A broad general variable separation solution with two arbitrary lower-dimensional functions of the (2+1)-dimensional Broer–Kaup (BK) equations was derived by means of a projective equation method and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as oscillating solitons, instantonlike and cross-like fractal structures are revealed by selecting appropriate functions of the general variable separation solution.

Making use of an ansatz for the eigenfunction, we investigate closed-form solutions of the Schrödinger equation for an even power complex deictic potential and its variant in one dimension. For this purpose, extended complex phase-space approach is utilized and nature of the eigenvalue and the corresponding eigenfunction is determined by the analyticity property of the eigenfunction. The imaginary part of the energy eigenvalue exists only if the potential parameters are complex, whereas it reduces to zero for real coupling parameters and the result coincides with those derived from the invariance of Hamiltonian under $\mathcal{PT}$ operations. Thus, a non-Hermitian Hamiltonian possesses real eigenvalue, if it is $\mathcal{PT}$-symmetric.

In this paper, the new generalized ($G'/G$)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solutions has been demonstrated. It is shown that the new approach of generalized ($G'/G$)-expansion method is a straightforward and effective mathematical tool for solving nonlinear evolution equations in applied mathematics, mathematical physics and engineering. Moreover, this procedure reduces the large volume of calculations.

In this paper, we investigate a special 𝐶(3, 2, 2) equation $$u_t + ku_x − u_{xxt} + 3(u^3)_x = u_x(u^2)_{xx} + u(u^2)_{xxx}$$.

The bifurcation and some new exact representations of peakons, bell-shaped solitary wave solutions and periodic cusp wave solutions for the equation are obtained using the qualitative theory of dynamical systems. It is shown that the peakons are actually the limit of bell-shaped solitary waves and periodic cusp waves. Moreover, a new characteristic of non-smooth solutions, two peakons coexisting for the same wave speed, is found. Some previous results are extended.

The projected shell model (PSM) calculations have been performed for the neutron-rich even–even ^102−110Mo and odd–even ^103−109Mo isotopes. The present calculation reproduces the available experimental data on the yrast bands. In case of even–even nuclei, the structure of yrast bands is analysed and electromagnetic quantities are compared with the available experimental data. The 𝑔-factors have been predicted for high spin states. For the odd-neutron nuclei, the structures of yrast positive- and negative-parity bands are analysed and found to be in reasonable agreement with the experiments for ${}^{103−107}$Mo. The disagreement of the calculated and observed plots for energy staggering quantity clearly establishes the occurrence of sizable triaxiality in ${}^{103,105}$Mo and also predicts a decrease in the quantum of triaxiality with increasing neutron number and angular momentum for odd mass neutron-rich Mo isotopes.

Energy levels and $\Lambda\Lambda$ bond energy of the double-𝛬 hypernucleus are calculated by considering two- and three-cluster interactions. Interactions between constituent particles are contact interactions for reproducing the low binding energy of nuclei. The effective action is constructed to involve three-body forces. In this paper, we also compare the obtained binding energy result with experimental and other cluster and shell models. The results of all schemes agree very well showing the high accuracy of our method to calculate the other many-body hyperonic nuclei using three-cluster interactions. The experimental values of $B_{\Lambda\Lambda}$(${}^{10}_{\Lambda\Lambda}$ Be) = (11.90 ± 0.13) MeV, $B_{\Lambda\Lambda}$(${}^{11}_{\Lambda\Lambda}$Be) = (20.49 ± 1.15) MeV and $B_{\Lambda\Lambda}$(${}^{12}_{\Lambda\Lambda}$Be) = (22.23 ± 1.15) MeV seem to be more compatible with our calculated value of $B_{\Lambda\Lambda}$(${}^{10}_{\Lambda\Lambda}$Be) = 14.04 MeV, $B_{\Lambda\Lambda}$(${}^{11}_{\Lambda\Lambda}$Be) = 19.31 MeV and $B_{\Lambda\Lambda}$(${}^{12}_{\Lambda\Lambda}$Be) = 21.45 MeV in comparison with the other calculated results by Hiyama et al, Gal et al and Guleria et al.

This article focusses on the study of clan model parameters and their target dependence in light of void probability scaling for heavy (Ag and Br) and light (C, N and O) groups of target present in nuclear emulsion detector using ⁸⁴Kr₃₆ at ∼1 A GeV. The variation of scaled rapidity–gap (rap–gap) probability with single moment combination has been studied. We found that experimental points lie approximately on the negative binomial distribution (NBD) curve, indicating a scaling behaviour. The increase in average clan multiplicities ($\bar{N}$) for interactions with the pseudorapidity interval ($\Delta \eta$) was also observed. The values of $\bar{N}$ for AgBr targets are larger than those for C/N/O target and also average number of particles per clan ($\bar{n}_c$) increases with increase in pseudorapidity interval. We further observed that for a particular target, the average number of particles per clan ($\bar{n}_c$) increases with an increase in the size of projectile nucleus.

