In this paper, we implemented the functional variable method for the exact solutions of the Zakharov-Kuznetsov-modified equal-width (ZK-MEW), the modified Benjamin-Bona-Mohany (mBBM) and the modified kdV-Kadomtsev-Petviashvili (kdV-KP) equation. By using this scheme, we found some exact solutions of the above-mentioned equation. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider-applicability for handling nonlinear wave equations.

The Nikiforov–Uvarov method is used to investigate the bound state solutions of Schrödinger equation with a generalized inverted hyperbolic potential in D-space. We obtain the energy spectrum and eigenfunction of this potential for arbitrary 𝑙-state in 𝐷 dimensions. We show that the potential reduces to special cases such as Rosen–Morse, Poschl–Teller and Scarf potentials. The energy spectra and wave functions of these special cases are also discussed. The numerical results of these potentials are presented.

The qubit (or a system of two quantum dots) has become a standard paradigm for studying quantum information processes. Our focus is decoherence due to interaction of the qubit with its environment, leading to noise. We consider quantum noise generated by a dissipative quantum bath. A detailed comparative study with the results for a classical noise source such as generated by a telegraph process, enebles us to set limits on the pplicability of this process $\nu is à \nu is$ its quantum counterpart, as well as lend handle on the parameters that can be tuned for analysing decoherence. Both Ohmic and non-Ohmic dissipations are treated and appropriate limits are analysed for facilitating comparison with the telegraph process.

Coupled discrete models are ubiquitous in a variety of physical contexts. We provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lamé polynomials of arbitrary order. The models discussed are: (i) coupled Salerno model, (ii) coupled Ablowitz–Ladik model, (iii) coupled $\phi^4$ model and (iv) coupled $\phi^6$ model. In all these cases we show that the coefficients of the Lamé polynomials are such that the Lamé polynomials can be re-expressed in terms of Chebyshev polynomials of the relevant Jacobi elliptic function.

Travelling and solitary wave solutions of certain coupled nonlinear diffusion-reaction equations have been constructed using the auxiliary equation method. These equations arise in a variety of contexts not only in biological, chemical and physical sciences but also in ecological and social sciences.

High-spin states of ²¹⁶Ra $(Z = 88,N = 128)$ have been investigated through ²⁰⁹Bi(¹⁰B, 3n) reaction at an incident beam energy of 55 MeV and ²⁰⁹Bi(¹¹B, 4n) reaction at incident beam energies ranging from 65 to 78 MeV. Based on $\gamma \gamma$ coincidence data, the level scheme for ²¹⁶Ra has been considerably extended up to $\sim 33\hbar$ spin and 7.2 MeV excitation energy in the present experiment with placement of 28 new 𝛾-transitions over what has been reported earlier. Tentative spin-parity assignments are done for the newly proposed levels on the basis of the DCO ratios corresponding to strong gates. Empirical shell model calculations were carried out to provide an understanding of the underlying nuclear structure.

In the present work, the isospin admixtures in the nuclear ground states of the parent nuclei and isospin structure of the isobar analog resonance (IAR) states have been investigated by studying the $0^{+} \rightarrow 0^{+}$ superallowed Fermi 𝛽 decays using Pyatov’s restoration method. Within the random phase approximation (RPA), in this method, the effect of isospin breaking due to the Coulomb forces has been evaluated, taking into account the effect of pairing correlations between nucleons.

The factors influencing the trajectory of long-range 𝛼-particle in the cold ternary fission of ²⁵²Cf are discussed. The trajectory of the 𝛼-particle is studied by considering the influence of the force on the 𝛼-particle due to Coulomb and proximity potentials and is found to have sensitive dependence on the initial position and initial energy of the 𝛼-particle. The sensitivity to initial conditions signifies the presence of deterministic chaos which is characterized by Lyapunov exponent (LE). The LE is calculated using Wolf’s algorithm and found positive which implies that the objectives of trajectory calculations are restricted.

Considering interactions and scattering of positrons with argon (Ar) and krypton (Kr) atoms, we have calculated total cross-sections $(Q_{T} = Q_{el} + Q_{inel})$ using complex spherical potentials for these systems. In positron–atom scattering it is difficult to bifurcate the ionization and cumulative excitation contained in the total inelastic cross-section. An approximate method called CSP-ic (complex scattering potential-ionization contribution) similar to electron–atom scattering has been applied to bifurcate ionization and cumulative excitation cross-sections at energies from the threshold to 2000 eV. Adequate comparisons of the present results are made, with available data.

