Thermoelastic properties of minerals at high temperature

The knowledge of elasticity of the minerals is useful for interpreting the structure and composition of the lower mantle and also in seismic studies. The purpose of the present study is to discuss a simple and straightforward method for evaluating thermoelastic properties of minerals at high temperatures. We have extended the Kumar’s formulation by taking into the account the concept of anharmonicity in minerals above the Debye temperature (θ _D). In our present study, we have investigated the thermophysical properties of two minerals (pyrope-rich garnet and MgAl₂O₄) under high temperatures and calculated the second-order elastic constant (C _ij ) and bulk modulus (K _T) of the above minerals, in two cases first by taking Anderson–Gruneisen parameter (δ _T) as temperature-independent and then by treating δ _T as temperature-dependent parameter. The results obtained when δ _T is temperature-dependent are in close agreement with experimental data.     

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 1024³, 2048³, and 4096³ grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.     

Curvy steps for density matrix based energy minimization: tensor formulation and toy applications

A unitary transformation-based framework is explained for varying the one-particle density matrix in a non-orthogonal expansion basis while preserving both the idempotency and electron number constraints. The equations are presented in a compact tensor formulation that permits the use of any representation for the matrices. A connection with the LNV method is established. Curvy steps, which are high order line searches along a chosen descent direction, are defined. Calculations with two toy model systems are presented to illustrate the nature of the displacements in this approach.     

Relativistic models of a class of compact objects

A class of general relativistic solutions in isotropic spherical polar coordinates which describe compact stars in hydrostatic equilibrium are discussed. The stellar models obtained here are characterized by four parameters, namely, ??, k, A and R of geometrical significance related to the inhomogeneity of the matter content of the star. The stellar models obtained using the solutions are physically viable for a wide range of values of the parameters. The physical features of the compact objects taken up here are studied numerically for a number of admissible values of the parameters. Observational stellar mass data are used to construct suitable models of the compact stars.     

Long term performance evaluation of the TACTIC imaging telescope using ∼400 h Crab Nebula observation during 2003–2010

The TeV atmospheric Cherenkov telescope with imaging camera (TACTIC) γ-ray telescope has been in operation at Mt. Abu, India since 2001 to study TeV γ-ray emission from celestial sources. During the last 10 years, apart from consistently detecting a steady signal from the Crab Nebula above ～1.2 TeV energy, at a sensitivity level of ～5.0 σ in ～25 h, the telescope has also detected flaring activity from Mrk 421 and Mrk 501 on several occasions. Although we used Crab Nebula data partially, in some of the reported results, primarily for testing the validity of the full data analysis chain, the main aim of this work is to study the long term performance of the TACTIC telescope by using consolidated data collected between 2003 and 2010. The total on-source data, comprising ～402 h, yields an excess of ～(3742±192) γ-ray events with a statistical significance of ～19.9 σ. The off-source data, comprising ～107 h of observation, is found to be consistent with a no-emission hypothesis, as expected. The resulting γ-ray rate for the on-source data is determined to be ～(9.31±0.48) h ^?1. A power law fit (dΦ/dE=f ₀ E ^?Γ ) with f ₀ ～ (2.66±0.29) × 10^?11 cm^?2 s^?1 TeV^?1 and Γ ～ 2.56±0.10 is found to provide reasonable fit to the inferred differential spectrum within statistical uncertainties. The spectrum matches reasonably well with that obtained by other groups. A brief summary of the improvements in the various subsystems of the telescope carried out recently, which has resulted in a substantial improvement in its detection sensitivity (viz., ～5 σ in an observation period of ～13 h as compared to ～25 h earlier) are also presented in this paper. Encouraged by the detection of strong γ-ray signals from Mrk 501 and Mrk 421 on several occasions, there is considerable scope for the TACTIC telescope to monitor similar TeV γ-ray emission activity from other active galactic nuclei on a long-term basis.     

Relativistic effects on the modulational instability of electron plasma waves in quantum plasma

Relativistic effects on the linear and nonlinear properties of electron plasma waves are investigated using the one-dimensional quantum hydrodynamic (QHD) model for a two-component electron?Cion dense quantum plasma. Using standard perturbation technique, a nonlinear Schr?dinger equation (NLSE) containing both relativistic and quantum effects has been derived. This equation has been used to discuss the modulational instability of the wave. Through numerical calculations it is shown that relativistic effects significantly change the linear dispersion character of the wave. Unlike quantum effects, relativistic effects are shown to reduce the instability growth rate of electron plasma waves.     

Tensor sum and dynamical systems

In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.     

A Event Occurrence Rules based Compact Modeling Formalism for a Class of Discrete Event Systems

The analysis, failure diagnosis and control of discrete event systems (DESs) requires an accurate model of the system. In this paper we present a methodology which makes the task of modeling DESs considerably less cumbersome, less error prone, and more user-friendly than it usually is. In doing so we simplify the modeling formalism of [4, 5], proposed for obtaining valid models of complex discrete event systems, by eliminating ‘precedence relations’, and capturing them as part of the ‘event occurrence rules’. Under the new modeling formalism the size of the system model is polynomial in the number of signals; whereas the number of states in the commonly used automata models is exponential in the number of signals. We present automated techniques for deriving an automaton model from the model in the proposed formalism. We illustrate the modeling formalism using examples drawn from manufacturing and process control systems.     

On the Relation Between Monotone Methods and Temporal Evolution in Fully Non-linear Boundary-value Problems

A monotone, iterative approximation scheme for fully non-linearelliptic boundary value problems (the "chord method") is shownto be an approximation to the evolution in time of the solutionof a corresponding parabolic boundary value problem. This relationshiphelps to explain the success of the chord method constructionby establishing a relation between it and the temporal evolutionof a non-linear diffusion process. Alternatively, these resultsestablish stability properties and define domains of attractionfor maximal and minimal solutions of a fully nonlinear parabolicproblem.     

TENSOR SUM AND DYNAMICAL SYSTEMS

In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.