Manoj Kumar Yadav | Searcharxiv

arXiv2024

Comparative study on higher order compact RBF-FD formulas with Gaussian and Multiquadric radial functions

We generate Gaussian radial function based higher order compact RBF-FD formulas for some differential operators. Analytical expressions for weights associated to first and second derivative formulas (up to order 10) and 2D-Laplacian formulas (up to order 6) are derived. Then these weights are used to obtain analytical expression for local truncation errors. The weights are obtained by symbolic computation of a linear system in Mathematica. Often such linear systems are not directly amenable to symbolic computation. We make use of symmetry of formula stencil along with Taylor series expansions for performing the computation. In the flat limit, the formulas converge to their respective order polynomial based compact FD formulas. We validate the formulas with standard test functions and demonstrate improvement in approximation accuracy with respect to corresponding order multiquadric based compact RBF-FD formulas and compact FD schemes. We also compute optimal value of shape parameter for each formula.

math.NA↗

arXiv2015

A systematic study of structural, electronic and optical properties of atomic scale defects in 2D transition metal dichalcogenides MX$_2$ (M = Mo,W; X = S, Se, Te)

In this work, we have systematically studied structural, electronic and magnetic properties of atomic scale defects in 2D transition metal dichalcogenides MX$_2$, (M = Mo and W; X = S, Se and Te) by density functional theory. Various types of defects, e.g., X vacancy, X interstitial, M vacancy, M interstitial, MX and XX double vacancies have been considered. It has been found that the X interstitial has the lowest formation energy ($\sim$ 1 eV) for all the systems in the X--rich condition whereas for M--rich condition, X vacancy has the lowest formation energy except for \ce{MTe2} systems. Both these defects have very high equilibrium defect concentrations at growth temperatures (1000K-1200K) reported in literature. A pair of defects, e.g., two X vacancies or one M and one X vacancies tend to occupy the nearest possible distance. No trace of magnetism has been found for any one of the defects considered. Apart from X interstitial, all other defects have defect states appearing in the band gap, which can greatly affect the electronic and optical properties of the pristine systems. Our calculated optical properties show that the defect states cause optical transitions at $\sim$ 1.0 eV, which can be beneficial for light emitting devices. The results of our systematic study are expected to guide the experimental nanoengineering of defects to achieve suitable properties related to band gap modifications and characterization of defect fingerprints via optical absorption measurements.

cond-mat.mes-hall↗