Fully constrained Majorana neutrino mass matrices using $$\varvec{\varSigma (72\times 3)}$$

In 2002, two neutrino mixing ansatze having trimaximally mixed middle (\(\nu _2\)) columns, namely tri-chi-maximal mixing (\(\text {T}\chi \text {M}\)) and tri-phi-maximal mixing (\(\text {T}\phi \text {M}\)), were proposed. In 2012, it was shown that \(\text {T}\chi \text {M}\) with \(\chi =\pm \,\frac{\pi }{16}\) as well as \(\text {T}\phi \text {M}\) with \(\phi = \pm \,\frac{\pi }{16}\) leads to the solution, \(\sin ^2 \theta _{13} = \frac{2}{3} \sin ^2 \frac{\pi }{16}\), consistent with the latest measurements of the reactor mixing angle, \(\theta _{13}\). To obtain \(\text {T}\chi \text {M}_{(\chi =\pm \,\frac{\pi }{16})}\) and \(\text {T}\phi \text {M}_{(\phi =\pm \,\frac{\pi }{16})}\), the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, \(m_1:m_2:m_3=\frac{\left( 2+\sqrt{2}\right) }{1+\sqrt{2(2+\sqrt{2})}}:1:\frac{\left( 2+\sqrt{2}\right) }{-1+\sqrt{2(2+\sqrt{2})}}\). In this paper we construct a flavour model based on the discrete group \(\varSigma (72\times 3)\) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric \(3\times 3\) matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of \(\varSigma (72\times 3)\). Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.     

Study of surface-bulk mass transport and phase transformation in nano-TiO2 using hyperfine interaction technique

Phase transition from anatase to rutile for the 70 nm TiO₂ crystallite has been investigated by the time differential perturbed angular correlation (TDPAC) technique. The study involved the annealing of the TiO₂ nanocrystals, adsorbed with the nuclear probe (¹⁸¹Hf/¹⁸¹Ta) at trace level, at different temperatures for different durations. The TDPAC measurement was also supported by XRD measurement where the width of the peaks increases with the increase in annealing temperature indicating a crystal growth. The samples annealed up to 823 K for 4 h showed no phase transition, except for the growth of the crystallites. However, it showed phase transition at the same temperature (823 K), when annealed for longer duration, indicating the slower kinetics of the phase transition process. Further the sample, when annealed at 1123 K for 4 h, showed phase transition. It has also been observed that the ¹⁸¹Hf tracer, adsorbed on 70 nm anatase TiO₂, diffuses from surface to bulk during the phase transition process and the extent of diffusion in anatase differs from that in rutile phase. However, surface to bulk mass-transfer is found to play a significant role in the phase transition process.     

Reactive Pulsed Laser Deposition of titanium nitride thin film: Optimization of process parameters using Secondary Ion Mass Spectrometry

Reactive Pulsed Laser Deposition is a single step process wherein the ablated elemental metal reacts with a low pressure ambient gas to form a compound. We report here a Secondary Ion Mass Spectrometry based analytical methodology to conduct minimum number of experiments to arrive at optimal process parameters to obtain high quality TiN thin film. Quality of these films was confirmed by electron microscopic analysis. This methodology can be extended for optimization of other process parameters and materials.     

Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity by mapping and ansatz methods

Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity are obtained using the mapping method. Several solutions are determined inclusing the cnoidal waves, shock waves, solitary waves, periodic singular waves and others. Finally, the ansatz method is applied to solve the equation with power law nonlinearity. It has been proved that the shock waves or topological solitons exist only for specific values of the power law parameter.     

Mössbauer studies of Ni70Fe10Si8B12 metglass: Reentrant properties

Amorphous metal Fe₁₀Ni₇₀Si₈B₁₂ has been studied by Mössbauer spectroscopy without and with an weak applied field in the plane of ribbons. Reentrant properties have been confirmed with the existence of a canted state at low temperature. Studies with different values of the applied field have shown that a field near 50 0e is sufficient to saturate the average direction of the ferromagnetism.     

