Thermodynamic model first published in 1909, is being used extensively to understand the size-dependent melting of nanoparticles. Pawlow deduced an expression for the size-dependent melting temperature of small particles based on the thermodynamic model which was then modified and applied to different nanostructures such as nanowires, prism-shaped nanoparticles, etc. The model has also been modified to understand the melting of supported nanoparticles and superheating of embedded nanoparticles. In this article, we have reviewed the melting behaviour of nanostructures reported in the literature since 1909.

A low-cost apparatus for measuring Hall effect and magnetoresistance is designed and built indigenously. This includes a 6.5 T superconducting magnet and a variable temperature sample holder assembly. A superinsulated liquid helium dewar with a low liquid helium boil-off rate is chosen as the low-temperature bath for doing magnetotrans-port measurements. A pair of high-$T_{c}$ superconducting leads for energizing the magnet reduces the liquid helium consumption further and makes it economically beneficial, especially for laboratories with limited budget. The performance of the apparatus is tested over a wide range of temperatures (4.2 to 300 K) and fields up to 6.5 T. Reproducible magnetotransport data are obtained with excellent temperature and field stability.

The transmission efficiency, frequency and amplitude alteration have been measured by a simple technique of coupled oscillators with a frequency gradient and in a system of non-Newtonian fluid in the form of corn-flour slime. The system of coupled oscillators was found to exhibit preferential energy transfer towards the low frequency end with the reverse propagation severely damped. Energy transfer in all directions was damped in the non-Newtonian fluid in comparison with water. Also the damping in non-Newtonian fluids works only after a lower limit for input amplitude. While most of the previous studies focussed on dissipation of energy within shock-absorbing systems, we demonstrate the contribution of re-distribution of energy reaching the output end to achieve shock absorbing.

We deal with the difficulties claimed by the author of [Ann. Phys. 206, 90 (1991)] while solving the Schrödinger equation for the ground states of two-dimensional anharmonic potentials. It is shown that the ground state energy eigenvalues and eigen-functions for the coupled quadratic and quartic potentials can be obtained by making some simple assumptions. Expressions for the energy eigenvalues and the eigenfunctions for the first and second excited states of these systems are also obtained.

A few years ago, Mathur proposed a `fuzzball' conjecture to give a microscopic description of black hole entropy. In the fuzzball scenario, the entropy in a two-charge black hole corresponds to microstates of a two-charge string (brane) system, e.g., a winding fundamental string with momentum modes. The geometry of such a two-charge system is fuzzy near the horizon, and is very difficult to get analytically in general. In this paper, we show a new method to get geometries of two-charge fuzzball. Our method is based on the multipole expansion. We find that the method is powerful enough to get a clean analytic form of metric of the fuzzball with one-momentum mode. It is expected to get multi-mode geometries using this method in the near future.

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Triple heavy flavour baryons are studied using the hypercentral description of the three-body system. The confinement potential is assumed as hypercentral Coulomb plus power potential with power index 𝑝. The ground state ($J^{P} = \dfrac{1}{2}^{+}$ and $\dfrac{3}{2}^{+}$) masses of heavy flavour baryons are computed for different power index, 𝑝 starting from 0.5 to 2.0. The predicted masses are found to attain a saturated value with respect to variation in p beyond the power index $p$ > 1.0. Using the spin-flavour structure of the constituting quarks and by defining effective mass of the confined quarks within the baryons, the magnetic moments are computed with no additional free parameters.

Based on the concept of cold valley in fission and fusion, the radioactive decay of superheavy^280−314116 nuclei was studied taking Coulomb and proximity potentials as the interacting barrier. It is found that the inclusion of proximity potential does not change the position of minima but minima become deeper which agrees with the earlier findings of Gupta and co-workers. In addition to alpha particle minima, the other deepest minima occur for ⁸Be, ^12,14C clusters. In the fission region two deep regions are found each consisting of several comparable minima, the first region centred on ²⁰⁸Pb and the second is around ¹³²Sn. The cluster decay half-lives and other characteristics are computed for various clusters ranging from alpha particle to ⁷⁰Ni. The computed half-lives for alpha decay match with the experimental values and with the values calculated using Viola–Seaborg–Sobiczewski (VSS) systematic. The plots connecting computed 𝑄 values and half-lives against neutron number of daughter nuclei were studied for different clusters and it is found that the next neutron shell closures occur at $N$ = 162, 172 and 184. Isotopic and isobaric mass parabolas are studied for various cluster emissions and minima of parabola indicate neutron shell closure at $N$ = 162, 184 and proton shell closure at $Z$ = 114. Our study shows that $^{276}_{162}$114 is the deformed doubly magic and $^{298}_{184}$114 is the spherical doubly magic nuclei.

