This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.

The Einstein–Maxwell equations describing static charged spheres with uniform density and variable electric field intensity are studied. The special case of constant electric field is also studied. The evolution of the model is governed by a hypergeometric differential equation which has a general solution in terms of special functions. Several classes of exact solutions are identified which may be considered as charged generalizations of the incompressible Schwarzschild interior model. An analysis of the physical features is undertaken for the uniform case. It is demonstrated that uniform density spheres with constant electric field intensity are not realizable with isotropic pressures. This highlights the necessity of studying the criteria for physical admissability of gravitating spheres in general relativity which are solutions to the Einstein–Maxwell equations.

The limits $g \rightarrow$ large, $M \rightarrow$ large with ($g^{3}/M$) = const. of the $1+1$-dimensional Yukawa model are discussed. The conclusion of the results on bound states of the Yukawa model in this limit (obtained in arXiv:0908.4510v3 [hep-th]) is taken into account. It is found that model reduces to an effective non-local $\phi^{3}$ theory in this limit. Causality violation also is observed in this limit.

The sd-interacting boson approximation (sd-IBA) and the df-interacting boson approximation (df-IBA) can be related to each other and the states of the interacting boson approximation model can be identified with the fully symmetric states in the sdf interacting boson approximation model. A systematic study of the sdf-IBA model showed that the constructed Hamiltonian can successfully describe the strong octupole correlations in the deformed nuclei. We showed that the interacting boson approximation may account for many of these $K^{\pi} = 0^{+}$ states. It was found that the calculated energy spectra of the gadolinium isotopes agree quite well with the experimental data. The observed $B(E2)$ values were also calculated and compared with the experimental data.

With an aim to understand the effects of breakup and transfer channels on elastic scattering and fusion cross-sections in the $^{7}{\text{Li}} + ^{27}{\text{Al}}$ reaction, simultaneous measurement of elastic scattering angular distributions and fusion cross-sections have been carried out at various energies ($E_{\text{lab}} = 8.0–16.0$ MeV) around the Coulomb barrier. Optical model (OM) analysis of the elastic scattering data does not show any threshold anomaly or breakup threshold anomaly behaviour in the energy dependence of the real and imaginary parts of the OM potential. Fusion cross-section at each bombarding energy is extracted from the measured $\alpha$-particle evaporation energy spectra at backward angles by comparing with the statistical model prediction. Results on fusion cross-sections from the present measurements along with data from the literature have been compared with the coupled-channels predictions. Detailed coupled-channels calculations have been carried out to study the effect of coupling of breakup, inelastic and transfer, channels on elastic scattering and fusion. The effect of $1n$-stripping transfer coupling was found to be significant compared to that of the projectile breakup couplings in the present system.

The transient analytical solutions of temperature distribution, stress, strain and optical path difference in convectional cooled end-pumped laser rod are derived. The results are compared with other works and good agreements are found. The effects of increasing the edge cooling and face cooling are studied. It is found that an increase in the edge cooling has significant effect on reducing the maximum temperature that can be reached in the laser rod but it has no effect on the value of optical path difference. It is also found that increasing this type of cooling significantly reduces the time required to reach the thermal equilibrium with a slight increase in the max. tensile hoop stress that can be reached as the cooling increases. On the other hand, increase in face cooling reduces the response time, optical path difference and the maximum temperature that can be reached in the laser rod but a significant increase in the max. tensile hoop stress is observed. A matching between the advantages of these two type of cooling may be useful for a designer.

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on $1024^{3}$, $2048^{3}$, and $4096^{3}$ grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good `weak' and `strong' scaling for Tarang on these systems.

