arXiv subjects
Publications and source records attributed to S. Nayak.
Residual-based a~posteriori error estimators are derived for the modified Morley FEM, proposed by Wang, Xu, Hu [J. Comput. Math, 24(2), 2006], for the singularly perturbed biharmonic equation and the nonlinear von Kármán equations. The error estimators are proven to be reliable and efficient. Moreover, an adaptive algorithm driven by these error estimators is investigated in numerical experiments.
This article reports dependence of exchange bias (EB) effect on interparticle interactions in nanocrystalline Co/CoO core/shell structures, synthesized using conventional sol-gel technique. Analysis via powder X-Ray diffraction (PXRD) studies and transmission electron microscope (TEM) images confirm absence of crystalline phases other than core-shell Co-CoO with average particle size $\approx$18 nm. Volume fraction ($φ$) is varied (from 20\% to 1\%) by introduction of stoichiometric amount of non-magnetic amorphous silica matrix (SiO$_2$) which leads to a change in interparticle separation/interaction. The influence of exchange and dipolar interactions on the EB effect, caused by the variation in interparticle interaction/separation is studied for a series of Co/CoO core/shell nanoparticle systems. Studies of thermal variation of magnetization ($M- T$) and magnetic hysteresis loops ($M- H$) for the series point towards strong dependence of magnetic properties on dipolar interaction in concentrated assemblies whereas individual nanoparticle response is dominant in isolated nanoparticle systems. The analysis of the EB effect reveals a monotonic increase of coercivity ($H_C$) and EB field ($H_E$) with increasing volume fraction. When the nanoparticles are close enough and the interparticle interaction is significant, collective behavior leads to an increase in the effective antiferromagnetic (AFM) CoO shell thickness which results in high $H_C$, $H_E$. Moreover, in concentrated assemblies, the dipolar field superposes to the local exchange field and enhances the EB effect contributing as an additional source of unidirectional anisotropy.
This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently developed method. Here the concepts of fuzzy numbers are combined with Finite Difference Method (FDM) and then Fuzzy Finite Difference Method (FFDM) has been proposed. The proposed FFDM has been used to solve the fluid flow problem bounded by two parallel plates. Finally sensitivity of the fuzzy parameters has also been analysed.