For quantum systems, we expect to see the classical behaviour at the limit of large quantum numbers. Hence, we apply Bohmian approach for describing the evolution of Earth around the Sun. We obtain possible trajectories of the Earth system with different initial conditions which converge to a certain stable orbit, known as the Kepler orbit, after a given time. The trajectories are resulted from the guiding equation $p = \nabla S$ in the Bohmian mechanics, which relates the momentum of the system to the phase part of the wave function. Except at some special situations, Bohmian trajectories are not Newtonian in character. We show that the classic behaviour of theEarth can be interpreted as the consequence of the guiding equation at the limit of large quantum numbers.

This paper investigates the Newtonian heating effect on nanofluid flow over a nonlinear permeable stretching/shrinking sheet near the region of stagnation point. Only two important mechanisms on the transportation of nanoparticles in base fluid are discussed: the Brownian motion and thermophoresis. This physical problem is modelled using the Buongiorno (ASME J. Heat Transfer 128, 240 (2006) model in terms of nonlinear governing partial differential equations and transformed into dimensionless ordinary differential equations by using similarity transformation and the solution is calculated using the numerical scheme known as the Chebyshev spectral collocation method. The main interest of this study is the region of the boundary layer where viscous effects are dominant. Dual solutions are reported against the shrinking parameter in which the first solution is stable due to positive eigenvalues and the second is unstable due to negative eigenvalues and ranges of these solutions are effected by the suction parameter which is discussed using graphs and tables. The effects of dimensionless parameters, namely, velocity ratio, suction, Schmidt number, Prandtl number, thermophoresis and Brownian motion on temperature and concentration profiles, skin friction coefficient and Nusselt number are also shown using graphs. For the validity of the applied scheme, a comparison is established with published studies in the limiting case. Through the results, it is concluded that temperature and concentration increase by increasing the values of the thermophoresis parameter and the opposite behaviour is observed in the case of Brownian motion and Schmidt number. Skin friction coefficient, Nusselt and Sherwood numbers increase on increasing the suction parameter. Also, an enhancement in temperature and concentration profiles is observed in the presence of Newtonian heating parameter.

The flow of a second grade fluid by a rotating stretched disk is considered. Brownian motion and thermophoresis characterise the nanofluid. Entropy generation in the presence of heat generation/absorption, Joule heating and nonlinear thermal radiation is discussed. Homotopic convergent solutions are developed. The behaviour of velocities (radial, axial, tangential), temperature, entropy generation, Bejan number, Nusselt number, skin friction and concentration is evaluated. The radial, axial and tangential velocities increase for larger viscoelastic parameters while the opposite trend is noted for temperature. Concentration decreases when Schmidt number and Brownian diffusion increase. Entropy generation increases when the Bejan number increase while the opposite is true for the Brinkman number and the magnetic parameter.

Quantum confinement of electrons in atomic chains provides the most powerful and versatile means to control electronic, optical, magnetic and thermoelectric properties of materials needed to make diodes, spin valves and optical labels. Furthermore, the alloying of metallic atoms in different compositions produces novel mechanical, electronic and chemical behaviours in bimetallic chains as well as in other structures. This motivated us to perform theoretical investigations on the structure, stability, magnetic and electronic properties of bimetallic atomic chains of Au–Ag and Au–Pt, by using Vienna ab-initio simulation package (VASP), which is based on the density functional theory (DFT) within generalised gradient approximation. We have used tension and cohesive energy criteria to assess the stability of the Au–Ag and Au–Pt atomic chains. A comparison between the computed cohesive energies of various possible structures are made to suggest the most probable chain structures that can occur in break junction experiments. Our computed results suggest that the ground state of the Au–Ag and Au–Pt atomic chains should have zig-zag geometry. Furthermore, the most favoured chain structures that can be formed at the last stage of nanowires stretching are: (i) an atomic chain with alternate arrangement of equal number of Au and Ag/Pt atoms and (ii) an atomic chain where two Ag/Pt atoms are separated by one Au atom. Our results on the electronic band structure and optical properties suggest that the Au–Ag atomic chain could be of semiconducting nature, while the most stable Au–Pt chain is metallic in nature. A spin-polarised calculation with the inclusion of spin–orbit coupling shows that the Au–Pt atomic chains are magnetic, if the number of Au atoms is not more than the number of Pt atoms.

