Charge on the dust in the plasma.

The grain in the plasma gets charged until the net plasma flux to the grain surface vanishes. In the absence of any analytical formula, this ambipolar condition is utilized to compute the grain charge indirectly. The present work proposes an approximate analytical expression for the grain charge that is exact in the asymptotic limit and in which the relative error between analytical and numerically computed solutions is less than 3%. Using this formula, we show that, much like the plasma sheath, the Bohm criterion is satisfied near the dust surface.

Protein flexibility prediction by an all-atom mean-field statistical theory.

We extended a mean-field model to proteins with all atomic detail. The all-atom mean-field model was used to calculate the dynamic and thermodynamic properties of a three-helix bundle fragment of Staphylococcal protein A (Protein Data Bank [PDB] ID 1BDD) and alpha-spectrin SH3 domain protein (PDB ID 1SHG). We show that a model with all-atomic detail provides a significantly more accurate prediction of flexibility of residues in proteins than does a coarse-grained residue-level model. The accuracy of flexibility prediction is further confirmed by application of the method to 18 additional proteins with the largest size of 224 residues.

Thermodynamics of a dusty plasma.

In the present work, we develop the thermodynamics of a dusty plasma and give an equation of state for two cases: (a) when the dust forms a stationary background and the charge on the grain does not vary and (b) when the dust charge fluctuates either due to the fluctuations in the electron and ion number densities or due to the dust density variation. Application of the results to the various space plasma situations has been indicated.

Electrostatic interaction in dusty plasma.

Two modifications of the standard description of electrostatic interaction in a dusty plasma are emphasized. First, the Coulomb-type potential profile is not applicable at very short distances around a dust grain, due to the polarization of the charge on the grain, i.e., the image charge effect, and, second, at larger distances, the standard Debye-Hückel potential screening is modified due to nonlinear corrections in the expanded Boltzmann distribution for plasma particles.

Effects of dust charge fluctuations on current-driven dust-ion-acoustic waves.

The effects of fluctuating grain charge on current-driven dust-ion-acoustic modes are investigated in the presence of various physical parameters which are varied in order to describe the behavior of the mode in detail. Variation of the charge clearly influences the ion-acoustic mode by changing of its frequency and growth rate. We report here the existence of a dust charge fluctuation mode in the system, and it is shown that the mode is unstable for a negative charge on the dust per unit volume not exceeding some critical value.

Kinetic theory of Jeans instability of a dusty plasma.

A kinetic theory of the Jeans instability of a dusty plasma has been developed in the present work. The effect of grain charge fluctuations due to the attachment of electrons and ions to the grain surface has been considered in the framework of Krook's collisional model. We demonstrate that the grain charge fluctuations alter the growth rate of the gravitational collapse of the dusty plasma. The Jeans length has been derived under limiting cases, and its dependence on the attachment frequency is shown. In the absence of gravity, we see that the damping rate of the dust acoustic mode is proportional to the electron-dust collision frequency.