Chemical potential and internal energy of a noninteracting Fermi gas at low temperature are evaluated using the Sommerfeld method in the fractional-dimensional space. When temperature increases, the chemical potential decreases below the Fermi energy for any dimension equal to 2 and above due to the small entropy, while it increases above the Fermi energy for dimensions below 2 as a result of high entropy. The ranges of validity of the truncated series expansions of these quantities are extended from low to intermediate temperature regime as well as from high to relatively low density regime by using the Pad ́e approximant technique.

We discuss the emergence and destruction of complex, critical and completely chaotic attractors in a nonlinear system when subjected to a small parametric perturbation in trigonometric, hyperbolic or noise function forms. For this purpose, a hybrid optical bistable system, which is a nonlinear physical system, has been chosen for investigation. We show that the emergence of new attractors is responsible for transients in many trajectories obeying power-law decay. The effect of perturbation on certain critical bifurcations such as period-2, onset of chaos, chaotic attractor with less complexity etc., has been studied and characterized using certain statistical features. Further, the effect of Gaussian noise with other types of perturbation has also been studied.

An irrational trial equation method was proposed to solve nonlinear differential equations. By this method, a number of exact travelling wave solutions to the Burgers–KdV equation and the dissipative double sine-Gordon equation were obtained. A more general irrational trial equation method was discussed, and many exact solutions to the Fujimoto–Watanabe equation were given.

We used variationally improved perturbation theory (VIPT) in calculating the slope and curvature of Isgur–Wise (I–W) function with the Cornell potential $− \dfrac{4\alpha_{s}}{3r} br + c$ instead of the usual stationary state perturbation theory as done earlier. We used $−(4\alpha_{s} /3r)$, i.e. the Coulombic potential, as the parent and the linear one, i.e. $br +c$ as the perturbed potential in the theory and calculated the slope and curvature of Isgur–Wise function including three states in the summation involved in the first-order correction to wave function in the method.

In several scenarios of beyond Standard Model physics a new heavy resonance is invoked which may decay preferentially, to a pair of taus. Identification of the decay of Standard Model $Z$ resonance to tau pairs at LHC via subsequent decays of the taus to leptons as well as hadrons is the first step towards the discovery. A method has been suggested to discriminate $Z$ to tau pair to electron $+$ muon final state against various backgrounds, for early phase of 14 TeV LHC.

The influence of the isovector coupling channel on the central depression parameter and the central value of the charge density distribution in heavy spherical nuclei was studied. The isovector coupling channel leads to about 50% increase of the central depression parameter, and weakens the dependency of both central depression parameter and central density on the asymmetry, impressively contributing to the semibubble form of the charge density distribution in heavy nuclei, and increasing the probability of larger nuclei with higher proton numbers and higher neutron-to-proton ratios stable.

Mass attenuation coefficients ($\mu/\rho$) for Zr, Nb, Mo and Pd elements around their $K$-edges are measured at 14 energies in the range 15.744–28.564 keV using secondary excitation from thin Zr, Nb, Mo, Rh, Pd, Cd and Sn foils. The measurements were carried out at the $K_{\alpha} and $K_{\beta}$ energy values of the target elements by two techniques: (1) Proton-induced X-ray emission (PIXE) and (2) $^{241}$Am (300 mCi) source. In PIXE, 2 MeV proton-excited X-rays were detected by a Si(Li) detector. In the second case, X-rays excited by 59.54 keV photons from the targets were counted by an HPGe detector under a narrow beam good geometry set-up with sufficient shielding. The results are consistent with theoretical values derived from the XCOM package and indicate that the PIXE data have better statistical accuracy.

An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions. Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process, however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical state.

The design of a medium energy beam transport (MEBT) line comprising of a re-buncher and four quadrupoles, two upstream and the other two downstream of the re-buncher, has been presented. The design was done to ensure almost 100% transport of heavy-ion beams of about 99 keV/u energy from RFQ having a $q/A$ not less than 1/14 through the re-buncher and then through IH Linac of about 0.6 m length in which beam would be accelerated to about 185 keV/u. The re-buncher has been designed to operate at 37.8 MHz, the resonating frequency of both the RFQ and the IH Linac. The entire beam line has been installed and recently O$^{5+}$ beam from RFQ has been transported through the re-buncher and subsequently accelerated in the IH Linac successfully.