We have numerically explored different optical schemes for manipulating the composition of a coherent vibrational wavepacket on the ground electronic state of the $\rm{HD^{+}}$ ion. This was achieved by simulating the impulsive interaction of one or more ultrashort laser pulses with stationary eigenstates of $\rm{HD^{+}}$. Such a study highlights the use of various laser fields for the preparation of a molecular ion vibrational wavepacket, with variable constituents, in its ground electronic state. We have investigated different control scenarios through proper optimisation of the laser parameters and plausible interpretations of the results were proposed.

The modified exp($−\Omega(\zeta)$)-expansion function method is applied to the Wu–Zhang system with conformable time-fractional derivative to construct new analytical solutions. We have obtained some soliton-type solutions such as dark, singular and combined soliton solutions. We have seen that all solutions have provided the mentioned equation system. For the suitable value of the solutions, the 2D–3D and contour surfaces have been plotted.

This paper presents a comprehensive study of the design and parametric investigation of a diode pump alkali laser (DPAL): an emerging, high quantum efficiency, challenging laser system in the near-infrared region with potential for numerous applications. It covers the design and development of a diode pumped alkali (rubidium) laser (Rb:DPAL) gain cell and associated subsystems including the glove box-based alkali transfer set-up. Laser generation ($\lambda \sim 795 \rm{nm}$) in a continuous wave (CW) mode with end-pumped geometry in the Rb cell is reported. Comparative studies on the Rb-DPAL output were carried out with various critical operating parameters such as buffer gas pressure, buffer gas composition, gain medium temperature and pump power/intensity. The experimental results were analysed and discussed in light of the efficacy of the pump beam absorption, the laser level kinetics and effective lasing volume in the Rb-DPAL gain cell.

This paper investigates the new coupled (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) system with time-dependent coefficients for multiple types of exact solutions by using the Lie symmetry transformation method.Similarity transformation reduces the system of equations into ordinary differential equations and further, these are solved for solutions having bright, dark and singular solitons as well as periodic waves. Also, the solutions appeared in terms of time-dependent coefficient $\beta(t)$ and analysed graphically to show the effect of this arbitrary function. It is proved that the given system is nonlinear self-adjoint, and some conservation laws are obtained by applying the new conservation theorem.

In this study, the fully self-consistent Hartree–Fock (HF)-based random phase approximation (RPA) calculations were done for the $^{40}\rm{Ca}$ and $^{48}\rm{Ca}$ nuclei using 20 Skyrme-type interactions: KDE0, KDE0v1, SLy4, SLy5, SLy6, SK255, SKI2, SKI3, SKI5, SKM, SKMP, SKP, LNS, SGII, RAPT, SV-bas, SV-m56-O, SV-m64-O, SV-min and T6. Having a large number of Skyrme-force parameterisations requires a continuous search for the bestfor describing the experimental data. To examine our results, we compared the strength functions $S(E)$, the charge density distribution and centroid energies $E_{CEN}$ of the isoscalar giant monopole resonance (ISGMR), $J^{\pi} = 0^{+}, T = 0$, the isovector giant dipole resonance (IVGDR), $J^{\pi} = 1^{−}, T = 1$, and isoscalar giant quadrupole resonance (ISGQR), $J^{\pi} = 2^{+}, T = 0$ with the available experimental data. Moreover, we discussed the sensitivities of the centroid energy $m_{1}/m_{0}$ and moment $m_{1}$ of the $S(E)$ to the bulk properties of nuclear matter (NM), such as $K_{NM}$,the effective mass $m^{\ast}/m$ and the enhancement factor $κ$.

This letter demonstrates that there are some mistakes in the article of Roshan et al (Pramana – J. Phys. 90(3): 30, 2018) in dealing with the scattering of neutrons on $\alpha$-particles in three-dimensional space. In fact, there is no one-to-one correspondence between the incident neutron energy and the scattering angle of the α-particle even if they have definite velocities before scattering. Instead, the situation is complex, and all the scattered $\alpha$-particles will emit in a cone, which is called the velocity cone. At each scattering angle, which is smaller than the apex angle of the velocity cone, there are two groups of $\alpha$-particles with different kinetic energies.

