An hp-Local Discontinuous Galerkin method for Parabolic\ud Integro-Differential Equations

In this article, a priori error analysis is discussed for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that the L2 -norm of the gradient and the L2 -norm of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data

In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result

Optimal L2 estimates for semidiscrete Galerkin methods for\ud parabolic integro-differential equations with nonsmooth data

In this article, we discuss an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth initial data. It is based on energy arguments and on a repeated use of time integration, but without using parabolic type duality technique. Optimal L2-error estimate is derived for the semidiscrete approximation, when the initial data is in L2

An extended Falicov-Kimball model on a triangular lattice

The combined effect of frustration and correlation in electrons is a matter of considerable interest of late. In this context a Falicov-Kimball model on a triangular lattice with two localized states, relevant for certain correlated systems, is considered. Making use of the local symmetries of the model, our numerical study reveals a number of orbital ordered ground states, tuned by the small changes in parameters while quantum fluctuations between the localized and extended states produce homogeneous mixed valence. The inversion symmetry of the Hamiltonian is broken by most of these ordered states leading to orbitally driven ferroelectricity. We demonstrate that there is no spontaneous symmetry breaking when the ground state is inhomogeneous. The study could be relevant for frustrated systems like $GdI_2$, $NaTiO_2$ (in its low temperature C2/m phase) where two Mott localized states couple to a conduction band.Comment: 6 pages, 8 figure

Characterization of Zinc oxide & Aluminum Ferrite and Simulation studies of M-H plots of Cobalt/Cobaltoxide

Zinc oxide and Aluminum Ferrite were prepared Chemical route. The samples were characterized by XRD and VSM. Simulation of M-H plots of Co/CoO thin films were performed. Effect of parameters was observed on saturation magnetization.Comment: Working paper (11 pages, 8 figures

Nature of the spiral state, electric polarisation and magnetic transitions in Sr-doped YBaCuFeO5_5: A first-principles study

Contradictory results on the ferroelectric response of type II multiferroic YBaCuFeO$_{5}$, in its incommensurate phase, has of late, opened up a lively debate. There are ambiguous reports on the nature of the spiral magnetic state. Using first-principles DFT calculations for the parent compound within LSDA+U+SO approximation, the multiferroic response and the nature of spiral state is revealed. The helical spiral is found to be more stable below the transition temperature as spins prefer to lie in ab plane. The Dzyaloshinskii-Moriya (DM) interaction and the spin current mechanism were earlier invoked to account for the electric polarisation in this system. However, the DM interaction is found to be absent, spin current mechanism is not valid in the helical spiral state and there is no electric polarisation thereof. These results are in good agreement with the recent single-crystal data. We also investigate the magnetic transitions in YBa$_{1-x}$Sr$_x$CuFeO$_5$ for the entire range $0\le x\le 1$ of doping. The exchange interactions are estimated as a function of doping and a quantum Monte Carlo (QMC) calculation on an effective spin Hamiltonian shows that the paramagnetic to commensurate phase transition temperature increases with doping till $x=0.5$ and decreases beyond. Our observations are consistent with experimental findings.Comment: 8 pages, 7 figure

AstroSat observation of GX 5-1: Spectral and timing evolution

We report on the first analysis of AstroSat observation of the Z-source GX 5- 1 on February 26-27, 2017. The hardness-intensity plot reveals that the source traced out the horizontal and normal branches. The 0.8-20 keV spectra from simultaneous SXT and LAXPC data at different locations of the hardness-intensity plot can be well described by a disk emission and a thermal Comptonized component. The ratio of the disk flux to the total i.e. the disk flux ratio increases monotonically along the horizontal to the normal one. Thus, the difference between the normal and horizontal branches is that in the normal branch, the disk dominates the flux while in the horizontal one it is the Comptonized component which dominates. The disk flux scales with the inner disk temperature as T_{in}^{5.5} and not as T_{in}{4} suggesting that either the inner radii changes dramatically or that the disk is irradiated by the thermal component changing its hardness factor. The power spectra reveal a Quasi Periodic Oscillation whose frequency changes from \sim 30 Hz to 50 Hz. The frequency is found to correlate well with the disk flux ratio. In the 3-20 keV LAXPC band the r.m.s of the QPO increases with energy (r.m.s \prop E0.8), while the harder X-ray seems to lag the soft ones with a time-delay of a milliseconds. The results suggest that the spectral properties of the source are characterized by the disk flux ratio and that the QPO has its origin in the corona producing the thermal Comptonized component