Dynamic calibration of shock overpressure transducers

Piezoelectric transducers for dynamic overpressure measurements are commonly calibrated with static or quasistatic loads and the calibration is extrapolated to frequencies up to 30% of the resonant frequency of the piezoelectric crystal. Sinusoidal pressure generators are also used for dynamic calibration up to 500 Hz in the range of 3 MPa. This paper describes a method for dynamic calibration using transient overpressures, with rise time of 2 μsec and width 40 μsec, generated by exploding wires in air. The calibration is done in the range of 600 kPa.     

Effect of Laser Fluence on the Structural and Optical Properties of Tantalum Oxide Films Ablated by Pulsed Laser

The influence of laser fluence on the properties of thin films of tantalum oxide is studied in this paper, varying the laser fluence from 5.7 to 8.3 J/cm². Thin films of tantalum oxide were deposited on glass substrates using pulsed-laser ablation technique. X-ray diffraction studies confirm the amorphous/nanocrystalline nature of all the films irrespective of the laser fluence. The Tauc plot analysis suggests that tantalum oxide is an indirect band gap material, whose band gap decreases with increase in laser fluence. The refractive index of the films is found to decrease with increase in laser fluence but the extinction coefficient of the films increases with increase in laser fluence. Fourier transform infrared studies suggest the use of tantalum oxide thin films as oxygen sensors. Micro-Raman analysis reveals the sensitiveness of Ta-O-Ta and Ta-O vibration modes to laser fluence. Among all the films, the film deposited at a laser fluence of 7 J/cm² is found to be superior in quality.     

Exact solutions for Ostrovsky equation

This paper obtains solutions to the Ostrovsky equation by employing the mapping method. Several solutions are determined including the cnoidal waves, shock waves, solitary waves, periodic singular waves and others in the case of no rotation. Finally, the ansatz method is applied to solve the equation with the rotation term present.     

Fluorescence Dynamics of Three UV-B Sunscreens

Polarity of the surrounding medium affects the excited states of UV-B sunscreens. Therefore understanding excited state processes in a mixed polarity model system similar to skin is essential. We report the excited state lifetimes, quantum yields, radiative and non-radiative rates of three sunscreens. Among the three UV-B sunscreens studied, octyl salicylate emits from a single excited state, while padimate O and octyl methoxy cinnamate show multiple states. The radiative rates of salicylate and cinnamate are approximately constant, while that of padimate O depends strongly on solvent. The non-radiative rates of all sunscreens vary with solvent polarity. Compared to salicylate and cinnamate, padimate O is complex to analyze because of its two emission peaks and one peak’s strong dependence on the dielectric constant. High absorbance, broad absorption peak with small fluorescence quantum yield, and low radiative rate make octyl methoxy cinnamate a superior UV-B sunscreen ingredient. The complexity in excited-state analysis shows that the lifetimes of the sunscreens are critical parameters, in addition to absorbance and quantum yield. Fluorescence lifetime substantiates the use of polystyrene nanospheres as a model host to study the photo-physical properties of sunscreen in a heterogeneous environment.     

Character tables of n-dimensional hyperoctahedral groups and their applications*

We have shown that powerful matrix-type-based multinomial generators together with combinatorial techniques can be applied to derive the conjugacy classes, irreducible representations and the character tables of n-dimensional hyperoctahedral or hypercube groups of order n! × 2ⁿ, which are generalisations of non-rigid molecular theory formulated by Longuet-Higgins. The hyperoctahedral groups appear in the symmetry groups of non-rigid molecules, non-rigid water clusters, and other weakly bound van der Waals complexes that exhibit rapid tunnelling motion among various low-lying surmountable potential energy minima. These groups also have applications in quantum chromodynamics in the classification of states of quarks. The associated combinatorics has applications in enumerations, nuclear spin statistics and NMR spectroscopy. Finally, the groups enhance understanding of chirality in biosystems, that is, the functionality of intrinsically disordered proteins. We have derived the character tables of hyperoctahedral groups of sixth dimension, and techniques have been outlined to generalise for higher dimensions in the form of matrix generators.