The problem of thermal instability, having bearing on the formation of astrophysical condensations, is investigated for a hydromagnetic fluid obeying generalized Ohm’s law, both for self-gravitating and nongravitating configurations. Effects of finite Larmor frequency, resistivity, and finite plasma frequency on the stability of the system are studied and the condition of instabilities are derived for a temperature-dependent and density-dependent heat-loss function. It is found that the condition of instability for propagation parallel to the ambient magnetic field is independent of finite resistivity, Hall current, and electron inertia effects and also of the magnetic field strength. For transverse propagation, however, the instability criterion involves the field strength, resistivity, and electron inertia terms. The Hall current is found to modify the growth rates for generally inclined propagation only. Both monotonically unstable and overstable modes of instability arise in the system depending on the dependence of the heat-loss function on the local density and temperature.

The influence of toroidal sheared equilibrium flows on the nonlinear evolution of classical and neoclassical tearing modes is studied through numerical solutions of a set of reduced generalized MHD equations that include viscous force effects based on neoclassical closures. In general, differential flow is found to have a strong stabilizing influence leading to lower saturated island widths for the classical tearing mode and reduced growth rates for the neoclassical mode. Velocity shear, on the other hand, is seen to make a destabilizing contribution.

We present a modelling and analysis of the COVID-19 outbreak in India with an emphasis on the socio-economic composition, based on the progress of the pandemic (during its first phase-from March to August 2020) in 11 federal states where the outbreak is the largest in terms of the total number of infectives. Our model is based on the susceptible-exposedinfectives-removed (SEIR) model, including an asymptomatic transmission rate, time-dependent incubation period and time-dependent transmission rate. We carry out the analysis with the available disease data up to the end of August 2020, with a projection of 42 days into the months of September and October 2020, based on the past data. Overall, we have presented a projection up to 351 days (till February 2021) for India and we have found that our model is able to predict correctly the first phase of the pandemic in India with correct projections of the peak of the pandemic as well as daily new infections. We also find the existence of a critical day, signifying a sudden shift in the transmission pattern of the disease, with interesting relation of the behaviour of the pandemic with demographic and socio-economic parameters. Towards the end, we have modelled the available data with the help of logistic equations and compare this with our model. The results of this work can be used as a future guide to follow in case of similar pandemics in developing countries.

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A new hybrid-particle-in-cell (PIC)-Monte Carlo Collision (h-PIC-MCC) algorithm is presented here. The code correctly simulates the damping of ion acoustic wave due to dust charge fluctuation in a dusty plasma along with other kinetic effects such as Landau damping. In the model, on event of a collision between a charged particle and a dust particle, a randomised probability determines whether the charged particle is absorbed by the dust with the collision cross section being determined dynamically by the overall interaction scenario. We find that this method is versatile enough as it can also include the size and mass distribution for the dust particles, in addition to the charged species dynamics. As such, it can be adopted to study numerous phenomena that occur in diverse dusty plasma environments. We believe that the damping of the ion acoustic wave through dust charge fluctuation is being demonstrated, for the first time, with a PIC code, in this work.