We report a theoretical investigation of the dust lattice (DL) mode in two-dimensional Yukawa crystals in the presence of asymmetric ion flow and an external magnetic field perpendicular to the crystal plane. Two mutually perpendicular modes are found to be coupled due to Lorentz force. Interaction among the dust grains along the vertical direction of ion flow is strongly affected due to the formation of an ion wake. This causes anisotropy in interaction strength along two mutually perpendicular directions. Both hybrid modes are studied as characteristics of different ion flow speeds and magnetic field strengths. The study shows a fluctuation in DL mode frequency driven by the strength of the particle-wake interaction. The effect of ion flow on polarization of the hybrid wave amplitudes is discussed in detail. Results show a possible mechanism of anomalous phase transition in dusty plasma.

A systematic theoretical investigation has been carried out on the role of dust charging dynamics on the nature and stability of DIA (Dust Ion Acoustic) mode in complex plasma. The study has been made for both linear and non-linear scale regime of DIA mode. The observed results have been characterized in terms of background plasma responses towards dust surface responsible for dust charge fluctuation, invoking important dusty plasma parameters, especially the ion flow speed and dust size. The linear analyses confirm the nature of instability in DIA mode in presence of dust charge fluctuation. The instability shows a damping of DIA mode in subsonic flow regime followed by a gradual growth in instability in supersonic limit of ion flow. The strength of non-linearity and their existence domain is found to be driven by different dusty plasma parameters. As dust is ubiquitous in interstellar medium with plasma background, the study also addresses the possible effect of dust charging dynamics in gravito-electrostatic characterization and the stability of dust molecular clouds especially in proto-planetary disc. The observations are influential and interesting towards the understanding of dust settling mechanism and formation of dust environments in different regions in space.

Mechanism among dust grains immersed in plasma has been reported theoretically in presence of asymmetric ion flow and dynamical charging of dust grains. The ion flow induced particle-wake interaction in addition to repulsive Yukawa type of interaction found to play a significant role in tuning the coupling strength between charged grains and hence the vibrational mode. The transition in coupling strength is obtained as a characteristic of ion flow speed and grain size. The results show a damping in strength of interaction in presence of dynamical charging of dust. The type of interaction shows a mixed phase of Wake-Yukawa in subsonic regime and highly Yukawa dominating phase in supersonic regime of ion flow. The results are significant for understanding the thermodynamic properties and the phase behavior of colloidal systems and nano-crystals.