The electric field enhancement inside a nanotube irradiated by intense ultrashort laser pulse ($\ll 1$ ps) is calculated. The hollowness of the nanotubes determines the field enhancement and the electron density at which such structures exhibit resonance. The electric field in a nanotube plasma is shown to be resonantly enhanced at multiple densities during the two phases of interaction: the ionization phase and the hydrodynamic expansion phase. It is further shown that by a proper choice of hollowness of the nanotubes, a continued occurrence of the resonance over a longer time can be achieved. These properties make nanotubes efficient absorbers of intense ultrashort laser pulses.

Swelling kinetics of water-swollen polyacrylamide (PAAm) hydrogels (WSG) was investigated in various concentrations of aqueous NaCl by macroscopic swelling measurements. For lower concentration of NaCl, WSG showed exponential swelling whereas at higher concentration of NaCl it underwent deswelling at short times and exponential swelling at long times. From these studies, collective diffusion coefficient, 𝐷, of the polymer network and polymer–solvent interaction parameter, 𝜒 , were calculated and found to decrease with increase in [NaCl]. Collective diffusion coefficients measured from dynamic light scattering (DLS) and that obtained from macroscopic swelling measurements are found to agree well. Measured ensemble-averaged dynamic structure factor $f (q, t)$ for WSG and salt-swollen gels (SSG) showed an initial decay followed by a plateau at long times and it can be described by harmonically bound Brownian particle (HBBP) model. Enhanced scattering intensity at low scattering angles using static light scattering (SLS) measurements revealed the presence of inhomogeneities in PAAm gels. The reasons for increased scattering intensity of SSG over WSG gel and the linear decrease of 𝐷 with increase in NaCl concentration are explained.

We investigate the relaxation dynamics of photogenerated carriers in silicon nanowires consisting of a crystalline core and a surrounding amorphous shell, using femtosecond time resolved differential reflectivity and transmission spectroscopy at 3.15 eV and 1.57 eV photon energies. The complex behaviour of the differential transmission and reflectivity transients is the mixed contributions from the crystalline core and the amorphous silicon on the nanowire surface and the substrate where competing effects of state-filling and photoinduced absorption govern the carrier dynamics. Faster relaxation rates are observed on increasing the photogenerated carrier density. Independent experimental results on crystalline silicon-on-sapphire (SOS) help us in separating the contributions from the carrier dynamics in crystalline core and the amorphous regions in the nanowire samples. Further, single-beam z-scan nonlinear transmission experiments at 1.57 eV in both open- and close-aperture configurations yield two-photon absorption coefficient 𝛽 (∼3 cm/GW) and nonlinear refraction coefficient 𝛾 ($−2.5 × 10^{−4}$ cm² /GW).

In this paper we study the Indian highway network as a complex network where the junction points are considered as nodes, and the links are formed by an existing connection. We explore the topological properties and community structure of the network. We observe that the Indian highway network displays small-world properties and is assortative in nature. We also identify the most important road-junctions (or cities) in the highway network based on the betweenness centrality of the node. This could help in identifying the potential congestion points in the network. Our study is of practical importance and could provide a novel approach to reduce congestion and improve the performance of the highway network.

Random geographical networks are realistic models for wireless sensor networks which are used in many applications. Achieving average consensus is very important in sensor networks and the faster the consensus is, the durable the sensors’ life, and thus, the better the performance of the network. In this paper we compared the performance of a number of linear consensus algorithms with application to distributed averaging in random geographical networks. Interestingly, the simplest algorithm – where only the degree of receiving nodes is needed for the averaging – had the best performance in terms of the consensus time. Furthermore, we proved that the network has guaranteed convergence with this simple algorithm.

We examine the role of space-time geometry in the non-adiabatic collapse of a star dissipating energy in the form of radial heat flow, studying its evolution under different initial conditions. The collapse of a star filled with a homogeneous perfect fluid is compared with that of a star filled with inhomogeneous imperfect fluid under anisotropic pressure. Both the configurations are spherically symmetric. However, in the latter case, the physical space 𝑡 = constant of the configurations endowed with spheroidal or pseudospheroidal geometry is assumed to be inhomogeneous. It is observed that as long as the collapse is shear-free, its evolution depends only on the mass and size of the star at the onset of collapse.