Direct calculation of lattice sums. A method to account for the crystal field effects

A method of direct calculation of lattice sums in three-dimensional crystals is reported. The method is based on annihilation of some lowest multipole moments of the unit cell by a redefinition of the unit cell content. As a result, properties of the infinite crystal can be calculated as usual by taking a finite cluster of unit cells, but surrounded by an additional surface layer of a charge density (e.g., a layer of point charges). This charge density distribution produces the electric field approximating that one of the rest of the infinite crystal. The method proposed is easily applicable in the SCFLCAO procedure as well as in any method using a cluster representation for an infinite crystal. The validity of the infinite crystal model for a finite crystal is also discussed.     

Molecular tight-binding method. I. Many-electron method for hole bands of molecular crystals

A method for calculating ab initio electronic excitation energies of molecular crystals, based on a many-electron tight-binding approximation, is described. The method follows Frenkel's model for excitons and allows a many-electron treatment of the band-structure problem of molecular crystals. The case of hole bands is studied in detail and various versions of the method are considered. A computational scheme is proposed, in which approximate correlation corrections to the HFR matrix equations of the one-electron LCMO method are calculated. The main effects contributing to these corrections are the effect of relaxation of a molecular ion, the effect of intramolecular electronic-correlation change, and the effect of polarization of the remaining molecules in a crystal. The method developed in the present paper is applied to calculation of the hole bands of the HCP helium crystal.     

Multidimensional gravitational waves. I. Purely radiative spacetimes

The concept of gravitational radiation in multidimensional Einstein gravity is studied. Due to technical difficulties the Petrov classification of the conformal tensor and the peeling off theorem cannot be generalized to spaces of dimensiond > 4. A multidimensionalpp wave is defined by analogy with that ford = 4. If the definition is supplemented by the Lichnerowicz condition for purely radiative spacetimes, the admitted solutions of the dimensionally reduced gravity theory describe a scalar (dilaton) and a gravitationalpp wave moving in the external spacetime in the same direction. The existence of the extra dimensions can be traced back by measuring the frequence of thepp wave in the external space. The condition is equally restrictive in a more general case of the internal space being a flat anisotropic manifold (i.e. an abelian group space).     

Thermodynamic properties of the NdBr3–MBr binary systems (M = Na,K)

Thixoforming involves heating different types of alloys to the semisolid state at high heating rates and forming in die-casting machines or conventional presses. At temperatures higher than the solidus and lower than the liquidus, the mush metal behaves like a high-viscosity thixotropic material. Therefore, determining the thermodynamic behavior of the solid-to-liquid transition is paramount to control thixoforming processes. This article describes a simple, novel experimental setup based on differential thermal analysis (DTA) for analyzing the phase transitions in an alloy heated using high heating rates typical of industrial applications. A365 alloy was chosen to demonstrate the effectiveness of the method as the phase transformations for this alloy in semisolid materials (SSM) processing are well understood. Samples were heated to 750 °C using constant linear heating rates of 5, 10, 15, 20, 25, 50, 75, 100 and 125 °C min in a Norax 25 kW 8 kHz induction furnace with an Omron E5CK temperature controller. AISI 316 austenitic stainless steel was used as the inert reference. Comparison of the results of DTA using the proposed method and the results of simulation with Thermo-Calc^® indicates that the proposed in situ DTA device and its method is suitable for analyzing phase transitions when high heating rates are used.     

The effect of increase in concentration of Na(I) ions on biosorption of Cr(III) ions by Enteromorpha prolifera and Spirulina sp

In this study, the effect of the increase in the initial concentration of Na(I) ions in the solution during biosorption of Cr(III) ions by two edible algae: marine macroalga — Enteromorpha prolifera and microalga — Spirulina sp. was investigated. During biosorption, essential elements are exchanged with alkali and alkaline earth metal ions (e.g. Na(I) ions), which are naturally bound with the biomass. The goal of this study was to investigate the effect of the increase in concentration of Na(I) ions on biosorption performance. The equilibrium of the process is described by Langmuir equation. It was found that with the increase in the initial concentration of NaCl (from 132 to 7331 mg L^?1), there was a lower biosorption capacity of Enteromorpha prolifera (from 85.8 to 51.0 mg g^?1) and Spirulina sp. (74.2 to 20.7 mg g^?1) towards Cr(III) ions. It was also possible to determine the number of times the solution used in the biosorption process can be recycled and yet mantain high biosorption capacity. The determined numbers were: 16 for Enteromorpha prolifera and 19 for Spirulina sp.      

Tunable dual-band liquid crystal based near-infrared perfect metamaterial absorber with high-loss metal

ABSTRACT

In this work, a tunable dual-band near-infrared perfect metamaterial absorber formed by combining a highly birefringent nematic liquid crystal with a nanoscale metamaterial cavity arranged in mirror symmetry is designed and numerically investigated. Electromagnetic simulations indicate that the absorbance greater than 99.4% may be achieved at 328 THz and 364 THz. Perfect absorbance results both form the use of highly lossy metal and the optimization of the metamaterial structure. In addition, absorbance of the metamaterial device can be substantially tuned both in terms of its magnitude and wavelength with the spectral tunability up to 8 THz by switching of liquid crystal alignment. The soft-matter-based metamaterial absorbers may pave a crucial role towards various active multifunctional systems working in the near-infrared range.     

Resonant equations with the Neumann p-Laplacian plus an indefinite potential

We consider a nonlinear Neumann problem driven by the p  -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C¹$C^1$-functionals.