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.

The dimensional reduction of eleven dimensional supergravity is discussed. It is shown that there is no dimensional reduction onto Robertson-Walker space with the asymmetric tensorF giving a realistic fluid. Furthermore it is shown that the ansatz’s for the scale factorR:R=atⁿ, R=a exp (btⁿ), andR=aZⁿ, there is no dimensional reduction except the known example of the Freund-Rubin-Englert solution.

The quantisation of a charged scalar field in an externally specified electromagnetic field, described by the vector potentialA_i=∂_if withf(t,r,θ,z)=Bθ is discussed. The electromagnetic field is zero everywhere except at the origin; a singular magnetic field (Aharonov-Bohm field) exists at the origin. The vacuum polarization around such a magnetic field is computed and the non-local behaviour is discussed.

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.

We construct a closed form expression for the off-shell Jost function for scattering by the Coulomb-distorted Graz separable potential and express it in the ‘maximal reduced form’. Our result is particularly suitable for numerical computation. We present a case study in support of this and examine the role of Coulomb interaction in thep — p half-shell scattering in the¹S₀ channel.

The integro-differential equation in two variables for a many boson system has been solved by expanding its solution in the complete set of Jacobi polynomials and subsequent projection. This results in a system of coupled differential equations. This has been solved for the triton. The integrals in the potential matrix elements can be done analyticaly for potentials having Gaussian type terms. Calculated binding energy for several simple potentials agree closely with those calculated by other methods.

We investigate the change in the calculated value of asymptotic normalization constant (ANC) by the hyperspherical harmonics expansion method with the inclusion of three nucleon force (3BF) in addition to two nucleon force. We see that ANC does not change very much with the inclusion of 3BF indicating that the 3BF does not alter the asymptotic behaviours of HHE wavefunction significantly.

The binary encounter approximation has been used for calculations of electron impact single ionization cross-sections for F, Cl, Br and I and double ionization cross-sections for Br and I. Contributions of ionization from inner shells have also been included in the calculations. Hartree-Fock momentum distribution has been used for the bound electron as far as possible. The results have been found to be in satisfactory agreement with experimental observations.

Using multifractal analysis we study extended, self-similar and non-self-similar type of wave functions in the Fibonacci model. Extended states arising due to commutation of transfer matrices for certain blocks of atoms in quasiperiodic systems are shown to have the same signature as the Bloch states in terms of the singularity spectrum withf(α)=α=1. Numerically, however, the extended states show a typical multifractal behaviour for finite chain lengths. Finite size scaling corrections yield results consistent with that obtained analytically. The self-similar states at the band edges show a multifractal behaviour and they are energy dependent in the case of blocks of atoms arranged in a Fibonacci sequence. For non-self-similar states we obtain a non-monotonic behaviour off(α) as a function of the chain length. We also show that in cases where extended states exist, the cross-over from extended to non-self-similar states in gradual.