The dispersion relations for three principal wave modes sustained in two-dimensional (2D) plasma crystals are derived taking into account particle-wake interactions. The rigorous analysis of the mode coupling shows that if the normalized frequency of the vertical confinement is below a certain critical value, then resonance coupling between the longitudinal in-plane mode and out-of-plane mode sets in. This results in the emergence of a hybrid mode and drives the mode-coupling instability. The universal dependence of the critical confinement frequency on plasma parameters is calculated, which allows us to specify the conditions when stable 2D plasma crystals can be formed in experiments.

The effect of the polarization force acting on the grains in a nonuniform plasma background on the propagation of low-frequency waves in complex (dusty) plasmas is analyzed. It is shown that polarization interaction leads to a renormalization (decrease) of the dust acoustic phase velocity. The effect becomes more pronounced as the grain size increases. Finally, there is a critical grain size above which the dust acoustic waves cannot propagate, but aperiodic (nonpropagating) perturbations form instead.

The heat transport in a two-dimensional complex (dusty) plasma undergoing a phase transition was studied experimentally. A single layer of highly charged polymer microspheres was suspended in a plasma sheath. A part of this lattice was heated by two counterpropagating focused laser beams that moved rapidly around in the lattice and provided short intense random kicks to the particles. Above a threshold, the lattice locally melted. The spatial profiles of the particle kinetic temperature were analyzed to find a thermal conductivity, which did not depend on temperature.

Dust lattice (DL) wave modes in a one-dimensional plasma crystal suspended in the plasma sheath are studied. The ion flow in the sheath introduces an anisotropy, in particular "ion wakes" below the crystal particles. This leads to two types of transverse wave mode. It is shown that the "horizontal transverse mode" remains independent, but the "vertical transverse mode" and the longitudinal mode are coupled due to the particle-wake interaction. The coupling can drive an instability of the modes close to the point where their branches intersect. In addition, the particle-wake interaction might decrease the frequencies of the DL modes considerably.

Momentum transfer in complex plasmas (systems consisting of ions, electrons, neutrals, and charged macroscopic grains) is investigated assuming an interaction potential between the charged species of the screened Coulomb (Yukawa) type. Momentum transfer cross sections and rates are derived. Applications of the results are discussed; in particular, we classify the possible states of complex plasmas in terms of the momentum transfer due to grain-grain collisions and its competition with that due to interaction with the surrounding medium. The resulting phase diagrams are presented.