Volume 74, Issue 7

The alpha decay half-lives of Z = 118–121 superheavy nuclei with A ≤ 300 are calculated by using the density-dependent nuclear potential in the framework of the WKB method. The Paris and Ried M3Y nucleon-nucleon potentials are used in the calculation of the double-folding potential, which the Paris potential predicts to be the larger value of the half-lives. The obtained half-lives with Paris parameterisation are compared with those using three semi-empirical formulas, namely the improved Sahu formula, the universal decay law for alpha decay, and the formula for both alpha decay and cluster decay. The predicted half-lives with double-folding lie in between the improved Sahu and universal decay law formulas for both alpha and cluster decay. However, it is closer to the universal decay law formula and obeys its trend in all the studied superheavy nuclei.

The multiple acceleration–recombination process in high-order harmonic generation (HHG) has been investigated and discussed. Generally, the HHG can be explained through the ionization–acceleration–recombination process in each half-cycle waveform of the laser field. In this article, through the waveform control via the two-colour frequency-chirping laser field, the multiple acceleration–recombination process of the free electron in a specific “W” waveform structure can be found, which will lead to the larger emitted photon energies. Moreover, with the optimization of this “W” waveform by changing the frequency chirps, the carrier envelope phases, and the delay time, not only the efficiency of HHG can be enhanced compared with that from the original chirp-free pulse, but also the larger harmonic cutoff can be obtained. Further, with the assistance of the unipolar pulses, the cutoff and the efficiency of HHG can be further improved, showing a water window spectral continuum with the intensity enhancement of 66 times. As a result, by properly superposing some selected harmonics on the spectral continuum, three intense 38-as pulses in the water window region can be obtained.

The present work investigates the performance of Ga-doped ZnO (GZO) and Ca-doped ZnO (CZ) nanopowders as an efficient nanomaterials for the removal of lead ions from aqueous solutions. The sol–gel method was used to synthesise the nanoparticles from zinc acetate dihydrate. To incorporate Ca and Ga in ZnO, adequate quantities of calcium chloride hexahydrate and gallium nitrate hydrate were added to ZnO, and supercritical drying conditions of ethyl alcohol were used. Different Ca and Ga concentrations (1, 2, 3, 4, 5 at.%) were used to synthesise CZ and GZO. The structural and morphological properties of the as-prepared nanoparticles were determined using X-ray diffraction and transmission electron microscopy. Batch-mode experiments were used to remove lead from aqueous solution and to determine the adsorption equilibrium isotherms of lead ions using ZnO doped by 3 at.% of weight of Ca (CZ3) and Ga (GZO3). The effects of temperature, contact time, and pH on the removal of lead ions from aqueous solution by CZ3 and GZO3 were studied.

In the present article, we investigate the impact of fear effect in a predator–prey model, where predator–prey interaction follows Beddington–DeAngelis functional response. We consider that due to fear of predator the birth rate of prey population reduces. Mathematical properties, such as persistence, equilibria analysis, local and global stability analysis, and bifurcation analysis, have been investigated. We observe that an increase in the cost of fear destabilizes the system and produces periodic solutions via supercritical Hopf bifurcation. However, with further increase in the strength of fear, system undergoes another Hopf bifurcation and becomes stable. The stability of the Hopf-bifurcating periodic solutions is obtained by computing the first Lyapunov coefficient. Our results suggest that fear of predation risk can have both stabilizing and destabilizing effects.

A detailed analysis of the invariant point transformations for the first four partial differential equations which belong to the complex Burgers’ hierarchy is performed. Moreover, a detailed application of the reduction process through the Lie-point symmetries is presented while we construct the similarity solutions. We conclude that the differential equations of our consideration are reduced to first-order equations such as the Abel, Riccati, and to a linearisable second-order differential equation by using similarity transformations.

This article investigates the viscous dissipation effect on steady generalised Couette flow of heat-generating/absorbing fluid in a vertical channel. Equations of energy and momentum are obtained and solved using the homotopy perturbation method. The influences of the dimensionless flow parameter have been plotted graphically and discussed for varying values of the controlling parameters. During the course of computation, it is found that fluid temperature and velocity increase with an increase in viscous dissipation and also seen that growing mixed convection parameter Gre leads to a corresponding rise in temperature and velocity. It is further discovered that heat absorption leads to increase in the heat transfer on the heated wall. Finally, it is concluded that heat generation contributes to increase the mixed convection, hence, it requires decrease in mixed convection parameter to bring about a reverse flow near the stationary plate.

We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65 , 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space–time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity are both seen as emergent phenomena, resulting from coarse graining of the underlying noncommutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space–time–matter, and indeed entanglement appears to be more fundamental than quantum theory or space–time. We also comment on possible implications for black hole entropy and evaporation and for cosmology. We list the intermediate mathematical analysis that remains to be done to complete this programme.

Titanium dioxide (TiO 2 ) thin films were deposited on CR-39 by a sol-gel dip coating route with different withdrawal speeds ranging from 250 to 350 mm/s. The TiO 2 thin films were characterised by x-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy, ellipsometry, and ultraviolet (UV)-visible (VIS)-near infrared (NIR) spectro-photometry. The role of withdrawal speed on the thickness of thin films to tailor properties of TiO 2 thin films was studied. The XRD results revealed that all the films are amorphous in nature. TiO 2 thin films deposited at different withdrawal speeds exhibit a decrease in transmission with an increase in speed. The direct optical band gap of the films has been estimated to be in the range 3.48–3.00 eV by UV-VIS-NIR spectro-photometry and 3.52–3.38 eV by ellipsometry. TiO 2 is a potential prospect in microelectronic applications and can serve as an absorber layer for photovoltaic devices. Surface morphology is granular with an increase in grain size and an increase in withdrawal speed.