Interaction of nonplanar ion-acoustic solitary waves is an important source of information for studying the nature and characteristics of ion-acoustic solitary waves (IASWs). The head-on collision between two cylindrical/spherical IASWs in un-magnetized plasmas comprising of nonthermal distributed electrons and warm ions is investigated using the extended version of Poincaré–Lighthill–Kuo (PLK) perturbation method. How the interactions are taking place in cylindrical and spherical geometries are shown numerically. Analytical phase shifts are derived for nonplanar geometry. The effects of the ion to electron temperature parameter and the nonthermal electrons parameter on the phase shift are studied. It is shown that the properties of the interaction of IASWs in different geometries are very different.

An analysis is performed to study the unsteady, incompressible, one-dimensional, free convective flow over an infinite moving vertical cylinder under combined buoyancy effects of heat and mass transfer with thermal and mass stratifications. Laplace transform technique is adopted for finding solutions for velocity, temperature and concentration with unit Prandtl and Schmidt numbers. Solutions of unsteady state for larger times are compared with the solutions of steady state. Velocity, temperature and concentration profiles are analysed for various sets of physical parameters. Skin friction, Nusselt number and Sherwood number are shown graphically. It has been found that the thermal as well as mass stratification affects the flow appreciably.

Critical current ($I_{c}$) characteristics of 2G YBCO superconducting tape under the influence of twisting moment was experimentally investigated at varying current ramp rates in the self-field. Under a uniform twist, the degradation in the current-carrying capacity of YBCO tape up to $30\%$ was observed at 77 K. The degradation is largely attributed to the shear stress and torsional shear strain resulting from the twisting. The superconductor to resistive transition index, $n$, is also found to behave in an identical manner with increase in the twisting. Finite element analysis (FEA) of the tape in the experimental configuration with twisting moment being applied on to it has been carried out in COMSOL. The torsional strain calculated analytically as per the experimental configuration matches closely with that of FEA results, which shows that the critical current degradation is a function of strain.

We report an investigation of the oscillation death (OD) of a parametrically excited coupled van der Pol–Mathieu (vdPM) system. The system can be considered as a pair of harmonically forced van der Pol oscillators under a double-well potential. The two oscillators are coupled with a cubic nonlinearity. We have shown that the system arrives at an OD regime when coupling strength crosses a threshold value at which the system undergoes saddle-node bifurcation and two limit cycles coalesce onto a fixed point of the system. We have further shown that this nonautonomous system possesses a centre manifold corresponding to the OD regime.

Cosmological models with modified Chaplygin gas (MCG) in the framework of Horava–Lifshitz (HL) theory of gravity, both with and without detailed balance, are obtained. The equation of state (EOS) for a MCG contains three unknown parameters namely, $A, \alpha, B$. The allowed values of some of these parameters of the EOS are determined using the recent astrophysical and cosmological observational data. Using observational data from $H(z)-z$, baryon acoustic oscillation (BAO) peak parameter and cosmic microwave background (CMB) shift parameter we study cosmologies in detailed-balance and beyond detailed-balance scenario. In this paper we take up the beyond detailed-balance scenario in totality and contribution of dark radiation in detailedbalance scenario on the parameters of the EOS. We explore the effect of dark radiation on the whole range of the effective neutrino parameter ($\Delta N_{\nu}$) to constrain matter contributing parameter $B$ in both the detailed-balance and the beyond detailed-balance scenarios. It has been observed that greater the dark radiation less the matter contribution in the MCG in both the scenario considered here. In order to check the validity of beyond detailed-balance scenario we plot supernovae magnitudes ($\mu$) with red-shift of Union2 data and then the variation of state parameter with redshift is studied. It is noted that beyond detailed-balance scenario is suitable for cosmological model in HL gravity with MCG.

The feasibility study for searching neutrinoless double beta decay in $^{124}$Sn using cryogenic bolometer has been initiated. For this purpose, a custom-built cryogen-free dilution refrigerator, having a large cooling power of 1.4 mW at 120 mK, has been installed at TIFR, India. This paper describes the design, installation and performance of a cryogen-free dilution refrigerator (CFDR-1200). The performance of CFDR-1200 has been analysed using Takano’s model developed for conventional (wet) dilution refrigerators.