We demonstrate the generation of an isotopically pure beam of laser-cooled Yb atoms by deflection using 1D-optical molasses. Atoms in a collimated thermal beam are first slowed using a Zeeman slower. They are then subjected to a pair of molasses beams inclined at 45° with respect to the slowed atomic beam. The slowed atoms are deflected and probed at a distance of 160 mm. We demonstrate the selective deflection of the bosonic isotope ¹⁷⁴Yb and the fermionic isotope ¹⁷¹Yb. Using a transient measurement after the molasses beams are turned on, we find a longitudinal temperature of 41 mK.

One of the main concerns about the currentworking on nuclear power reactors is the potential hazard of their radioactive waste. There is hope that this issue will be reduced in next generation nuclear fusion power reactors. Reactors will release nuclear energy through microexplosions that occur in a mixture of hydrogen isotopes of deuterium and tritium. However, there exist radiological hazards due to the accumulation of tritium in the blanket layer. A catalytic fusion reaction of DT$_x$ mixture may stand between DD and an equimolar DT approach in which the fusion process continues with a small amount of tritium seed. In this paper, we investigate the possibility of DT$_x$ reaction in the fast ignition (FI) scheme. The kinematic study of the main mechanism of the energy gain–loss term, which may disturb the ignition and burn process, was performed in FI and the optimum values of precompressed fuel and proton beam driver were derived. The recommended values of fuel parameters are: areal density $\rho R \geq 5𝑔\cdot$cm^-2 and initial tritium fraction $x \leq 0.025$. For the proton beam, the corresponding optimum interval values are proton average energy $3\leq E_p \leq 10$ MeV, pulse duration $5 \leq t_p \leq 15$ ps and power $5\leq W_p \leq 12 \times 10^{22}$ (keV$\cdot$cm³$\cdot$ps^-1). It was proved that under the above conditions, a fast ignition DT$_x$ reaction stays in the catalytic regime.

First-principles calculations were performed to study the elastic stiffness constants ($C_{ij}$) and Debye temperature ($\theta_D$) of wurzite (wz) AlN and GaN binary semiconductors at high pressure. The lattice constants were calculated from the optimized structure of these materials. The band gaps were calculated at 𝛤 point using local density approximation (LDA) approach. The unit cell volume, lattice parameters, $c/a$, internal parameter (𝑢), elastic constant ($C_{ij}$), Debye temperature ($\theta_D$), Hubbard parameter (𝑈) and band gap ($E_g$) were studied under different pressures. The bulk modulus ($B_0$), reduced bulk modulus ($B'_0$) and Poisson ratio ($\vee$) were also calculated. The calculated values of these parameters are in fair agreement with the available experimental and reported values.

An interesting phenomenon is observed while carrying out thermal carbonization of porous silicon (PS) with an aim to arrest the natural surface degradation, and it is a burning issue for PS-based device applications. A tubular carbon structure has been observed on the PS surface. Raman, Fourier transform infrared spectroscopy (FTIR) and electron microscope studies, revealed that the tubular structure is nothing but amorphous carbon nanofibres sprouted within the pores in the absence of a metal catalyst, for which a suitable explanation is proposed.

In this paper we investigate the effect that naturally occurring impurities in salt mines have both on effective permittivity of the medium and on radio wave propagation at ∼200 MHz. The effective permittivity is determined based on the dielectric properties of salt and the characteristics of the main impurities. We conclude that at such frequencies the scattering is negligible compared to absorptions. The effect of trapped water in different forms is also evaluated.

Action-at-a-distance electrodynamics – alternative approach to field theory – can be extended to cosmological models using conformal symmetry. An advantage of this is that, the origin of arrow of time in electromagnetism can be attributed to the cosmological structure. Different cosmological models can be investigated, based on Wheeler–Feynman absorber theory, and only those models can be considered viable for our Universe which have net full retarded electromagnetic interactions, i.e., forward direction of time. This work evaluates the quasi-steady-state model and demonstrates that it admits full retarded and not advanced solution. Thus, quasi-steady-state cosmology (QSSC) satisfies this necessary condition for a correct cosmological model, based on action-at-a-distance formulation.