The steady laminar boundary layer flow of Carreau nanofluid over a stretching sheet is investigated. Effects of Brownian motion and thermophoresis are present. Heat transfer is characterized using convective boundary condition at the sheet. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations through suitable transformations. Results of velocity, temperature and concentration fields are computed via homotopic procedure. Numerical values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed. A comparative study with existing solutions in a limiting sense is made.

Schrödinger equations arise in modelling various physical and engineering problems. In this paper, we introduce a new homotopy perturbation method (NHPM) to improve the accuracy and computational efficiency of the homotopy perturbation method (HPM).We show that this technique enables one to determine the exact solution of the system of Schrödinger equations. Several illustrative examples are given to demonstrate the effectiveness of this method.

We examine the dynamical evolution of wave packets in a cubical billiard where three quantum numbers (𝑛_𝑥, 𝑛_𝑦, 𝑛_𝑧) determine its energy spectrum and consequently its dynamical behaviour. We have constructed the wave packet in the cubical billiard and have observed its time evolution for various closed orbits. The closed orbits are possible for certain specific values of quantum numbers (𝑛_𝑥, 𝑛_𝑦, 𝑛_𝑧) and initial momenta (𝑘_𝑥, 𝑘_𝑦, 𝑘_𝑧). We observe that a cubical billiard exhibits degenerate energy levels and the path lengths of the closed orbits for these degenerate energy levels are identical. In spite of the identical path lengths, the shapes of the closed orbits for degenerate levels are different and depend upon angles 𝜃 and 𝜙 which we term as the sweep and the elevation angles, respectively. These degenerate levels owe their origin to the symmetries prevailing in the cubical billiard and these levels disappear completely or partially for a parallelepiped billiard as the symmetry breaks due to commensurate or incommensurate ratio of sides.

The Kramer radiating star uses the interior Schwarzschild solution as a seed solution to generate a model of dissipative collapse. We investigate the thermal behaviour of the radiating star by employing a causal heat transport equation. The causal temperature is explicitly determined for the first time by integrating the transport equation. We further show that the dissipation of energy to the exterior space-time renders the core more unstable than the cooler surface layers.

In this paper, we have discussed the local stability of the Mathieu–van der Pol hyperchaotic system with the fractional-order derivative. The fractional Routh–Hurwitz stability conditions were provided and were used to discuss the stability. Feedback control method was used to control chaos in the Mathieu–van der Pol system with fractional-order derivative and after controlling the chaotic behaviour of the system the synchronization between the fractional-order hyperchaotic Mathieu–van der Pol system and controlled system was introduced. In this study, modified adaptive control methods with uncertain parameters at various equilibrium points were used. Also the analysis of control time with respect to different fractional-order derivatives is the key feature of this paper. Numerical simulation results achieved using Adams–Boshforth–Moulton method show that the method is effective and reliable.

A seminumerical solution to the valon model at next-to-leading order (NLO) in the Laguerre polynomials is presented. We used the valon model to generate the structure of proton with respect to the Laguerre polynomials method. The results are compared with H1 data and other parametrizations.

Magnetic electron scattering (𝑀3) form factors with core polarization effects, energy levels and 𝐵(𝑀3) values to 3⁺ states of the ²⁶Mg nucleus have been studied using shell model calculations. The universal sd of the Wildenthal interaction, universal sd-shell interaction A, universal sd-shell interaction B, are used for the sd-shell orbits. Core polarization effects according to microscopic theory are taken into account by the excitations of nucleons from the (1𝑠_1/2 1𝑝_3/2 1𝑝_1/2) core and also from valence 1𝑑_5/2 2𝑠_1/2 1𝑑_3/2 orbits into higher shells, with $4\hbar \omega$ excitation. In form factor calculations, the universal sd-shell interaction B for the sd-shell is used with the Michigan three-range Yakawa effective NN interaction as a residual interaction for the core polarization calculations. The wave functions of the radial single-particle matrix elements have been calculated using harmonic oscillator potentials. The level schemes are compared with the experimental data up to 9.902 MeV. In this study, very good agreements are obtained for all nuclei. Results from 𝑀3 form factor calculations with the inclusion of core polarization and new 𝑔-factors give good agreement with the experimental data.

