Einstein's field equations are considered for a locally rotationally symmetric Bianchi Type-II space–time in the presence of a massless scalar field with a scalar potential. Exact solutions of scale factors and other physical parameters are obtained by using a special law of variation for Hubble's parameter that yields a constant value of deceleration parameter. To get inflationary solutions, a flat region is considered in which the scalar potential is constant. Power-law and exponential cases are studied and in both solutions there is an anisotropic expansion of the cosmic fluid, but the fluid has vanishing vorticity. A detailed study of geometrical and kinematical properties of solutions has been carried out.

We have studied the evolution of a homogeneous, anisotropic universe given by a Bianchi Type-V cosmological model filled with viscous fluid, in the presence of cosmological constant 𝛬. The role of viscous fluid and 𝛬-term in the Bianchi Type-V universe has been studied.

In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of generalized diagonal metric, we consider the Einstein, Bergmann–Thomson and Landau–Lifshitz energy and/or momentum definitions both in Einstein's theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation). We find same energy distribution using Einstein and Bergmann–Thomson formulations, but we also find that the energy–momentum prescription of Landau–Lifshitz disagree in general with these definitions. We also give eight different well-known space-time models as examples, and considering these models and using our results, we calculate the energy distributions associated with them. Furthermore, we show that for the Bianchi Type-I models all the formulations give the same result. This result agrees with the previous works of Cooperstock–Israelit, Rosen, Johri et al, Banerjee–Sen, Xulu, Vargas and Saltı et al and supports the viewpoints of Albrow and Tryon.

Synchronization behaviour of two mutually coupled double-well Duffig oscillators exhibiting cross-well chaos is examined. Synchronization of the subsystems was observed for coupling strength $k > 0.4$. It is found that when the oscillators are operated in the regime for which two attractors coexist in phase space, basin bifurcation sequences occur leading to $n + 1$, $n \geq 2$ basins as the coupling is varied – a signature of Wada structure and final-state sensitivity. However, in the region of complete synchronization, the basins structure is identical with that of the single oscillators and retains its essential features including fractal basin boundaries.

We calculate the interfacial surface tension of a QGP-fireball in a hadronic medium in the Ramanathan et al statistical model. The constancy of the ratio of the surface tension with the cube of the critical transition temperature is in overall accordance with lattice QCD findings. It is in complete agreement with a recent MIT bag model calculation of surface tension. The velocity of sound in the QGP droplet is predicted to be in the range $(0.27 \pm 0.02)$ times the velocity of light in vacuum and this value is independent of both the value of the transition temperature and the model parameters.

In this study, we determined the most appropriate Hamiltonian that is needed for the present calculations of energy levels and $B(E2)$ values of ^128−138Ce nuclei which have a mass around $A \cong 130$ using the interacting boson model (IBM). Using the best-fitted values of parameters in the Hamiltonian of the IBM-2, we have calculated energy levels and $B(E2)$ values for a number of transitions in ^{128,130,132,134,136,138}Ce. The results were compared with the previous experimental and theoretical (PTSM model) data and it was observed that they are in good agreement. Also some predictions of this model have better accuracy than those of PTSM model. It has turned out that the interacting boson approximation (IBA) is fairly reliable for calculating spectra in the entire set of ^{128,130,132,134,136,138}Ce isotopes and the quality of the fits presented in this paper is acceptable.

We have calculated the one-neutron absorption cross-section and the longitudinal momentum distribution of the core fragment coming out from the breakup of ¹¹Be and ¹⁹C on ⁹Be target at 63 MeV/A and 88 MeV/A beam energies respectively. The reaction mechanism is treated within the framework of the eikonal approximation. The effective range of the nuclear interaction between the core and the valence neutron within the projectile has been determined by comparing the predicted stripping crosssection with the recently measured one. The effective range for ¹⁹C has been found to besmaller than that for ¹¹Be. It qualitatively indicates that ¹⁹C is slightly more halo than ¹¹Be. The smaller width, predicted as well as measured, of the LMD of ¹⁸C than ¹⁰Be also strengthens this fact. The experimental data concerning the LMD of core fragments have been well represented.

