The filamentary structure of the magnetic fields as well as the coherent radiations that emanate from a sunspot are explained considering solar burst as a non-equilibrium process. Methods of irreversible statistical mechanics have been applied to the problem of an electron gas in a constant magnetic field to explain the above features. We have obtained the non-equilibrium distribution function in the self-consistent field approximation. The dielectric function, we obtained, is a function of time, besides being a function of frequency and wavevector. We have thus taken the non-linearity of the system as well. This theory explains many features of stria bursts, chain bursts as well as the type III bursts. This also accounts for the bunching of the magnetic field lines as a consequence of quantisation of flux in the Landau sense.

In this paper we have made a spectral analysis study of matter distribution in the asteroidal belt. We have Fourier analysed this distribution and obtained the autocorrelation and power spectrum, and have identified the ratios from the resonance theory. We have shown that the Kirkwood gaps cannot be satisfactorily interpreted as due to mere resonance between the asteroid and Jupiter orbital motions. We propose that they may be regarded as a consequence of density waves generated in the gas dise in the ecliptic plane in the neighbourhood of the Sun. We have also shown that the process is non-Marcovian and hence cannot be subjected to a hydrodynamical analysis.

We have developed a kinematical theory for the asteroidal belt and Kirkwood gaps from the point of view of stellar dynamics. We have generated the potential that would produce these gaps and have made a spectral analysis study. We have shown that these gaps could be due to spiral tubes of matter in the ecliptic plane as a consequence of differential rotation and spatial interference of density waves. We have also shown that this mechanism could account for depletion of matter from this region.

An electron gas in crossed electric and magnetic fields of arbitrary strength is considered in the framework of nonequilibrium statistical mechanics. It is known that more than one independent frequency existing in a system, which are of comparable magnitude, can generate coherent synergic radiation. In the present system three independent frequencies exist: viz the synchrotron frequency due to the magnetic field, the hopping frequency due to the electric field, and the plasma frequency. It is shown that all these can combine to generate a new synergic coherent radiation. The results also show the possibility of interpreting the quantum nature of Hall conductance as due to density function alone. Besides these, the solution admits the Schubnikov-de Haas oscillation of the electrical conductivity due to change in the fields.

A microscopic many body correlation dynamics has been worked out for a 3DEG in degenerate state far removed from equilibrium, placed in crossed electric and magnetic fields of arbitrary strength. It is shown that linear electric field case gives only σ₁₂, even though the response function retains all the nonlinear effects in the system. The nonanalytic behaviour of the response function is explicitly shown. The quantisation of Hall current comes out as a direct consequence both for odd and even filling factors, and this is due to an exact evaluation of the dynamics in the self consistent field case. Radiated energy for this system is also calculated. A comparison of the present results with those obtained based on Kubo formalism has brought out the incompatability of using external fields as ordering parameters in any expansion scheme. A further new result is the nonanalytic property of the response function obtained in the present formulation.

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.