Cross-sections for one- and multinucleon transfer reactions, namely, ⁵⁸Ni(¹²C, ¹³C), ⁵⁸Ni(¹²C, ¹¹C), ⁵⁸Ni(¹²C, ¹¹B), ⁵⁸Ni(¹²C, ¹⁰B), ⁵⁸Ni(¹²C, ¹⁰Be), ⁵⁸Ni(¹²C, ⁹Be), ⁵⁸Ni(¹²C, ⁸Be_𝑔.s.), ⁵⁸Ni(¹²C, ⁷Be), ⁵⁸Ni(¹²C, ⁷Li) and ⁵⁸Ni(¹²C, ⁶Li) have been measured at an incident energy of 60 MeV. The reaction cross-section for the corresponding transfer channels in the system ¹²C+⁵⁶Fe have also been measured under the same kinematical conditions. Angular distribution of the elastic scattering cross-section is measured at 60 MeV. The measured elastic scattering angular distributions for these two systems have been analysed using the optical model search code SFRESCO and the potential parameters are extracted. The multinucleon transfer data are analysed to obtain cross-section dependence on the number of nucleons transferred and on the ground state 𝑄-values. The transfer probabilities for multinucleon stripping are extracted. A detailed comparison in the multiparticle stripping and elastic scattering cross-sections between these two systems are made to understand the mechanism of multinucleon transfer and possible role of two extra protons in ⁵⁸Ni target nucleus as compared to the ⁵⁶Fe core.

Using B3LYP/6-31G* density functional level of theory, the structural and optical properties of the C₆₀ and M@C₅₉X cages have been investigated. Results indicate that the charge on C atoms and band gap of C₆₀ cage are changed dramatically with the substitution of one B or N atom at one of the C sites and the Li and Na atom encapsulations in the C₆₀ cage. The Mulliken analyses show that the charge is transferred completely between the alkali atoms and the C₅₉X cage. The substitutional and encapsulation doping (SED) reduce the optical gaps of the C₆₀ cage. Also, the oscillator strengths of the absorption peaks are dependent on dopant types.

Ab-initio calculations of thermal properties of rutile (TiO₂) have been performed by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). Both pressure- and temperature-dependent thermodynamic properties such as the bulk modulus, thermal expansion, thermal expansion coefficient, heat capacity at constant volume and constant pressure were calculated using two different models based on the quasiharmonic approximation (QHA): the Debye–Slater and Debye–Grüneisen model with Dugdale–MacDonald (DM) approximation. Also, the empirical energy corrections were applied to the results to correct the systematic errors in the density functional theory. It is found that the Debye–Grüneisen model provides more accurate estimates than the Debye-Slater models, especially after empirical energy correction.

Two polycrystalline V₄-cluster compounds of GaV₄S₈ were prepared at different annealing temperatures (GaV₄S₈-1 sintered at 800°C and GaV₄S₈-2 sintered at 500°C). Their temperature-dependent resistivity and structural phase transformation temperature (45 K for GaV₄S₈-1 and 43K for GaV₄S₈-2) are found to be very sensitive to the annealing condition. Above 320 K, activation energy 𝜀₃ is calculated to be ∼0.23 eV which decreases to ∼0.18 eV around 300 K in GaV₄S₈-1 and GaV₄S₈-2 on cooling. According to percolation theory, the gradual decrease in 𝜀₃ below 300 K is expected due to the increase in separation between V₄-clusters are significantly different in GaV₄S₈-1 and GaV₄S₈-2. This statement is strongly supported by the calculated bandwidth 𝛤 per cluster in GaV₄S₈ (∼0.342 eV in GaV₄S₈-1 and ∼0.374 eV in GaV₄S₈-2). A negative magnetoresistance (MR) is also found around 43 K in GaV₄S₈-2 at 6.0 T magnetic field associated with structural transition.

