The stretching and bending vibrational energies of SnBr₄ and CCl₄ are calculated in the one-dimensional framework. The dynamical symmetry group of tetrahedral molecule was taken into consideration to construct the model Hamiltonian in this frame-work. Casimir and Majorana invariant operators were also determined accordingly. Using the model Hamiltonian so constructed, we reported the vibrational energy levels of SnBr₄ and CCl₄ molecules accurately.

The Bianchi Type-I Universe filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the Universe has been used. It is modeled on the equation of state $p = \gamma(\rho − \rho_{*})$ which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for both power-law and exponential forms. The cases $\gamma = 1$ and $\gamma = 0$ have also been analysed.

A method based on wavelet transform is developed to characterize variations at multiple scales in non-stationary time series. We consider two different financial time series, S&P CNX Nifty closing index of the National Stock Exchange (India) and Dow Jones industrial average closing values. These time series are chosen since they are known to comprise of stochastic fluctuations as well as cyclic variations at different scales. The wavelet transform isolates cyclic variations at higher scales when random fluctuations are averaged out; this corroborates correlated behaviour observed earlier in financial time series through random matrix studies. Analysis is carried out through Haar, Daubechies-4 and continuous Morlet wavelets for studying the character of fluctuations at different scales and show that cyclic variations emerge at intermediate time scales. It is found that Daubechies family of wavelets can be effectively used to capture cyclic variations since these are local in nature. To get an insight into the occurrence of cyclic variations, we then proceed to model these wavelet coefficients using genetic programming (GP) approach and using the standard embedding technique in the reconstructed phase space. It is found that the standard methods (GP as well as artificial neural networks) fail to model these variations because of poor convergence. A novel interpolation approach is developed that overcomes this difficulty. The dynamical model equations have, primarily, linear terms with additive Padé-type terms. It is seen that the emergence of cyclic variations is due to an interplay of a few important terms in the model. Very interestingly GP model captures smooth variations as well as bursty behaviour quite nicely.

We propose a better differential method for the computation of the equation of state of QCD from lattice simulations. In contrast to the earlier differential method, our technique yields positive pressure for all temperatures including the temperatures in the transition region. Employing it on temporal lattices of 8, 10 and 12 sites and by extrapolating to zero lattice spacing we obtained the pressure, energy density, entropy density, specific heat and speed of sound in quenched QCD for $0.9 \leq T/T_{c} \leq 3$. At high temperatures comparisons of our results are made with those from the dimensional reduction approach and also with those from a conformal symmetric theory.

Evolution of gluon distribution function from Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equation in next-to-leading order (NLO) at low-𝑥 is presented assuming the Regge behaviour of quark and gluon at this limit. We compare our results of gluon distribution function with MRST2004, GRV98LO and GRV98NLO parametrizations and show the compatibility of Regge behaviour of quark and gluon distribution functions with perturbative quantum chromodynamics (PQCD) at low-𝑥.

The violated commutation condition between the total shell model Hamiltonian and Gamow–Teller operator (GT) has been restored by Pyatov method (PM). The considered nuclear model Hamiltonian in PM includes the separable GT residual interaction in ph and pp channels and is differentiated from the traditional schematic model by $h_{0}$ (restoration term). The influence of the h0 effective interaction on the $2\nu\beta\beta$ decay of ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ¹¹⁶Cd, ^128,130Te and ¹³⁶Xe is investigated. All the calculations have been done within the framework of standard QRPA. The results obtained by PM are compared with those of other approaches and experimental data. The influence of the restoration term on the stability of the $2\nu\beta\beta$ decay nuclear matrix elements is analysed.

Laser material processing involving welding, ablation and cutting involves interaction of intense laser pulses of nanosecond duration with a condensed phase. Such interaction involving high brightness radiative flux causes multitude of non-linear events involving thermal phase transition at soild–liquid–gas interfaces. A theoretical perspective involving thermal dynamics of the vaporization process and consequent non-linear multiple thermal phase transitions under the action of laser plasma is the subject matter of the present work. The computational calculations were carried out where titanium (Ti) was treated as a condensed medium. The solution to the partial differential equations governing the thermal dynamics and the underlying phase transition event in the multiphase system is based on non-stationary Eulerian variables. The Mach number 𝑀 depicts significant fluctuations due to thermal instabilities associated with the laser beam flux and intensity. A conclusive amalgamation has been established which relates material surface temperature profile to laser intensity, laser flux and the pressure in the plasma cloud.

