The nuclear fission phenomenon continues to be an enigma, even after nearly 75 years of its discovery. Considerable progress has been made towards understanding the fission process. Both light projectiles and heavy ions have been employed to investigate nuclear fission. An extensive database of the properties of fissionable nuclei has been generated. The theoretical developments to describe the fission phenomenon have kept pace with the progress in the corresponding experimental measurements. As the fission process initiated by the neutrons has been well documented, the present article will be restricted to charged particle-induced fission reactions. The progress made in recent years and the prospects in the area of nuclear fission research will be the focus of this review.

In this article, we study time–space fractional advection–dispersion (FADE) equation and time–space fractional Whitham–Broer–Kaup (FWBK) equation that have significant roles in hydrology. We introduce suitable transformations to convert fractional-order derivatives to integerorder derivatives and as a result these equations transform into partial differential equations (PDEs). Then the Lie symmetries and the corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.

A modified static-exchange model is developed to study the collision of an atom with another atom. It includes the effect of long-range dipole–dipole van der Waals interaction between two atoms in addition to the exact effect of short-range force due to Coulomb exchange between two system electrons. Both these interactions dominate at colder energies. The system is treated as a four-centre problem in the centre-of-mass frame. The present ab-initio model is useful to study the two-atomic collisions at low energies, as well as cold energies. The new code is applied to study the scattering of positronium (Ps) by hydrogen (H), both in their ground states.

In the present article, we use negativity to investigate the entanglement between two massive particles in the spin degrees of freedom, as seen by moving observers. Assuming that the occurrence of spin-momentum states is determined by Gaussian probability distributions, we show that the degree of entanglement monotonically descends to a diminishingly small value at high rapidities. We further report, how the characteristics of this behaviour vary as the widths of distributions change. In particular, the degree of maximally entangled spin–spin states, resulting from equal distribution widths, is shown to exhibit extrema, depending on the width, at certain rapidities. The material presented in this paper then supports the idea that, for relativistic particles, a consistent reduced spin density (from which the negativity is derived) is impossible to construct.

We study the well-known one-dimensional problem of 𝑁 particles with nonlinear interaction. The 𝛽-Fermi–Pasta–Ulam model is the special case of quadratic and quartic interaction potential among nearest neighbours. We enumerate and classify the simple periodic orbits for this system and find the stability zones, employing Floquet theory. We quantize the nonlinear normal modes and construct a wavefunction for what we believe is a primitive nonlinear analogue of a `phonon’.

Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronization. In this article, we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We first indicate that synchronization frequency of oscillators in a completely connected network is always equal to the mean of the natural frequency distribution. In particular, shape of the natural frequency distribution does not affect the synchronization frequency in this case. Then, we analyse the case of oscillators in a directed ring network, where asymmetry in the natural frequency distribution is seen to shift the synchronization frequency of the network. We also present an estimate of the shift in the frequencies for slightly asymmetric distributions.

Author uses the condition in terms of contact point radial distribution function $G(\sigma, \lambda(\eta_c, \alpha))$ containing the self-consistent function $\lambda(\eta_c, \alpha)$ and condition of continuity at $\sigma/2$ = contact point, to determine equation of state, (EoS). Different EoSs in terms of built-in parameter, 𝑚, can be obtained with a suitable choice of $\lambda(\eta_c, \alpha)$ and the present EoSs have less r.m.s. deviation than Barker–Henderson BH2 for LJ fluids, and results are much closer to molecular dynamics (MD) simulations than expectations and reproduce the existing simulation data and present EoS for LJ potential, with the help of a set of minimum single-scaled parameter, $a_0(\eta_c, \alpha)$ for a given reduced temperature, $T^\ast = (1/\beta \epsilon)$= 1.4, 2, 3, 4, 5, 6. It has been found that parameter 𝛼 = 1.059128388 can be used to fix up the critical temperature parameter $T_c$ = 1.3120(7) to that of a computer simulation result.

In this work, we uphold and extend the formalism advocated by us more than a decade ago in order to extract information on various distribution functions describing nucleonic helicity structure and calculate a complete set of splitting functions relevant for their quantum chromodynamics (QCD) evolutions using light-front Hamiltonian perturbation theory in light front gauge $A^+$ = 0. Twist-two structures of the helicity distributions are self-evident in our calculation. Sum rules associated with these helicity distributions are also verified in a frame-independent way.

