In the present study we have calculated the elastic constants and the bulk modulus for NaCl, KCl, MgO and CaO under high temperatures using the three models due to Murnaghan (proc. Nat Acad. Sci (USA) 30 (1994) 244), Tallon (J. Phys. Chem. Solids 41 (1980) 837) and Vinet et al. (J. Phys. C 19 (1986) L467). The results are found to be in good agreement with the experimental data on the temperature dependences of elastic constants for the solids under study. The Murnaghan's model presents better agreement with the data at higher temperatures. It has been concluded that the Anderson–Gruneisen parameter remains nearly constant at higher temperatures. The present method has been found to be useful for predicting the elastic constants of the solids up to their melting temperatures.

Analysis of temperature dependence of elastic constants and bulk modulus for ionic solids

Volume and Temperature Dependence of the Second Grneisen Parameter of NaCl

Making the assumption that the value of the second Gruneisen parameter q is constant, we present a relation for the pressure dependence of the Gruneisen parameter y. The tests on four solids (NaCl, Li, Na, and K) show that the agreement between the calculated results given by the relation and the experimental data on the pressure dependence of y is excellent. A comparison between the linear relation suggested by Kumari and Dass and the relation presented in this paper demonstrates that the latter is better.

Pressure dependence of Grüneisen parameter in solids

In the present paper, the thermal pressure for the MgO is evaluated from room temperature to 3000 K at atmospheric pressure with the help of data suggested by Jacobs and Oonk. Various relationships between thermal pressure and volume expansion ratio are examined. Thermoelastic properties viz. C11, C44, CS, and KS are calculated at high temperatures for the solid under study, with the help of Murnaghan and Tallon models. Predicted values of thermoelastic properties at higher temperatures can be used to understand the high-temperature behavior of MgO at 1 bar pressure.

Analysis of temperature dependence of thermal pressure and thermoelastic properties of MgO

In the present communication a relationship between elastic constants and thermal expansivity is disclosed in high temperature region at atmospheric pressure. The relationship is shown for ionic solids viz. NaCl, KCl, CaO and MgO. The analysis is based on the experimental data tabulated by Anderson [Equation of State for Geophysics and Ceramic Science, Oxford University Press, New York, 1995] and the extrapolated data reported by Singh and Chauhan [Physica B 315 (2002) 74]. It is found that the relationship proposed by Singh et al. [Physica B 349 (2004) 401] for thermal expansivity and isothermal bulk modulus also holds well for other elastic moduli such as C 11 , C 44 , C S and K S .

Relationship between elastic constants and thermal expansivity for ionic solids

An analysis of the pressure and volume dependence of the Gruneisen parameter γ and the Debye temperature θ is presented for NaCl crystals using the model developed by Kumari and Dass. It is pointed out that the parameter q = d ln γ/d ln V should be taken nearly equal to unity for predicting γ and θ at different pressures. Various thermodynamic approximations implied in the analysis are discussed

On the Pressure and Volume Dependence of the Grüneisen Parameter and Debye Temperature for NaCl Crystals

Temperature dependence of elastic constants and thermal expansion coefficient of kcl crystal

The necessary condition for the termination of families of radial causal geodesics at the naked shell focusing singularity in self-similar spherically symmetric spacetimes is worked out. The curvature growth along these geodesics is then examined and it is shown that strong curvature condition is satisfied along all radial non-spacelike geodesics escaping from the singularity. Among all the counter-examples to cosmic censorship theorem, all the known examples of strong naked singularities so far are in self-similar spherically symmetric spacetimes (see Refs_ 1), 2) and 5), and references therein)_ Therefore the study of these singularities is valuable and a detailed analysis would certainly be helpful in the formulation of a suitable version of a proved cosmic censorship hypothesis_ Recently Waugh and Lake!) had worked out the necessary criteria for a single radial null geodesic escaping from the shell focusing singularity in a spherically symmetric self-similar spacetimes, and examined the curvature behavior along the radial null geodesics that terminate at the singularity_l),3) It is however asserted that to asses the strength of a singularity the strong curvature condition should be satisfied along all non-spacelike geodesics which join the same singular endpoint 4 ) The aim of this short paper is.to carry out such an investigation and find the necessary criteria for the formation of a naked singularity which is the endpoint of families of radial timelike as well as radial null geodesics and to show that the strong curvature condition is satisfied along the same_ Thus it is established that these curvature singularities are strong in a much stronger sense_ Following Waugh and Lake!) the self-similar spherically symmetric metric in co moving coordinates can be written asS)

Strength of Naked Shell Focusing Singularities in Self-Similar Spherically Symmetric Spacetimes

Association Rules Mining in Cloud Computing Environments using Improved Apriori Algorithm

In Model Driven Architecture (MDA), model and meta-model are the primary artifacts. In this work, a detailed analysis of the existing meta-model-based transformation tools is done for the declarative model using an exhaustive criterion. The evaluation of the eleven chosen tools, which are open source and has download page available using search engine like Google Scholar and Github, is analyzed; like UML–RSDS, Tefkat, JTL, PTL etc. Analysis is performed over fourteen different parameters like language, model query, type of transformation, compatibility, cardinality etc. Results show that all selected tools produce platform specific target model which mostly transform PSM to PSM and none produces platform independent target model transforming a PSM into PIM. Keywords—Model Driven Re-engineering, Model Transformation, Declarative User Interface, Transformation tools

Model to Model Transformation for Declarative Models

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