In the present work, the radiative condensation instability is investigated in the presence of dust charge fluctuations. We find that the charge variability of the grain reduces the growth rate of radiative mode only for fluctuation wavelength smaller or of the order of the Debye length and this reduction is not very large. Far from the Debye sphere, radiative mode can damp due to thermal conduction of electrons and ions

The dynamics of a self-gravitating unmagnetized, inhomogeneous, streaming dusty plasma is studied in the present work. The presence of the shear flow causes the coupling between gravitational and electrostatic forces. In the absence of self-gravity, the fluctuations in the plasma may grow at the expense of the density inhomogeneity and for certain wavelengths, such an unstable mode may dominate the usual streaming instability. However, in the presence of self-gravity, the plasma inhomogeneity causes an overlap between Jeans and streaming modes and collapse of the grain will continue at all wavelengths.

The formation of the sheath in a dusty plasma is investigated. The Bohm criterion is derived for two different cases: (a) when electrons are in thermodynamic equilibrium and dust grains provide the immobile, stationary background and (b) when both electrons and ions are in thermodynamic equilibrium and dust grains are moving. In the first case, Bohm criterion gets modified due to the fluctuation of the charge on the grain surface. In the second case, the collisional and Coulombic drag play important role in determining the Bohm criterion.

First-principles calculations were performed to study the elastic stiffness constants ($C_{ij}$) and Debye temperature ($\theta_D$) of wurzite (wz) AlN and GaN binary semiconductors at high pressure. The lattice constants were calculated from the optimized structure of these materials. The band gaps were calculated at 𝛤 point using local density approximation (LDA) approach. The unit cell volume, lattice parameters, $c/a$, internal parameter (𝑢), elastic constant ($C_{ij}$), Debye temperature ($\theta_D$), Hubbard parameter (𝑈) and band gap ($E_g$) were studied under different pressures. The bulk modulus ($B_0$), reduced bulk modulus ($B'_0$) and Poisson ratio ($\vee$) were also calculated. The calculated values of these parameters are in fair agreement with the available experimental and reported values.