Numerical Study of Some Statistical Quantities for Quantum Systems Under Damping Effects

We present a model of interaction between a four-level atom and the cavity field initially prepared in the coherent state in the presence of the phase damping effect. We discuss the atom–field entanglement and statistical properties under the damping effect in view of numerical calculations. We use the Mandel parameter as a quantifier of the statistical properties of the field; moreover, we study the different effects of the collective parameters in the master equation on the dynamical behavior of the field statistical properties and the entanglement measured by the negativity. Finally, we explore the link between the entanglement and statistical properties in view of the numerical results during the time evolution.     

B‐spline solution of fractional integro partial differential equation with a weakly singular kernel

The main objective of the paper is to find the approximate solution of fractional integro partial differential equation with a weakly singular kernel. Integro partial differential equation (IPDE) appears in the study of viscoelastic phenomena. Cubic B‐spline collocation method is employed for fractional IPDE. The developed scheme for finding the solution of the considered problem is based on finite difference method and collocation method. Caputo fractional derivative is used for time fractional derivative of order α, . The given problem is discretized in both time and space directions. Backward Euler formula is used for temporal discretization. Collocation method is used for spatial discretization. The developed scheme is proved to be stable and convergent with respect to time. Approximate solutions are examined to check the precision and effectiveness of the presented method.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1565–1581, 2017     

First-principle electronic, elastic, and optical study of cubic gallium nitride

The ab initio pseudopotential (PP) method within the generalized gradient approximation (GGA) has been used to investigate the electronic, elastic constants, and optical properties of zinc-blende GaN. An underestimated band gap along with higher DOS and squeezed energy bands around the fermi level is obtained. The d-band effect is briefly discussed for electronic band structure calculations. With the help of elastic constants, acoustic wave speeds are calculated in [100], [110], and [111] planes. The dielectric constant, refractive index, and its pressure coefficient are well illustrated. The effect of hydrostatic pressure is explicated for all these properties. The results of the present study are evaluated with the existing experimental and first-principle calculations.     

Synthesis,characterization, and antibacterial activities of copper(I) bromide complexes of thioureas: X-ray structure of [Cu(Metu)<Subscript>4</Subscript>]Br

Copper(I) complexes of thioureas having the general formulae [CuL_nBr] and [CuL_n]Br [where, n = 1 − 4 and L = thiourea (Tu), N-methylthiourea (Metu), N-ethylthiourea (Ettu), N,N^′-dipropylthiourea (Dprtu), N,N^′-dibutylthiourea (Dbtu) or N,N^′-diphenylthiourea (Dphtu)] were prepared and characterized by elemental analysis, IR, and NMR (¹H and ¹³C) spectroscopy. The crystal structure of one of them, [Cu(Metu)₄]Br (1), was determined by X-ray crystallography. The X-ray structure of 1 describes a tetrahedral geometry around copper(I) with all Metu ligands binding through sulfur atoms. An upfield shift in the ¹³C NMR and downfield shift in the ¹H NMR spectra are consistent with the thione coordination to copper(I). Antimicrobial activities of the complexes were evaluated by the minimum inhibitory concentration method. The results showed that only [Cu(Ettu)₃Br] was effective in inhibiting the growth of all the tested organisms (gram-positive, gram-negative bacteria, and Candida sp.), while the other complexes were not effective against all the organisms.     

Critical evaluation of laboratory performance from IAEA-452 (fish scallop) inter-comparison exercise results

The International Atomic Energy Agency Marine Environmental Laboratory (IAEA-MEL) conducted an intercomparison exercise for the “Trace elements and methyl mercury in fish scallop: IAEA-452” in 2009. The Neutron Activation Analysis (NAA) laboratory at PINSTECH, Pakistan took part in this exercise. Comparison with the IAEA results showed that of the 18 elements reported to the IAEA 7 had unacceptable z-scores while the data for two elements was questionable (2< |z-score| <3). Upon investigation it was discovered that the large number of elements having unacceptable z-scores was due to human error and the greater difficulty in analyzing biological samples which have low amounts of trace elements. Therefore selection of values corresponding to matrix matched reference materials (RMs), such as IAEA-436 and IAEA-407, and to non-interfering peaks the results obtained became comparable to the IAEA results with only the result for As having |z-score|> 3.     

Geological and radiological studies of the Mount Arafat, Mekkah, Saudi Arabia

Mount Arafat is a sacred place for Muslims. It has been classified as a granodiorite rock which mainly consists of feldspar and quartz, muscovite, etc. During the Hajj and Umra, Muslims visit this holly place and stay there for some time. In order to study the geology and thermal history as well as to assess the radiological hazards due to the presence of primordial radionuclides, systematic studies using petrographic, fission track dating and γ-spectrometric (HPGe) techniques were carried out. Our study yielded fission track age of 9.13 ± 1.05 Ma of the Mount Arafat granodiorite. Rifting, magmatism, volcanism and sea floor spreading that resulted in the formation of Red Sea seems may have altered the original age of the Arafat granodiorite under study to 9.13 ± 1.05 Ma. Measured radioactivity concentrations due to ²²⁶Ra, ²³²Th and ⁴⁰K were found to be 10.75 ± 3.92, 29.21 ± 4.34 and 664.49 ± 7.45 Bq kg^?1, respectively. From the measured radioactivity, gamma index (Iγ) and radium equivalent (Ra_eq) were calculated as 0.402 and 103.23 Bq kg^?1 whereas outdoor external dose (D_out) and annual effective dose (E_out) were estimated to be 40.30 nGyh^?1 and 0.045 mSvy^?1 respectively. All the above mentioned values are well below the recommended limits. The Mount Arafat thus does not pose any radiological health hazard to the general public.     

MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity

In this work, the effects of slip velocity on the flow and heat transfer for an electrically conducting micropolar fluid over a permeable stretching surface with variable heat flux in the presence of heat generation (absorption) and a transverse magnetic field are investigated. The governing partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformation, which is solved numerically using the Chebyshev spectral method. The effects of the slip parameter on the flow, micro-rotation and temperature profiles as well as on the local skin-friction coefficient, the wall couple stress and the local Nusselt number are presented graphically. The numerical results of the local skin-friction coefficient, the wall couple stress and the local Nusselt number are given in a tabular form and discussed.     

Quadratic spline solution for boundary value problem of fractional order

Fractional differential equations are widely applied in physics, chemistry as well as engineering fields. Therefore, approximating the solution of differential equations of fractional order is necessary. We consider the quadratic polynomial spline function based method to find approximate solution for a class of boundary value problems of fractional order. We derive a consistency relation which can be used for computing approximation to the solution for this class of boundary value problems. Convergence analysis of the method is discussed. Four numerical examples are included to illustrate the practical usefulness of the proposed method.