The effects of time-periodic forcing in a few-mode model for zero-Prandtl-number convection with rigid body rotation is investigated. The time-periodic modulation of the rotation rate about the vertical axis and gravity modulation are considered separately. In the presence of periodic variation of the rotation rate, the model shows modulated waves with a band of frequencies. The increase in the external forcing amplitude widens the frequency band of the modulated waves, which ultimately leads to temporally chaotic waves. The gravity modulation, on the other hand, with small frequencies, destroys the quasiperiodic waves at the onset and leads to chaos through intermittency. The spectral power density shows more power to a band of frequencies in the case of periodic modulation of the rotation rate. In the case of externally imposed vertical vibration, the spectral density has more power at lower frequencies. The two types of forcing show different routes to chaos.

This article reports a comparative study of the phase separation process in a polymer-dispersed liquid crystal, based on a Metropolis Monte Carlo simulation study of three lattice systems. We propose a model for the different processes occurring in the formation of polymer-dispersed liquid crystals (PDLCs). The mechanism of PDLC is studied as a function of quench temperature, concentration and degree of polymerization of liquid crystals and polymers. The obtained resultant phase diagrams of the three systems are approximated and compared with the Flory–Huggins theory, and show a good agreement. It has been observed in the simulation results that among all the three systems, the $40 \times 40 \times 40$ lattice showed the most accurate, reliable and stable results.

By calculating the optical spectrum band positions and EPR parameters (𝑔 factors, $g_{\parallel}$ , $g_{\perp}$ and zero-field splitting 𝐷) by diagonalizing the complete energy matrix of 3d⁸ ions in trigonal symmetry, the defect structure of Ni²⁺ centre in 𝛼-LiIO₃ crystal is studied. It is found that to reach the good fits of optical and EPR data between calculation and experiment, the Ni²⁺ ion should shift by $\Delta z \approx 0.298$ Å along C₃ -axis and the O²⁻ ions between the Ni²⁺ ion and Li⁺ vacancy (V$_{Li}$) should be displaced away from the V$_{Li}$ by $\Delta x \approx 0.097$ Å because of the electrostatic interaction. The results are discussed.

Organic thin film transistors (OTFTs) were fabricated using pentacene as the active layer with two different gate dielectrics, namely SiO₂ and poly(methyl methacrylate) (PMMA), in top contact geometry for comparative studies. OTFTs with SiO₂ as dielectric and gold deposited on the rough side of highly doped silicon (n⁺ -Si) as gate electrode exhibited reasonable field effect mobilities. To deal with poor stability and large leakage currents between source/drain and gate electrodes in these devices, isolated OTFTs with reduced source/drain contact area were fabricated by selective deposition of pentacene on SiO₂/PMMA through shadow mask. This led to almost negligible leakage currents and no degradation in electrical performance even after 14 days of storage under ambient conditions. But, the field effect mobilities obtained were lower than 10^-3 cm² V^-1 s^-1, whereas by using PMMA as gate dielectric with chromium deposited on the polished side of n⁺ -Si as gate electrode, improved field effect mobilities (> 0.02 cm² V^-1 s^-1) were obtained. PMMA-based OTFTs also exhibited lower leakage currents and reproducible output characteristics even after 30 days of storage under ambient conditions.

This paper presents the results of investigation on the influence of temperature on magnetoelastic characteristics of the two ring-shaped cores, made of Fe₇₀Ni₈Si₁₀B₁₂ amorphous alloy. The cores were annealed for 1 h at 350 and 400° C, respectively. The compressive force 𝐹 was applied perpendicular to the direction of the magnetizing field 𝐻 in the sample. Special cylindrical backing enables application of the uniform compressive stress 𝜎 to the wound ring sample. A resistive furnace heated the experimental set-up. Results presented in the paper indicate a significant influence of the temperature on the magnetoelastic characteristics of Fe₇₀Ni₈Si₁₀B₁₂ amorphous alloy. Information about the magnetoelastic characteristics of this material may be useful in the magnetoelastic sensor development. Also this will create new possibilities in the development of physical model of magnetoelastic effect.

AC impedance spectroscopy technique has been used to study electrical properties of Bi_3.25La_0.75Ti₃O₁₂ (BLT) ceramic. Complex impedance plots were fitted with three depressed semicircles, which are attributed to crystalline layer, plate boundary and grain boundary and all three were found to comprise of universal capacitance nature $[C = C_{0}w^{n−1}]$. Grain boundary resistance and capacitance evaluated from complex impedance plots have larger values than that of plate boundary and crystalline layer. The activation energies ($E_{a}$) for DC-conductance in grain boundary, plate boundary and crystalline layer are 0.68 eV, 0.89 eV and 0.89 eV, respectively. Relaxation activation energies calculated from impedance plots showed similar values, 0.81 eV and 0.80 eV for crystalline layer and plate boundary, respectively. These activation energy values are found to be consistent with the $E_{a}$ value of oxygen vacancies in perovskite materials. A mechanism is offered to explain the generation of oxygen vacancies in BLT ceramic and its role in temperature dependence of DC-conductance study.