A nuclear mass formula is derived using a few extremely reasonable assumptions within an independent particle model with residual interactions. The parameters in the mass formula are determined by a least square fit to the experimental energies. The mass formula is further used to study Garvey-Kelson and Franzini-Radicati mass relationships.

Simple considerations regarding the Hamiltonian and the ground state wavefunctions of Λ-hypernuclei are used to derive several mass formulae. The parameters that occur in the mass formulae are determined by fitting the experimental binding energies. Information regarding the various interactions in hypernuclal is deduced from the values of these parameters. The ‘best’ mass formula is further used to predict energies of other light hypernuclei. Relationship between binding energies are also suggested and checked with observed data.

A new method, that systematically combines results of random matrix theory and the usual statistical mechanics, is described to study thermodynamic properties of disordered systems. Two exactly solvable models are examined in this formulation to illustrate the usefulness of this method for systems described by random as well as non-random Hamiltonian.

Fluctuation properties of the regular and irregular energy levels for the Hénon-Heiles Hamiltonian are examined. The spacing distributions and the calculated values of the Δ₃-statistic show that there is no difference in the short range correlation properties of these spectra. Remarkably, the Δ₃ values agree with the results of random matrix theory.

The nuclear shell model is (over)viewed with examples from its early phase to its current status.

A model of electrical activity of human brain considered as a complex dynamical system is given based on the EEG time series. The model fits the data remarkably well. The predictive ability of the model is limited to a few time steps as expected for a chaotic time series.

A dynamic approach, based on deformed Hartree-Fock solution of a nucleus, is suggested for obtaining correlated identical nucleon pair wave function for neutrons and protons. Expressions for single pair energies and two pair interaction matrix elements amongst the neutron and proton pairs in the microscopic fermion basis are presented. These matrix elements define the IBM-2 Hamiltonian through Marumori mapping. The entire procedure is illustrated by obtaining the IBM-2 spectra of²⁰Ne,⁴⁴Ti,⁶⁰Zn and⁹⁴Mo and comparing them with shell model (SM) and/or experimental results. The Yrast levels given by our calculations match well with those of the SM and the experimental results for all the four nuclei, while the non-Yrast levels do not barring the case of⁹⁴Mo. This is due to the loss of isospin symmetry for light nuclei in IBM-2. These results are discussed in detail.

The role of filamentation instability of quark-gluon plasma, in explaining collective phenomena in relativistic heavy-ion collisions, has been analyzed. Using equations of SU(2) two fluid color hydrodynamics it is shown that this instability can significantly enhance nuclear stopping and might contribute to collective sideward flows.

Screening of a moving infinite color sheet source is examined in a quark plasma at finite temperature. The classical chromohydrodynamic equations for quarks are integrated, to obtain profiles for quark current density, which in turn are used to solve the SU(2) Yang-Mills equations numerically. This provides a classical but non-perturbative treatment for the screening of a moving source in quark plasma.

The results show two interesting features. We observe that if the test source is at rest the screening does not depend on the color dynamics and the behavior is very similar to that in Coulomb plasma. When the test source is moving with non-relativistic velocity the non-abelian features manifest themselves by weakening the screening and also by exhibiting an oscillatory profile with distance.

A simple dynamic procedure, based on the deformed Hartree-Fock solution of a nucleus, is presented to construct the IBM operators in microscopic basis. The parameters of these operators are evaluated by establishing a Marumori mapping from the truncated shell model space onto the boson space. The transitions from spherical to axial-rotor shape observed in the low-lying levels ofeven^96–108Mo and^146–154Sm isotopes are reproduced qualitatively by applying this procedure with a fixed set of fermion input parameters to each chain. Variation of a few parameters in fermion space leads to quantitative agreement.