In this communication, the impact of activation energy on the nonlinear binary chemically reactive flow of an Oldroyd-B nanofluid has been examined. Buongiorno’s nanofluid model is used in mathematical modelling. The flow behaviour is discussed over a nonlinear stretchable surface with variable thickness. Nonlinear mixed convection is considered. The energy equation is modelled subject to a heat source/sink and radiative flux. Furthermore, double stratification at the boundary of the sheet is considered for the heat and mass transfers. Important slip mechanisms such as Brownian and thermophoresis diffusions are accounted. The obtained flow expressions are analytically solved by using the optimal homotopy asymptotic method (OHAM). Computational analysis for concentration, temperature and velocity is obtained and discussed using plots. Nusselt and Sherwood numbers are discussed using a tabulated form. Total squared residual error is calculated for velocity, temperature andconcentration. The obtained results show that for increased values of Hartmann (magnetic parameter) and Deborah numbers, the fluid velocity decreases. The temperature field shows an increasing impact in the presence of larger radiative parameters. Sherwood and Nusselt numbers increase with higher values of thermophoresis and solutal stratified parameters.

In this paper, the changes of energetic intensity of Cern neutrinos during an experiment are analysed. For the analysis of energetic intensity of neutrinos, the theory of covariance functions was applied. The estimates of cross-covariance functions of digital data of energetic intensity of neutrinos or autocovariance functions of single data are calculated according to the random functions formed in the energetic intensity measuring data arrays in theform of vectors. The covariance functions have been calculated by varying the quantisation interval on the energetic scale and applying the computer program developed using MATLAB 7 package of procedures.

Functionalisation of nitrogen–nitrogen bonds of antisite defective boron nitride nanotubes (BNNTs), including exchange antisite defect which is produced by the rotation of BN bond, and substitutional antisite defect which is formed by substitution of an N with B, is investigated through their interaction with a $\rm{B^{−}_{6}}$ cluster. The smaller defect formation energies for the substitutional antisite defects indicate that the substitution of an N atom with B atom is easier than rotation of a BN bond. The formation of antisite defects at the edge or near the edges is more favourable than that in the middle of the tubes. When complexation between double ring $\rm{B^{−}_{6}}$ and nitrogen–nitrogen bonds of antisite defective BNNTs occurs, two-fold coordination, double ring configuration of boron cluster and N–N bond cleavage are seen. In the most stable complex, the $\rm{B^{−}_{6}}$ pulls apart the B–N bond and becomes an integral part of the tube by expanding the hexagonal BN ring, while in the other BNNT-B6 clusters, double ring $\rm{B^{−}_{6}}$ acts as a bridge at the top of the decagon. Functionalisation of N–N bonds at the edge or near the edges is more favourable than that in the middle of tubes.

The structural, elastic and lattice vibration properties of the ternary alloys ${\rm YP}_{1-x}{\rm As}_{x}$ at various As concentrations ($x$) from 0 to 1, $x=0, 0.25 ,0.5, 0.75$ and 1, are presented. The calculations were performed using the density functional perturbation theory (DFPT) within the generalised gradient approximation (GGA) and employing virtual crystal approximation (VCA). We studied the effect of arsenic composition on structural parameters, the phase transition pressure, the elastic constants, the optical and acoustic phonon frequencies at high symmetry points $\Gamma$, $X$ and $L$, the static and electronic dielectric constants, and the Born effective charge. It is established that all these properties follow a quadratic law in the concentration ($x$). There is a good agreement between our results and the available data for binary compounds YP and YAs. Our results are predictions of ${\rm YP}_{1-x}{\rm As}_{x}$.

The main purpose of this work is to suggest an efficient hybrid computational technique, namely the $q$-homotopy analysis transform method ($q$-HATM) to find the solution of the nonlinear time-fractional Zakharov–Kuznetsov (FZK) equation in two dimensions. The uniqueness and convergence analysis of the nonlinear time-FZK equation is presented. The Laplace decomposition method (LDM) is also employed to get the approximate solution of the nonlinear FZK equation. We implemented these techniques on two numerical examples, plotted the solution and compared the absolute error with the variational iteration technique and homotopy perturbation transform technique to show the efficiency of these techniques.