Volumetric, Ultrasonic and Transport Properties of Binary Liquid Mixtures Containing Dimethyl Formamide at 303.15 K

Excess volumes （v^E）, ultrasonic velocities （u）, isentropic compressibility （△Ks） and viscosities （η） for the binary mixtures of dimethyl formamide （DMF） with 1,2-dichlorobenzene, 1,3-dichlorobenzene, 1,2,4-trichlorobenzene, o-chlorotoluene, m-chlorotoluene, p-chlorotoluene, o-nitrotoluene and m-nitrotoluene at 303.15 K were studied. Excess volume data exhibit an inversion in sign for the mixtures of dimethyl formamide with 1,2- and 1,3-dichlorobenzenes and the property is completely positive over the entire composition range for the mixtures of dimethyl formamide with 1,2,4-trichlorobenzene, o-nitrotoluene and m-nitrotoluene. On the other hand, the quantity is negative for the mixtures of dimethyl formamide with chlorotoluenes. Isentropic compressibility （Ks） has been computed for the same systems from precise sound velocity and density data. Further, deviation of isentropic com- pressibility （△Ks） from ideal behavior was also calculated. AKs values are negative over the entire volume fraction range in all the binary mixtures. The experimental sound velocity data were analysed in terms of Free Length Theory （FLT） and Collision Factor Theory （CFT）. The viscosity data were analysed on the basis of corresponding state approach. The measured data were discussed on the basis of intermolecular interactions between unlike molecules.     

Existence of non-abelian representations of the near hexagon <Emphasis Type="BoldItalic">Q(5,2)⊗Q(5,2)</Emphasis>

In [5], a new combinatorial model with four types of points and nine types of lines of the slim dense near hexagon Q(5,2)?Q(5,2) was provided and it was then used to construct a non-abelain representation of Q(5,2)?Q(5,2) in the extraspecial 2-group \(2_{-}^{1+18}\). In this paper, we give a direct proof for the existence of a non-abelian representation of Q(5,2)?Q(5,2) in \(2_{-}^{1+18}\).     

On the Growth Properties of Solutions for a Generalized Bi-Axially Symmetric Schr\"{o}dinger Equation

In this paper, we have considered the generalized bi-axially symmetric Schr\"{o}dinger equation $$\frac{\partial^2\varphi}{\partial x^2}+\frac{\partial^2\varphi}{\partial y^2} + \frac{2\nu} {x}\frac{\partial \varphi} {\partial x} + \frac{2\mu} {y}\frac{\partial \varphi} {\partial y} + \{K^2-V(r)\} \varphi=0,$$ where $\mu,\nu\ge 0$, and $rV(r)$ is an entire function of $r=+(x^2+y^2)^{1/2}$ corresponding to a scattering potential $V(r)$. Growth parameters of entire function solutions in terms of their expansion coefficients, which are analogous to the formulas for order and type occurring in classical function theory, have been obtained. Our results are applicable for the scattering of particles in quantum mechanics.     

Brief report: Volume dependence of Grüneisen parameter for solids under extreme compression

The Nie expression is amended in such a way that the expression follows the infinite pressure behaviour, i.e., \(P\to \infty \) or V → 0. A new empirical relationship is developed to predict the values of volume dependence of Grüneisen parameter. NaCl and ε-Fe have been employed to test the suitability of the expression. The results obtained reveal that the relationship is reliable as there is a good agreement between the calculated and the experimental data.     

Soliton solutions of some nonlinear evolution equations with time-dependent coefficients

In this paper, we obtain exact soliton solutions of the modified KdV equation, inhomogeneous nonlinear Schrödinger equation and G(m, n) equation with variable-coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.     

Analysis of adiabatic transfer in cavity quantum electrodynamics

A three-level atom in a Λ configuration trapped in an optical cavity forms a basic unit in a number of proposed protocols for quantum information processing. This system allows for efficient storage of cavity photons into long-lived atomic excitations, and their retrieval with high fidelity, in an adiabatic transfer process through the ‘dark state’ by a slow variation of the control laser intensity. We study the full quantum mechanics of this transfer process with a view to examine the non-adiabatic effects arising from inevitable excitations of the system to states involving the upper level of Λ, which is radiative. We find that the fidelity of storage is better, the stronger the control field and the slower the rate of its switching off. On the contrary, unlike the adiabatic notion, retrieval is better with faster rates of switching on of an optimal control field. Also, for retrieval, the behaviour with dissipation is non-monotonic. These results lend themselves to experimental tests. Our exact computations, when applied to slow variations of the control intensity for strong atom–photon couplings, are in very good agreement with Berry’s superadiabatic transfer results without dissipation.     

Optimization for sinusoidal profiles in surface relief gratings recorded on photoresist

The formations of sinusoidal surface relief structures recorded in positive photoresist (Allresist AR-P 3120) have been studied and optimized for different recording parameters of gratings with spatial frequency of ～1200 grooves/mm. A stable sinusoidal pattern generated using a two-beam laser interferometric technique was recorded in thin films of positive photoresist deposited on glass substrates. Several gratings were generated by varying the exposure time of interference pattern and time of chemical development of exposed media. Time duration of exposure for 90 s and chemical development for 15 s were observed to be optimum for the translation of the sinusoidal interference pattern into nearly-sinusoidal profiled grooves in the gratings for a developer AR-300-26 of dilution of 2:1 (developer:de-ionized water).     

Development of tilted fibre Bragg gratings using highly coherent 255 nm radiation

This paper reports the study on development of tilted fibre Bragg gratings using highly coherent 255 nm radiation, obtained from the second harmonic generation (SHG) of copper vapour laser (CVL). The transmission and reflection spectra of the tilted fibre Bragg gratings (TFBG) were studied for the tilt angles of 0° (normal FBG), 1°, 3° and 4° between the fibre axis and the interference fringe plane. It was observed that as the angle of fibre axis and phase mask increased, the main Bragg peak shifted towards the higher wavelength and transmission dip decreased. The transmission dip of the cladding mode first increased and then decreased after reaching a maximum with the increase in the tilt angle.