Higher-Order (F,α,β,ρ,d,E)-Convexity in Fractional Programming

In this paper we define higher order (F,α,β,ρ,d,E)-convex function with respect to E-differentiable function K and obtain optimality conditions for nonlinear programming problem (NP) from the concept of higher order (F,α,β,ρ,d)-convexity. Here, we establish Mond-Weir and Wolfe duality for (NP) and utilize these duality in nonlinear fractional programming problem.     

The effect of laser beam size in a zig-zag collimator on transverse cooling of a krypton atomic beam

The effect of size of a cooling laser beam in a zig-zag atomic beam collimator on transverse cooling of a krypton atomic beam is investigated. The simulation results show that discreteness in the interaction between the cooling laser beam and atomic beam, arising due to finite size and incidence angle of the cooling laser beam, significantly reduces the value of transverse velocity capture range of the collimator. The experimental observations show the trend similar to that obtained from simulations. Our study can be particularly useful where a small zig-zag collimator is required.     

MODELING AND ANALYSIS OF THE DEPLETION OF ORGANIC POLLUTANTS BY BACTERIA WITH EXPLICIT DEPENDENCE ON DISSOLVED OXYGEN

In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of dissolved oxygen caused by interactions of organic pollutants with bacteria in a water body, such as lake. The system is assumed to be governed by three dependent variables, namely, the cumulative concentration of organic pollutants, the density of bacteria and the concentration of dissolved oxygen. In the model, the coefficient of interaction of organic pollutants with bacteria depends upon the concentration of dissolved oxygen nonlinearly and explicitly, which is the main focus of this paper, has never been studied before. The stability theory of differential equations is used to analyze the model and to confirm the analytical results numerical simulation is performed. The model analysis shows that if the coefficient of interaction mentioned above depends upon dissolved oxygen explicitly, the decrease in its concentration is more than the case when the interaction does not depend on dissolved oxygen and consequently the depletion of organic pollutants is also more in such a case.     

Motion through spherical droplet with non-homogenous porous layer in spherical container

The problem of the creeping flow through a spherical droplet with a nonhomogenous porous layer in a spherical container has been studied analytically. Darcy’s model for the flow inside the porous annular region and the Stokes equation for the flow inside the spherical cavity and container are used to analyze the flow. The drag force is exerted on the porous spherical particles enclosing a cavity, and the hydrodynamic permeability of the spherical droplet with a non-homogeneous porous layer is ca...     

A phenomenological theory for polarization flop in spiral multiferroic TbMnO<Subscript>3</Subscript>

A phenomenological Landau theory has been used to explain magnetic field-driven polarization flop in TbMnO ₃. The Néel wall-like magnetic structure in spiral multiferroics induces a space-dependent internal magnetic field which exerts a torque on spins to rotate bc-spiral to ab-spiral. The external magnetic field is argued to be competing with easy axis anisotropy and the system stabilizes when anisotropy is minimum. With the help of Landau free energy with DM magnetoelectric coupling and a general ansatz for magnetization, the phenomenon of polarization flop has been explained. Relation between T_flop and critical magnetic field has been established and found to be in good agreement with the experiment. This could be an indication that anisotropy of the system is temperature- and magnetic field-dependent.     

Optimization of transfer of laser-cooled atom cloud to a quadrupole magnetic trap

We present here our experimental results on transfer of laser-cooled atom cloud to a quadrupole magnetic trap. We show that by choosing appropriately the ratio of potential energy in magnetic trap to kinetic energy of cloud in molasses, we can obtain the maximum phase-space density in the magnetic trap. These results guide us to choose the value of current to be switched in the quadrupole coils used for magnetic trapping for a given temperature of the cloud after molasses. This study is also useful to set the initial phase-space density of the cloud before evaporative cooling.     

NUMERICAL SIMULATION OF THREE-DIMENSIONAL SHOCK-SHOCK INTERACTIONS ON A BLUNT BODY

A numerical study is conducted to simulate the effects of extraneous shock impingement on a blunt body in viscous hypersonic flow. The interaction of extraneous shock with the leading-edge shock results in a very complex flow field that contains local regions of high pressure and intense heating. The heating and pressure can be orders of magnitude higher than the peak values in the absence of shock impingement. The flow field is calculated by solving thin-layer Navier-Stokes equations with a finite-volume flux splitting technique developed by van Leer. For a zero or small sweep of the body, a type IV interaction occurs, which produces a lambda shock structure with a supersonic jet embedded in the otherwise subsonic flow; for a moderate sweep of about 25^°, a type V interaction occurs in which a subsonic shear layer sandwiched in supersonic flow is produced with a transmitted shock. In the present study, both type IV and type V interactions are investigated. Results of the present numerical investigation are compared with available experimental results. For the present conditions, the peak pressure is 2.2 times the unimpinged stagnation point pressure and the peak heating is 3 times the unimpinged stagnation point heating. The flow for a type IV interaction is found to be unsteady.     

Development of copper bromide laser master oscillator power amplifier system

Development of master oscillator power amplifier (MOPA) system of copper bromide laser (CBL) operating at 110 W average power is reported. The spectral distribution of power at green (510.6 nm) and yellow (578.2 nm) components in the output of a copper bromide laser is studied as a function of operating parameters. The electrical input power was varied from 2.6 to 4.3 kW, the pulse repetition frequency (PRF) was changed from 16 to 19 kHz, and the pressure of the buffer gas (neon) was kept fixed at 20 mbar. When the electrical input power was increased to 4.3 kW from 2.6 kW, the tube-wall temperature also increased to 488°C from 426°C but the ratio of the green to yellow power decreased to 1.53 from 3.73. The ratio of green to yellow power decreased to 1.53 from 1.63 when the PRF of the laser was increased to 19 kHz from 16 kHz. These observations are explained in terms of electron temperature, energy levels of transitions, and voltage and current waveforms across the laser head.     

L subshell fluorescent X-ray measurements to study CK transitions in the 66<Emphasis Type="Italic">≤</Emphasis> <Emphasis Type="Italic">Z</Emphasis> <Emphasis Type="Italic">≤</Emphasis>83 region

L subshell fluorescent X-rays in Dy, Ho, Er, Lu, Ta, W, Pt, Au, Hg, Pb and Bi have been measured using synchrotron with selective creation of electron vacancies in individual subshells. Coster–Kronig (CK) yields were derived from the measured intensities. Present measurements have been made at photon energies above the edges where differences between measured and theoretical attenuation coefficients are almost negligible. Parametric trends for the results with Z were developed to cover all Zs in the range of 66–83. The trends predict the switching-off of L 1–L 2, N₁ transition at Z = 67. The extent of fall /rise of f_Lij values corresponding to off /on of certain transitions is found inversely proportional to the difference in binding energies of two consecutive subshells involved in the transition. For Zs above /below these rises /falls, f_L13 and f_L12 values are almost constants. f_L23 values involving no break at Zs follow the general photoionization behaviour that ionization probability is highest at the edge energy and decreases with photon energy. Yield measurements with synchrotron radiation for Dy, Ho, Lu, Hg and Bi and experimental values for f_L23, f_L12 in Lu and for f_L13 in Ta are being quoted for the first time.     

Strictly convex functions on complete Finsler manifolds

The purpose of the present paper is to investigate the influence of strictly convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss the properties of the group of isometries and the exponential maps on a complete Finsler manifold admitting strictly convex functions.