We investigate the issue of observability of high-energy collisions around Kerr naked singularity and show that results are in contrast with the Kerr black hole case. We had shown that it would be possible to have ultrahigh energy collisions between the particles close to the location 𝑟 = M around the Kerr naked singularity if the Kerr spin parameter transcends unity by an infinitesimally small amount 𝑎 $\to$ 1⁺. The collision is between initially ingoing particle that turns back as an outgoing particle due to angular momentum barrier, with another ingoing particle. We assume that two massless particles are produced in such a collision and their angular distribution is isotropic in the centre-of-mass frame. We calculated the escape fraction for the massless particles to reach infinity. We showed that the escape fraction is finite and approximately equal to half for the ultrahigh energy collisions. Therefore, the particles produced in high-energy collisions would escape to infinity providing the signature of the nature of basic interactions at those energies. This result is in contrast with the case of extremal Kerr black hole where almost all particles produced in high-energy collisions are absorbed by the black hole rendering collisions unobservable.

In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field (the fractal quintessence) according to the evolution of ghost dark energy density.

Nonlinear oscillations of a bubble carrying a constant charge and suspended in a fluid, undergoing periodic forcing due to incident ultrasound are studied. The system exhibits period-doubling route to chaos and the presence of charge has the effect of advancing these bifurcations. The minimum magnitude of the charge 𝑄_min above which the bubble’s radial oscillations can occur above a certain velocity 𝑐₁ is found to be related by a simple power law to the driving frequency 𝜔 of the acoustic wave. We find the existence of a critical frequency $\omega_{H}$ above which uncharged bubbles necessarily have to oscillate at velocities below $c_{1}$. We further find that this critical frequency crucially depends upon the amplitude $P_{s}$ of the driving acoustic pressure wave. The temperature of the gas within the bubble is calculated. A critical value 𝑃_tr of $P_{s}$ equal to the upper transient threshold pressure demarcates two distinct regions of 𝜔 dependence of the maximal radial bubble velocity 𝑣_max and maximal internal temperature 𝑇_max. Above this pressure, 𝑇_max and 𝑣_max decrease with increasing 𝜔, while below 𝑃_tr, they increase with 𝜔. The dynamical effects of the charge, the driving pressure and frequency of ultrasound on the bubble are discussed.

Symmetry analysis of a 2D nonlinear evolutionary equation with mixed spatial derivative and general source term involving the dependent variable and its spatial derivatives is performed. The source terms for which the equation admits nontrivial Lie symmetries are identified for two different forms of the symmetry operator. In one of these cases, the symmetries do not depend on the form of nonlinearities and in the other case, nonlinearities of power, exponential and trigonometric forms are considered. There are no supplementary nonclassical symmetries for the investigated equation. The results reported here generalize the previous results on the 2D heat equation and the 2D Ricci model.

By exploiting supersymmetry and factorization method, higher partial wave nucleon–nucleon potentials ($\ell = 1,2,3$) for a few selected triplet and singlet states are generated from the ground-state interaction and wave function. The nuclear Hulthen potential and the corresponding wave function with the parameters of Arnold and Mackellar which fit the deuteron binding energy are used as the starting point of our calculation. The scattering phase shifts are computed for the constructed potentials using phase function method to examine the merit of our approach to the problem.

A theoretical study of the nuclear reaction cross-section for the production of ⁶⁴Cu and ⁸⁶Y was performed from the nuclear reactions ⁶⁴Ni(p, n)⁶⁴Cu, ⁶⁴Ni(d, 2n)⁶⁴Cu, ⁶⁶Zn(d, 𝛼)⁶⁴Cu, ⁶⁸Zn(p, n𝛼)⁶⁴Cu, ⁸⁶Sr(p, n)^86gY, ⁸⁷Sr(p, 2n)^86gY and ⁸⁸Sr(p, 3n)^86gY. The calculations were performed using three codes EMPIRE, TALYS and ALICE-IPPE. The excitation function curves for the investigated reactions have been constructed from the enriched targets using ⁶⁴Ni, ⁶⁶Zn, ⁶⁸Zn, ⁸⁶Sr, ⁸⁷Sr and ⁸⁸Sr. The calculated excitation functions and the experimental data were compared. Mean standardized deviation, mean relative deviation and mean ratio statistical parameters were introduced to control the quality of the fitting between both the experimentally and the theoretically calculated cross-sections.

