A strongly coupled dusty plasma containing strongly correlated negatively charged dust grains and weakly correlated (Maxwellian) electrons and ions has been considered. The effects of polarization force (which arises due to the interaction between thermal ions and highly negatively charged dust grains) and effective dust temperature (which arises from the electrostatic interactions among highly negatively charged dust and from the dust thermal pressure) on the dust-acoustic (DA) solitary and shock waves propagating in such a strongly coupled dusty plasma are taken into account. The DA solitary and shock waves are found to exist with negative potential only. It has been shown that the strong correlation among the charged dust grains is a source of dissipation and is responsible for the formation of the DA shock waves. It has also been shown that the effects of polarization force and effective dust-temperature significantly modify the basic features (e.g., amplitude, width, and speed) of the DA solitary and shock waves. It has been suggested that a laboratory experiment be performed to test the theory presented in this work.

The properties of nonplanar (cylindrical and spherical) quantum dust ion-acoustic (QDIA) solitary waves in an unmagnetized quantum dusty plasma, whose constituents are inertial ions, Fermi electrons with quantum effect, and negatively charged immobile dust particles, are investigated by deriving the modified Gardner (MG) equation. The reductive perturbation method is employed to derive the MG equation, and the basic features of nonplanar QDIA Gardner solitons (GSs) are analyzed. It has been found that the basic characteristics of GSs, which are shown to exist for the value of Zdnd0/ni0 around 2/3 (where Zd is the number of electrons residing on the dust grain surface, and nd0 and ni0 are, respectively, dust and ion number density at equilibrium), are different from those of the Korteweg-de Vries solitons, which do not exist for the value of Zdnd0/ni0 around 2/3. It is also seen that the properties of nonplanar QDIA GSs are significantly different from those of planar ones.

A molecular dynamics simulation of ion flow past dust grains is used to investigate the interaction between a pair of charged dust particles and streaming ions. The charging and dynamics of the grains are coupled and derived from the ion–dust interactions, allowing for detailed analysis of the ion wakefield structure and wakefield-mediated interaction as the dust particles change position. When a downstream grain oscillates vertically within the wake, it decharges by up to 30% as it approaches the upstream grain and then recharges as it recedes. There is an apparent hysteresis in charging depending on whether the grain is approaching or receding from a region of higher ion density. Maps of the ion-mediated dust–dust interaction force show that the radial extent of the wake region, which provides an attractive restoring force on the downstream particle, increases as the ion flow velocity decreases, though the restoring effect becomes weaker. As also shown in recent numerical results, there is no net attractive vertical force between the two grains. Instead, the reduced ion drag on the downstream particle allows it to “draft” in the wakefield of the upstream particle.

Time-dependent cylindrical and spherical dust-acoustic (DA) solitary and shock waves propagating in a strongly coupled dusty plasma in the presence of polarization force (which arises due to the interaction between thermal ions and highly negatively charged dust grains) are investigated. It is shown that cylindrical and spherical DA solitary and shock waves exist with negative potential, and that the strong correlation among the charged dust grains is a source of dissipation, and is responsible for the formation of cylindrical or spherical DA shock structures. It is also shown that the effects of polarization force significantly modify the basic features (e.g. amplitude, width, and speed) of cylindrical or spherical DA solitary or shock structures. The implications of our results in laboratory experiments are briefly discussed.

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