A self-affne analysis of charged-particle multiplicity distribution (protons + pions) in $\pi^{−}$ –AgBr interaction at 350 GeV/c is performed according to the two-dimensional factorial moment methodology using the concept of Hurst exponent in $X_{\cos \theta^{-}} $X_{\phi}$ phase space. Comparing with the results obtained from self-similar analysis, the self affine analysis shows a better power-law behaviour. Corresponding results are compared with shower multiplicity distribution (pions). Multifractal behaviour is observed for both types of distributions.

For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to generate necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for axisymmetric bending and stretching of a circular plate when stress or mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of plate theories. More importantly, appropriate boundary conditions with a set of mixed edge-data are obtained for the first time. Furthermore, the corresponding necessary conditions for transversely isotropic elastic plate are obtained directly, and their isotropic elastic counterparts are also obtained.

We use different determinantal Hartree–Fock (HF) wave functions to calculate true variational upper bounds for the ground state energy of 𝑁 spin-half fermions in volume $V_{0}$, with mass 𝑚, electric charge zero, and magnetic moment 𝜇, interacting through magnetic dipole–dipole interaction. We find that at high densities when the average interparticle distance $r_{0}$ becomes small compared to the magnetic length $r_{m} \equiv 2m\mu^{2}/\hbar^{2}$, a ferromagnetic state with spheroidal occupation function $n_{\uparrow} (\vec{k})$, involving quadrupolar deformation, gives a lower upper bound compared to the variational energy for the uniform paramagnetic state or for the state with dipolar deformation. This system is unstable towards infinite density collapse, but we show explicitly that a suitable short-range repulsive (hard core) interaction of strength $U_{0}$ and range a can stop this collapse. The existence of a stable equilibrium high density ferromagnetic state with spheroidal occupation function is possible as long as the ratio of coupling constants $\Gamma_{cm} \equiv (U_{0}a^{3}/\mu^{2})$ is not very smallcompared to 1.

The laser speckle photography is used to calculate the average surface roughness from the autocorrelation function of the aluminum diffuse objects. The computed results of surface roughness obtained from the profile shapes of the autocorrelation function of the diffuser show good agreement with the results obtained by the stylus profile meter.

In this paper, a new design and construction of a low intensity (100 mCi) ²⁴¹Am 𝛾-ray Compton spectrometer is presented. The planar spectrometer is based on a small disc source with the shortest geometry. Measurement of the momentum density of polycrystalline Al is used to evaluate the performance of the new design. The measured profile is in good agreement with the existing theoretical data and our density functional calculations.

Dielectric relaxation measurements of formamide (FMD)–$N,N$- dimethylaminoethanol (DMAE) solvent mixtures have been carried out over the entire concentration range using time domain reflectometry technique at 25, 35 and 45° C in thefrequency range of 10 MHz to 20 GHz. The mixtures exhibit a principle dispersion of the Davidson–Cole relaxation type at microwave frequencies. Bilinear calibration method is used to obtain complex permittivity $\epsilon^{∗}(\omega)$ from complex reflection coefficient $\rho^{∗} (\omega)$ over the frequency range of 10 MHz to 10 GHz. The excess permittivity ($\epsilon^{E}$), excessinverse relaxation time $(1/\tau)^{E}$, Kirkwood correlation factor ($g^{eff}$), activation energy and Bruggeman factor ($f_{B}$) are also calculated to study the solute–solvent interaction.

By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.

Pure magnesium ferrite sample was prepared by standard ceramic technique and characterized by X-ray diffraction method. XRD pattern revealed that the sample possess single-phase cubic spinel structure. The linear attenuation coefficient (𝜇), mass attenuation coefficient ($\mu/\rho$), total atomic cross-section ($\sigma_{\text{tot}}$), total electronic cross-section ($\sigma_{\text{ele}}$) and the effective atomic number ($Z_{\text{eff}}$) were calculated for pure magnesium ferrite (MgFe₂O₄). The values of 𝛾-ray mass attenuation coefficient were obtained using a NaI energy selective scintillation counter with radioactive 𝛾-ray sources having energy 0.36, 0.511, 0.662, 1.17 and 1.28 MeV. The experimentally obtained values of $\mu/\rho$ and $Z_{\text{eff}}$ agreed fairly well with those obtained theoretically.

A complete normal coordinate analysis was performed for five-coordinate non-rigid triarylantimony diester SbPh₃(O₂CR₂), known to be a bioactive molecule, using Wilson G-D matrix method and Urey Bradley force field. The study of vibrational dynamics was performed using the concept of group frequencies and band intensities.