The steady-state amplification of light beam during two-wave mixing in photorefractive materials has been analysed in the strong nonlinear regime. The oscillation conditions for unidirectional ring resonator have been studied. The signal beam can be amplified in the presence of material absorption, provided the gain due to the beam coupling is large enough to overcome the cavity losses. Such amplification is responsible for the oscillations. The gain bandwidth is only a few Hz. In spite of such an extremely narrow bandwidth, unidirectional oscillation can be observed easily at any cavity length in ring resonators by using photorefractive crystals as the medium and this can be explained in terms of the photorefractive phase-shift. The presence of such a phase-shift allows the possibility of the non-reciprocal steady-state transfer of energy between the two light beams. Dependence of gain bandwidth on coupling constant, absorption coefficient of the material's cavity length (crystal length) and modulation ratio have also been studied.

A project of ultrafast pulse generation has been presented and demonstrated by utilizing the combined nonlinear effects of stimulated Raman scattering (SRS) and non-degenerate two-photon absorption (TPA) based on silicon nanophotonic chip, in which a continuous wave (CW) and an ultrafast dark pulse are co-propagating in the silicon chip so that the CW will be modulated inversely by the dark pulse during the propagation. As a result, an ultrafast bright pulse is achieved using the technique. Simulation results show that an ultrafast pulse with a pulsewidth (full-width at half-maximum (FWHM)) of about 50 fs is generated at the end of a 5-mm long silicon chip, when the initial conditions, including an input maximum of 0.5 W and FWHM of $\sim 176$ fs for dark pulse, and CW with power of 5 W, are chosen.

By taking into account slight interactions, i.e. spin-spin, spin-other-orbit and orbit-orbit interactions, in addition to spin-orbit interaction, the zero-field splitting of ⁴T₂ state for 3d³ ions at tetragonal symmetry has been studied. The convergence of the approximation perturbation formula of ⁴T₂ state for 3d³ ions at tetragonal symmetry has been investigated, and the contributions to zero-field splitting arising from magnetic interaction and tetragonal crystal field are discussed. It is found that there exists combined mechanism between magnetic interactions and tetragonal crystal field.

We have done a time series analysis of daily average data of solar wind velocity, density and temperature at 1 AU measured by ACE spacecraft for a period of nine years. We have used the raw data without filtering to give a faithful representation of the nonlinear behaviour of the solar wind flow which is a novel one. The sensitivity of the results on filtering is highlighted. The attractor dimension is estimated for every parameter of the solar wind and it is found that they differ substantially. Hence a chaotic picture for the problem from different angles have been obtained. The calculated Kolmogorov entropies and Lyapunov exponents are positive showing evidences that the complex solar wind near the Earth is most likely a deterministic chaotic system.

Half-lives for alpha radioactivity from proton-rich even Pb isotopes in the range $A = 182–202$ have been calculated using the unified fission-like approach. The geometrical shape of the potential barrier is parametrized in terms of a highly versatile, asymmetric and analytically solvable form of potential based on Ginnochio’s potential. Good agreement with the experimental data has been obtained with the variation of just one parameter. Half-lives of three unknown alpha emitters in the neutron-deficient Pb chain (¹⁹⁸Pb, ²⁰⁰Pb and ²⁰⁴Pb) have been predicted. The exact expression for the transmission coefficient has been compared with those obtained from WKB approximation method for symmetric Eckart potential.

Swift heavy ions interact predominantly through inelastic scattering while traversing any polymer medium and produce excited/ionized atoms. Here samples of the polycarbonate Makrofol of approximate thickness 20 𝜇m, spin coated on GaAs substrate were irradiated with 50 MeV Li ion ($+3$ charge state). Build-in modifications due to irradiation were studied using FTIR and XRD characterizations. Considerable changes have been observed in the polymer while varying the fluence from 1E11 ion/cm² to 1E13 ion/cm² Li ions. AFM images of the surface modifications caused by ion irradiation on the polymer are also presented.