The optical properties of Violet 1-doped polyvinyl alcohol (PVA) have been investigated using Wemble and Didomenico (WD) method. The optical constants such as refractive index 𝑛, the dispersion energy 𝐸_𝑑, the oscillation energy 𝐸₀, the lattice dielectric constant 𝜀_∞, light frequency dielectric constant 𝜀₀ and the ratio of carrier concentration to the effective mass 𝑁/𝑚* have been determined using reflection spectra in the wavelength range 300–900 nm. The singlebeam Z-scan technique was used to determine the nonlinear optical properties of Violet 1:polyvinylalcohol (PVA) thin film. The experiments were performed using continuous wave (cw) laser with a wavelength of 635 nm. The calculated nonlinear refractive index of the film, $n_{2} = -2.79 \times 10^{-7}$ cm²/Wand nonlinear absorption coefficient, $\beta = 6.31\times10^{−3}$ cm/W. Optical limiting characteristics of the dye-doped polymer film was studied. The result reveals that Violet 1 can be a promising material for optical limiting applications.

Metallodielectric (gold@silica) composites were prepared by seed and grow method. The dielectric microspheres (core material) of an average size of 400 nm were synthesized by sol–gel method and gold nanoparticles (AuNPs) were prepared by reducing the chloroauric solution. Shell growth around silica (SiO₂) microspheres was carried out in a multistep layer-by-layer process. The synthesized composites were characterized using techniques such as field emissionscanning electron microscopy (FE-SEM), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) and UV–Visible (UV–Vis) spectroscopy. FE-SEM and FTIR analyses have confirmed the functionalization of SiO₂ surfaces with the amine terminal group along with the gold shell growth. XRD analysis has given an average crystallite size of 12.3 nm for metallodielectric composites. Absorption spectra have demonstrated the dependence of surface plasmon resonance (SPR) peak on the successive shell growth by exhibiting a red shift.

The laser wakefield-driven plasma wave in a low-density plasma is seen to be susceptible to the oscillating two-stream instability (OTSI). The plasma wave couples to two short wavelength plasma wave sidebands. The pump plasma wave and sidebands exert a ponderomotive force on the electrons driving a low-frequency quasimode. The electron density perturbation associated with this mode couples with the pump-driven electron oscillatory velocity to produce nonlinear currents driving the sidebands. At large pump amplitude, the instability grows faster than the ion plasma frequency and ions do not play a significant role. The growth rate of the quasimode, at large pump amplitude scales faster than linear. The growth rate is maximum for an optimum wave number of the quasimode and also increases with pump amplitude. Nonlocal effects, however reduce the growth rate by about half.

Recently, it was shown that the absence of circular polarization of visible light from quasars severely constrains the interpretation of axion-like particles (ALPs) as a solution for the generation of linear polarization. Furthermore, the new observation of linear polarization in radio wavelength from quasars, similar to the earlier observation performed in the optical bands, makes the ALPs scenario inconsistent with at least one of the two observations. In this study, we extend this scenario by including more scalars. We find that the effects from scalar and pseudoscalar neutralize each other, thereby suppressing the circular polarization, while preserving consistent linear polarization, as observed in both the visible and radio wave bands.

The band-head spin (𝐼₀) of superdeformed (SD) rotational bands in 𝐴 ∼ 190 mass region is predicted using the variable moment of inertia (VMI) model for 66 SD rotational bands. The superdeformed rotational bands exhibited considerably good rotational property and rigid behaviour. The transition energies were dependent on the prescribed band-head spins. The ratio of transition energies over spin 𝐸𝛾/2𝐼 (RTEOS) vs. angular momentum (𝐼 ) have confirmed the rigid behaviour, provided the band-head spin value is assigned correctly. There is a good agreement between the calculated and the observed transition energies. This method gives a very comprehensive interpretation for spin assignment of SD rotational bands which could help in designing future experiments for SD bands.