational properties of the orthorhombic Pd₂Ga compound are investigated using the norm-conserving pseudopotentials within the local density approximation in the frame of density functional theory. The calculated lattice parameters have been compared with the experimental values and found to be in good agreement with these results. The second-order elastic constants and the other relevant quantities, such as the Young's modulus, shear modulus, Poisson's ratio, anisotropy factor, sound velocity, and Debye temperature, have been calculated. It is shown that this compound is mechanically stable after analysing the calculated elastic constants. Furthermore, the real and imaginary parts of the dielectric function and the optical constants, such as the optical dielectric constant and the effective number of electrons per unit cell, are calculated and presented. The phonon dispersion curves are derived using the direct method. The present results demonstrate that this compound is dynamically stable.     

Ab initio calculations of the elastic, electronic, optical, and vibrational properties of PdGa compound under pressure

The structural, elastic, electronic, optical, and vibrational properties of cubic PdGa compound are investigated using the norm-conserving pseudopotentials within the local density approximation (LDA) in the framework of the density functional theory. The calculated lattice constant has been compared with the experimental value and has been found to be in good agreement with experimental data. The obtained electronic band structures show that PdGa compound has no band gap. The second-order elastic constants have been calculated, and the other related quantities such as the Young’s modulus, shear modulus, Poisson’s ratio, anisotropy factor, sound velocities, and Debye temperature have also been estimated. Our calculated results of elastic constants show that this compound is mechanically stable. Furthermore, the real and imaginary parts of the dielectric function and the optical constants such as the electron energy-loss function, the optical dielectric constant and the effective number of electrons per unit cell are calculated and presented in the study. The phonon dispersion curves are also derived using the direct method.     

Numerical computation of eigenvalues of discontinuous Sturm–Liouville problems with parameter dependent boundary conditions using sinc method

In this paper, we consider a Sturm–Liouville problem which contains an eigenparameter appearing linearly in two boundary conditions, in addition to an internal point of discontinuity. Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. We apply the sinc method, which is based on the sampling theory to compute approximations of the eigenvalues. An error analysis is exhibited involving rigorous error bounds. Using computable error bounds we obtain eigenvalue enclosures in a simple way. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.     

A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations

A new explicit formula for the integrals of shifted Chebyshev polynomials of any degree for any fractional-order in terms of shifted Chebyshev polynomials themselves is derived. A fast and accurate algorithm is developed for the solution of linear multi-order fractional differential equations (FDEs) by considering their integrated forms. The shifted Chebyshev spectral tau (SCT) method based on the integrals of shifted Chebyshev polynomials is applied to construct the numerical solution for such problems. The method is then tested on examples. It is shown that the SCT yields better results.     

Characterization of pottery from Republic of Macedonia. III. A study of comparative mineralogical detection efficiency using micro‐Raman mapping and X‐ray diffraction

Point‐to‐point micro‐Raman and X‐ray diffraction (XRD) techniques were employed for characterization of minerals present in the pottery body of 27 glazed Byzantine and Ottoman pottery shreds, excavated at two different archaeological sites in the Republic of Macedonia: in Skopje (Skopsko Kale) and in Prilep (Markovi Kuli and Sv. Atanas Church). The Raman spectra of 18 Byzantine samples (dating from 12th−14th century) and nine Ottoman samples (dating from 17th−19th century) revealed 26 different minerals. XRD measurements were further performed on the same powder samples to validate the mineralogical assessment obtained by point‐to‐point micro‐Raman spectroscopy. Although only 13 different mineral phases were obtained by the XRD, the results obtained from the Raman and XRD spectra for the most abundant minerals in the investigated pottery bodies match quite well. However, the identification of the less abundant minerals in the clay matrixes from the XRD data was very difficult, if at all possible. The results emphasize the specifics of the applied techniques and their limits. Additionally, wavelength dispersive X‐ray fluorescence spectroscopy was used for the elemental analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Spin waves in the frustrated kagomé lattice antiferromagnet KFe3(OH)6(SO4)2

The spin wave excitations of the S=5/2 kagomé lattice antiferromagnet KFe3(OH)6(SO4)2 have been measured using high-resolution inelastic neutron scattering. We directly observe a flat mode which corresponds to a lifted "zero energy mode," verifying a fundamental prediction for the kagomé lattice. A simple Heisenberg spin Hamiltonian provides an excellent fit to our spin wave data. The antisymmetric Dzyaloshinskii-Moriya interaction is the primary source of anisotropy and explains the low-temperature magnetization and spin structure.     

Time evolution of an excited atom's position-momentum uncertainty

In this work, the position-momentum uncertainty of an excited two-level atom is analyzed for its time-dependent properties by taking into consideration the interaction between the atom and vacuum electromagnetic modes. For the purpose of comparison, the position-momentum uncertainty of a free particle is also considered. It is found that, because of the atom-field interaction, the uncertainty of the atom can be temporarily lower than that of the free particle.     

Homotopy perturbation method for the mixed Volterra–Fredholm integral equations

This article presents a numerical method for solving nonlinear mixed Volterra–Fredholm integral equations. The method combined with the noise terms phenomena may provide the exact solution by using two iterations only. Two numerical illustrations are given to show the pertinent features of the technique. The results reveal that the proposed method is very effective and simple.     

Heterograft brush copolymers via romp and triple click reaction strategies involving CuAAC,diels–alder,and nitroxide radical coupling reactions

In this study, an equimolar mixture of oxanorbornenyl‐anthracene (ONB‐anthracene), oxanorbornenyl‐bromide (ONB‐Br), and oxanorbornenyl tosylate (ONB‐OTs) was polymerized via ring opening metathesis polymerization using the first generation Grubbs' catalyst in CH₂Cl₂ at room temperature to form poly(ONB‐anthracene‐co‐ONB‐Br‐co‐ONB‐OTs)₁₀ copolymer as a main backbone. Next, this main backbone was sequentially clicked with a furan protected maleimide‐terminated poly(methyl methacrylate), 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐terminated poly(ethylene glycol), and alkyne‐terminated poly(ε‐caprolactone) (PCL₂₀‐alkyne) via Diels–Alder, nitroxide radical coupling, and copper‐catalyzed azide‐alkyne cycloaddition, respectively, to yield a poly(ONB‐g‐PMMA‐co‐ONB‐g‐PEG‐co‐ONB‐g‐PCL)₁₀ heterograft brush copolymer © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013