The effect of spatial quadrature on finite element galerkin approximations to hyperbolic integro-differential equations

The purpose of this paper is to study the effect of numerical quadrature on the finite element approximations to the solutions of hyperbolic intego-differential equations. Both semidiscrete and fully discrete schemes are analyzed and optimal estimates are derived in L ^∞(H ¹)L ^∞(L ²) norms and quasi-optimal estimate in L ^∞(L ^∞) norm using energy arguments. Further, optimal L(L ²)-estimates are shown to hold with minimal smoothness assumptions on the initial functions. The analysis in the present paper not only improves upon the earlier results of Baker and Dougalis [SIAM J. Numer. Anal. 13 (1976), pp. 577-598] but also confirms the minimum smoothness assumptions of Rauch [SIAM J. Numer. Anal. 22 (1985), pp. 245-249] for purely second order hyperbolic equation with quadrature.     

Finite element Galerkin approximations to a class of nonlinear and nonlocal parabolic problems

In this article, a finite element Galerkin method is applied to a general class of nonlinear and nonlocal parabolic problems. Based on an exponential weight function, new a priori bounds which are valid for uniform in time are derived. As a result, existence of an attractor is proved for the problem with nonhomogeneous right hand side which is independent of time. In particular, when the forcing function is zero or decays exponentially, it is shown that solution has exponential decay property which improves even earlier results in one dimensional problems. For the semidiscrete method, global existence of a unique discrete solution is derived and it is shown that the discrete problem has an attractor. Moreover, optimal error estimates are derived in both and ‐norms with later estimate is a new result in this context. For completely discrete scheme, backward Euler method with its linearized version is discussed and existence of a unique discrete solution is established. Further, optimal estimates in ‐norm are proved for fully discrete schemes. Finally, several numerical experiments are conducted to confirm our theoretical findings. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1232–1264, 2016     

Energetics and thermodynamic stability of the mixed valence ytterbium germanides

The results of an experimental study concerning the thermodynamic stability of the Yb germanides, described as intermediate valence compounds, complemented by a computational investigation for the Yb3Ge5 compound are reported. These compounds belong to the rare earth (RE) tetrelides (tetrel = Si, Ge, i.e., group 14 elements), a class of intermetallic materials showing unusual and promising physical properties (giant magnetocaloric effect, magnetostriction, and magnetoresistence). The high-temperature decomposition reactions of the Yb-Ge intermediate phases were studied experimentally by means of the KEMS (Knudsen effusion mass spectrometry) and KEWL (Knudsen effusion weight loss) techniques. From the reaction enthalpies derived by measuring the Yb(g) decomposition pressures as a function of temperature, the heats of formation of five out of six of the intermediate phases in the Yb-Ge system were calculated. From the computational side, the stability of the Yb3Ge5(s) compound has been investigated by DFT-LCAO-B3LYP (density functional theory-linear combination of atomic orbitals-hybrid b3lyp exchange-correlation functional) first principles calculations deriving its equilibrium geometry and the enthalpy of formation at 0 K in relation to the intermediate valence state of Yb in the lattice.     

Applications of liquid crystals in biosensing and organic light-emitting devices: future aspects

ABSTRACT

This article summarises recent advances made in our laboratory towards the development of new technological applications, such as biosensors and organic light-emitting diodes (OLEDs) based on liquid crystals (LCs) other than LC displays. The study of biomolecular interaction using LC material relies on the specific interaction between the LC and the biomolecule of interest at interfaces that permit the biomolecular events to be amplified into easily measured signals for various sensing applications. In the first part, we emphases recent studies in the design and modulation of LC-based interfaces based on robust colloidal LC gels for biological amplification, qualitative and quantitative understanding of important biomolecular interactions at LC–aqueous interfaces for diagnostic and laboratory applications and design of LC droplets that hold promise to act as a marker for cells and cell-based interactions. In the second part, we described design of organic materials for application in OLEDs on various discotic monomers, dimers and oligomers. These molecules have the ability to transport charges, holes and electrons. In addition, because of the high conductivity and π–π stacking, they are considered as the advanced materials for practical applications. The technological advances in our laboratory using discotic LCs will be briefly presented in this article.