The systematic investigation of ground-state shape evolution from 𝛾-unstable 𝑂(6) to spherical 𝑈(5) for even−even ^112-134Te has been presented by using the quadrupole momentconstrained Hartree–Fock–Bogoliubov (HFB) method. By examining potential energy curves of Te isotopes, it has been suggested that ¹²⁴Te nucleus may hold 𝐸(5) symmetry.

We present an experimental study on measurement of nonlinear refractive index ($n_2$) of organic liquids when the thermo-optic effects manifest into large nonlinear phase shifts ($\Delta\phi_0$) in an open-aperture 𝑍-scan configuration. Although we do not obtain the familiar peak–valley normalized transmittance curve as in the case of closed-aperture 𝑍-scan technique, we use a theoretical model using Gaussian beam decomposition (GD) technique to estimate the value of $n_2$. Using this recipe, we obtain the nonlinear refractive index $n_2 = −(4.90 \pm 1.20) \times 10^{−15}$ cm²/W for toluene (organic solvent) and $n_2 = −(10.60 \pm 2.10) \times 10^{−15}$ cm²/W for an organic polymer solution (10$^{−4}$ Min toluene). By carrying out absorption measurements directly with an unfocussed Gaussian beam, we found nonlinear absorptions $\beta_{\text{tol}} = (2.42 \pm 0.20) \times 10^{−13}$ m/W and $\beta_{\text{poly}} = (2.79 \pm 0.24) \times 10^{−13}$ m/W which are close to the expected results.

Surface plasmon polaritons (SPPs) beam filter (BF) and beam splitter (BS) constructed using metal heterostructures are proposed and demonstrated numerically. Both structures have a ring metal heterowaveguide, which is constructed by a metal cylinder and a ring dielectric cladding. The two-dimensional finite-difference time-domain (2D-FDTD) method is employed to study the properties of the proposed BF and BS, and the results show that SPPs can effectively propagate on bended plasmonic waveguides with dielectric claddings. By introducing dielectric and plasmonic waveguides on both sides of the resonant ring, SPPs can be efficiently excited at the output of the waveguide ring resonator (WRR) through mode coupling. The planar metal heterostructures provide a way for constructing various nanoscale counterparts of conventional planar integrated devices such as filters, splitters, resonators, sensors, optical switches, and so on.

In this paper, we studied the propagation of elastic longitudinal waves in quasi-onedimensional (1D) finite phononic crystal with conical section, and derived expressions of frequencyresponse functions. It is found that, contrary to the 1D phononic crystal with a constant section, the value of attenuation inside the band gaps decreases quickly when cross-sectional area increases, and the initial frequency also decreases, but the cut-off frequency increases, thus the width of the band gap increases. The effects of lattice constant and the filling fraction on the band gap are also analysed, and the change trends of the initial frequency and cut-off frequency are consistent with those of constant section. It is shown that the results using this method are in good agreement with the results analysed by the finite element software, ANSYS.We hope that the results will be helpful in practical applications of phononic crystals.

A theoretical investigation has been carried out on the growth rate of instability of the low-frequency electrostatic waves in a partially ionized four-component magnetodustyplasma in the presence of polarization force. Utilizing the method of linear mode analysis, the results of investigation have been presented. The findings of the investigation reveal that the polarization force, the external magnetic field and the dust temperature have a tendency to destabilize the system by increasing the growth rate of instability. On the other hand, the positive dust mass causes the instability growth rate to decrease, thereby stabilizing the system.

Anodization of aluminium surfaces containing linearly oriented scratches leads to the formation of nanoporous anodic alumina (NAA) with the nanopores arranged preferentially along the scratch marks. NAA, when coated with a thin gold film, support plasmonic resonances. Dark-field spectroscopy revealed that gold-coated NAA with such linearly arranged pores shows a polarization-dependent scattering, that is larger when the incident light is polarized parallel to the scratch direction than when polarized perpendicular to the scratch direction. Fluorescence studies from rhodamine-6G (R6G) molecules dissolved in polymethylmethacrylate (PMMA) and deposited on these NAA templates showed that fluorescence can be strongly enhanced with the bare NAA due to multiple light scattering in the NAA, while fluorescence from the molecules deposited on gold-coated NAA is strongly quenched due to the strong plasmonic coupling.