The propagation equation for a single- and a few-cycle pulses was derived in a cubic nonlinear medium including the Raman response. Using this equation, the propagation characteristics of a single- and a 4-cycle pulse, at 0.8 $\mu$m wavelength, were studied numerically in one spatial dimension. It was shown that Raman term does influence the propagation characteristics of a single- as well as a few-cycle pulses by counteracting the self-steepening effect.

In this paper, we report the electron irradiation effects on the properties of an organic NLO single crystal of 4-amino-5-mercapto-3-[1-(4-isobutylphenyl)ethyl]-1,2,4-triazole. The crystal was irradiated with electron beam of different doses and was characterized by powder XRD, UV–Vis, FTIR, DSC, microhardness and SHG measurements. In XRD, the peaks are shifted due to irradiation. The SHG efficiency has been found to enhance rapidly with irradiation. The investigation of the influence of electron irradiation on the surface morphology of the grown crystal reveals the formation of craters on the surface. The laser damage threshold remains constant as the dose rate increases whereas refractive index increases after irradiation.

Detailed classical molecular dynamics simulation of transport coefficients and collision frequencies at high densities in rare gases are presented in this paper with a view to investigate the likely cause of discrepancy between theory and experiments. The results, when compared with experiments, showed an underestimation of the viscosity calculated through the Green–Kubo formalism, but the results are in agreement with some other calculations performed by other groups. The origin of the underestimation was considered in the present work. Analyses of the transport coefficients showed a very high collision frequency which suggested that an atom might spend much less time in the neighbourhood of the fields of force of another atom. The distribution of atoms in the systems adjusts itself to a nearly Maxwellian type that resulted in a locally and temporarily slowly varying temperature. We showed that during collision, the time spent by an atom in the fields of force of other atoms is so small compared with its relaxation time, leading to a possible reduction in local velocity autocorrelation between atoms.

The synthesis of materials and the studies of crystal structure and $^{57}$Fe Mössbauer effect were performed for Tb_0.27Dy_0.73 (Fe$_{1−x}$Co$_{x}$)₂ intermetallics. Terfenol-D (Tb_0.27Dy_0.73Fe₂) is the starting compound of this Fe/Co-substituted series. X-ray measurements showed evidence of a pure cubic Laves phase C15, MgCu₂-type, and unit cell parameters were determined across the series. A Co substitution introduced local area, at sub-nanoscale, with random Fe/Co neighbourhoods of the $^{57}$Fe atoms.

Mössbauer effect spectra for the Tb_0.27Dy_0.73 (Fe$_{1−x}$Co$_{x}$)₂ series at room temperature are composed of a number of locally originated subspectra due to the random distribution of Fe and Co atoms in the transition metal sublattice, and due to [1 1 1] an easy axis of magnetization. Isomer shift, magnetic hyperfine field and quadrupole interaction parameter were obtained from the spectra, both for the local area and for the bulk sample.

As a result of Fe/Co substitution, a Slater–Pauling-type curve for the average magnetic hyperfine field vs. Co content was observed. It was found that the magnetic hyperfine fields corresponding to the local area also create a dependence of the Slater–Pauling-type vs. Co contribution in the Fe/Co neighbourhoods.

We discuss how phase-transitions may be detected in computationally hard problems in the context of anytime algorithms. Treating the computational time, value and utility functions involved in the search results in analogy with quantities in statistical physics, we indicate how the onset of a computationally hard regime can be detected and the transit to higher quality solutions be quantified by an appropriate response function. The existence of a dynamical critical exponent is shown, enabling one to predict the onset of critical slowing down, rather than finding it after the event, in the specific case of a travelling salesman problem (TSP). This can be used as a means of improving efficiency and speed in searches, and avoiding needless computations.