In this study, we have used the cascade exciton model (CEM) to investigate different characteristics of nuclear reactions. Number of nucleon–nucleon collisions in Pb+Pb collisions as a function of impact parameter and rapidity distributions of negative particles from p+Ar and p+Xe interactions at 𝑝_lab = 200 GeV/c have been studied. We could create inclusive spectra of pions for separate charged states from reactions and total neutron multiplicities per primary reaction at 1000 MeV for different thin targets. Also, cross-sections for the reactions ²⁰⁹Bi(p, f) and ²⁰⁹Bi(n, f) were studied. Interactions of 1.0 GeV protons with C, Al, Cu, Sn, and Pb are presented in this study. All the calculated characteristics are compared with other theoretical calculations and compared with the experimental data. CEM shows good agreement with both theoretical and experimental results. In this study, we have used quantum molecular dynamic (QMD) as a theoretical model to compare our results.

An analysis of the data based on 924 inelastic interaction events induced by ²⁸ Si nuclei in a nuclear emulsion is presented. The nuclear fragmentation process is studied by analysing the total charge (𝑄) distribution of the projectile spectators for different emulsion target groups along with the comparison of Monte Carlo Glauber model results. Probability distributions for total disintegrated events as a function of different projectile masses are shown and compared with cascade evaporation model results at same energy per nucleon. Further, mean multiplicities of different charged secondaries for different classes of events are presented and for each event, variation of mean multiplicities as a function of total charge (𝑄) is also presented. The pseudorapidity distributions and normalized pseudorapidity distributions of the produced charged particles in nucleus–nucleus collisions at 3.7 A GeV are analysed for total disintegration (TD) as well as minimum-bias events.

A theoretical method has been discussed to study the size dependency of thermal expansion of nanomaterials at higher temperature by considering the surface effect. A thermodynamical analysis of the equation of state (EoS) is studied from the knowledge of thermal expansion of nano-materials based on theoretical thermodynamical relations. It is observed that thermal expansion coefficient increases with decrease in grain size whereas, 𝑉/𝑉₀ increases with increase in temperature for nanomaterials of different grain sizes. We have studied the size and temperature dependence of thermal expansion of Cu, Ag, Ni, Sn, Se and Zn nanomaterials in different shapes (spherical, nanowire and nanofilm). The available experimental data confirm these theoretical predictions that demonstrate the validity of our work.

Pure and Cu-doped zinc oxide (ZnO) nanoparticles were prepared using a chemical method. The dopant concentration (Cu/Zn in atomic percentage (wt%)) is varied from 0 to 3 wt%. Structural characterization of the samples performed using X-ray diffraction (XRD) confirmed that all the nanoparticles of zinc oxide are having polycrystalline nature. Morphological studies were conducted using field emission scanning electron microscopy (FESEM) to confirm the grain size and texture. Electrical measurements showed that the AC conductivity initially decreases and then rises with increasing Cu concentration. The UV–Vis studies showed absorbance peaks in the 200–800 nm region. It is found that the absorbance does not significantly change with doping. This fact is further confirmed from the band-gap calculations using the reflectance graphs. When analysed in terms of Burstein–Moss shift, an increase of band gap from 3.42 to 3.54 eV with increasing Cu concentration is observed. In the photoluminescence (PL) studies a red-shift is observed with increasing dopant concentration.

The nonlinear wave modulation of planar and non-planar (cylindrical and spherical) dust-acoustic waves (DAW) propagating in dusty plasmas, in the presence of non-extensive distributions for ions and electrons is investigated. By employing multiple scales technique, a cylindrically and spherically modified nonlinear Schrödinger equation (NLSE) is derived. The presence of hot non-extensive 𝑞-distributed ions and electron is shown to influence the modulational instability (MI) of the waves. It is shown that the properties of the MI of DAW in cylindrical and spherical geometries differ from those in a planar one-dimensional geometry. Furthermore, it is observed that the non-extensive distributed ions have more effect on the MI of the DAW than electrons. Also, it is found that there is a MI period for cylindrical and spherical wave modulations, which does not exist in the one-dimensional case.

Poly(𝑜-toluidine) (POT) polymer was synthesized by chemical method and RF plasma polymerization at a radio frequency (RF) power input of 15 W on ultrasonically cleaned glass and silicon wafer substrates. These samples were characterized by DC conductivity measurements, UV–visible, XRD and FTIR techniques. The DC-conductivity was measured at 410 K, which was found to increase by two orders of magnitude for thin film as compared to pellet samples. It has been observed that the activation energy increases for RF plasma-polymerized POT. Transmission and reflectance spectra were studied for measuring optical constants like absorption coefficient (𝛼), extinction coefficient (𝐾), optical band gap (𝐸_g), Urbach energy (𝐸_e), and refractive index (𝑛). From XRD studies, one can infer that the samples grown by both the methods are amorphous in nature. The results indicate that the structures of plasma-polymerized POT are rather different from polymers synthesized by conventional chemical methods, due to a higher degree of cross-linking and branching reactions in plasma polymerization. This makes them suitable for various electroactive devices. A higher and more stable conductivity can be obtained with RF plasma-polymerized POT which is much smoother and more uniform.