The fascinating many-body physics involved in the interaction of a single magnetic impurity with the conduction electrons of its nonmagnetic metallic host is reflected in unconventional phenomena in magnetism, transport properties and the specific heat. Characteristic low-energy excitations, termed the Kondo resonance, are generally believed to be responsible for this striking behaviour. However, in spite of an intense research for over more than 30 years, a direct spectroscopic observation of the Kondo resonance on individual magnetic adatoms withstood experimental efforts hitherto. The development of low-temperature scanning tunneling microscopes (STM) operating under ultrahigh vacuum (UHV) conditions has provided new opportunities for investigating locally the electronic structure at surfaces. At low temperatures, due to the reduced broadening of the Fermi level of the STM tip and the sample, rather high energy resolution (≤ 1 meV) in scanning tunneling spectroscopy (STS) is achievable. Moreover, the absence of diffusion together with the spatial resolution of the STM enables detailed studies of electronic states on and near single adsorbed atoms and other nanoscale structures. Recently, for the first time, two such STS/STM experiments spatially resolved the electronic properties of individual magnetic adatoms displaying the Kondo effect. In particular, the observed Fano lineshape of the Kondo resonance reveals unambiguously the details of the quantum mechanical interference between the localized orbital and the conduction electrons on an atomic length scale [1,2]. This achievement of the detection of individual magnetic atoms with atomic resolution opens new perspectives for probing magnetic nanostructures.

In this paper, following recent results on generalized Vaidya solutions by Wang, we prove that under certain conditions on generalized mass function, strong curvature naked singularities exist in radiation collapse in monopole-Vaidya space-times and also in charged-Vaidya space-times. We thus unify and generalize results of Dwivedi-Joshi and Lake-Zannias. The general case also covers de Sitter-Vaidya space-time recently treated by Wagh-Maharaj with a view to study existence of naked singularities.

We study the characteristic features of certain statistical quantities near critical bifurcations such as onset of chaos, sudden widening and band-merging of chaotic attractor and intermittency in a periodically driven Duffing-van der Pol oscillator. At the onset of chaos the variance of local expansion rate is found to exhibit a self-similar pattern. For all chaotic attractors the variance Σ_n(q) of fluctuations of coarse-grained local expansion rates of nearby orbits has a single peak. However, multiple peaks are found just before and just after the critical bifurcations. On the other hand, Σ_n (q) associated with the coarse-grained state variable is zero far from the bifurcations. The height of the peak of Σ_n(q) is found to increase as the control parameter approached the bifurcation point. It is maximum at the bifurcation point. Power-law variation of maximal Lyapunov exponent and the mean value of the state variablex is observed near sudden widening and intermittency bifurcations while linear variation is seen near band-merging bifurcation. The standard deviation of local Lyapunov exponent λ(X,L) and the local mean valuex(L) of the coordinatex calculated after everyL time steps are found to approach zero in the limitL → ∞ asL^-Β. Β is sensitive to the values of control parameters. Further weak and strong chaos are characterized using the probability distribution of ak-step difference quantity δx_k = x_i+kx_i.

Two sets of nonlinear partial differential equations originating from two different physical situations have been combined and a new set of nonlinear partial differential equations has been formed wherefrom the previous two sets can be obtained as particular cases. One of the two sets of equations was obtained by Yang [1] while discussing the condition of self-duality ofSU(2) gauge fields on Euclidean four-dimensional space. The second one was reported by Charap [2] for the chiral invariant model of pion dynamics under tangential parametrization. Using the same type of ansatz in each case De and Ray [16] and Ray [7] obtained physical solutions of the two sets of equations. Here exact solutions of the combined set of equations with particular values of the coupling constants have been obtained for a similar ansatz. These solutions too are physical in nature.

The chiral perturbation theory has been used to calculate pionic and radiative decays ofb-hadrons. These particles are being studied and their decays have been predicted.

Excitation function and mean projected recoil ranges of nuclei produced in the⁷Li and¹⁶O induced reactions on⁵¹V target were measured by conventional stacked foil and thick-target thick-recoil-catcher technique for bombarding energiesE ≤ 50.0 MeV for⁷Li ions andE ≃ 60.0-96.0 MeV for the¹⁶O ions. The measured recoil ranges are converted to momentum transfer. The momentum transfer information was used to get clues about some aspects of the interaction such as complete and incomplete fusion reaction mechanism which correspond to full and reduced momentum transfer respectively. The measured excitation functions are compared with the calculation based on the statistical model which describes only equilibrium decay of the compound nucleus using the CASCADE code. The comparison of the CASCADE code with the measured excitation functions for the residue radioisotopes⁵¹Cr and⁵⁴Mn for the⁷Li +⁵¹V system indicates the reaction mechanisms is complete fusion of⁷Li with the target nucleus⁵¹V. Similarly the comparison of the CASCADE code with the measured excitation functions of the residue radioisotopes for the system¹⁶O +⁵¹ V indicates that the four reaction mechanisms (i) complete fusion of¹⁶O, (ii) incomplete fusion of¹²C, (iii) incomplete fusion of⁸Be and (iv) incomplete fusion of⁴He respectively with the target might be contributing to reaction cross sections.

A simple derivation, which relates the thermal lens focal length in solid state lasers to pump power and a method for direct estimation of thermal lens focal length, is reported. This method is applicable to any type of stable resonator. The method is used for the measurement of the thermal lens focal length with an accuracy of 8% in an axially pumped microchip laser. The variation of focal length with pump power is also measured.

Extensive theoretical results for the temperature dependence of the static and dynamical structure of undercooled alkali metals using Na and Cs as examples are presented. The static structural properties are obtained from the HMSA integral equations using pair potentials derived from an accurate non-local pscudopotential. The dynamical properties obtained from viscoelastic theory are compared with experiments and the results of memory function formalism. The study indicates that collective density excitations are more dominant in the undercooled region than at their melting points, and that the dynamical properties of Na and Cs exhibit subtle differences in their gross features.

In order to understand the mechanism of optical image storage in photorefractive polyvinyl alcohol (PVA) films, photo-EPR and photoacoustic spectral investigations were carried out on PVA films doped with Cr³⁺ and VO²⁺. The EPR spectrum of Cr³⁺ has shown reduction in intensity onin situ illumination with copper vapor laser (CVL). The decay and recovery of Cr³⁺ signal, with and without CVL illumination respectively, was monitored at different temperatures in 10–300 K region. These were found to obey a double exponential, with one time constant independent of temperature, and the other showing significant temperature dependence. From Τ(T), activation energy for the charge carrier transport in one of the processes was estimated to be 0.016 eV. The PA spectra showed shift towards lower wavelength side on consecutive runs. On the other hand, VO²⁺ doped PVA film has not shown any significant changes in intensity on laser illumination. These observations suggest (i) interaction of PVA matrix with excited Cr³⁺ and (ii) predominant non-radiative relaxation in VO²⁺: PVA system with no change in the oxidation state.