Linear and nonlinear waves in dusty plasmas

Theoretical investigations and numerical simulations are carried out on various types of waves in dusty plasmas, including their linear dispersion relations. Nonlinear dust dynamics that produce DIA shock wave, dust solitons, and compressional pulse are also studied. Two models of dusty plasmas are employed to perform these investigations: one is a multi-fluid model and the other is molecular dynamics.; Using a multi-fluid model, we explore the possibility of resonance between DIAW and DAW. The conditions for the formation of DIA shock wave are studied numerically by applying the parameters of an early UI DIA shock experiment. Our conclusions are: (i) the resonance is possible when electron density is reduced by introducing extremely high dust density; (ii) The DIA shock waves are most likely be observed when the percentage of dust charge is over 72%, which is in reasonable agreement with results of the UI experiment.; The dispersion relation is studied numerically in a 1D MD model. The numerical simulations on dust dynamics show that there are three regimes: linear regime with a pure normal mode, weak nonlinear regime with harmonics of the triggering mode, and strong nonlinear regime with spiky behavior in spectrum. The solitary wave is extensively studied through theoretical investigation and MD simulations, including mutual collision events. The relation between the generation of multi-solitary waves and the spiky pattern in the strong nonlinear dynamical regime is explored.; Under very general conditions, the 2D dispersion equation in the MD model is shown to produce essentially two modes whose wave fronts are orthogonal. A numerical exploration is carried out for one-soliton solution and it is found that shear solitary waves are possible in the direction of 12° ∼ 14° away from the primitive translation vectors for shielding parameters in a range of 0.5 ∼ 1.8.; A recent UI experiment on a compressional pulse is also numerical simulated in 2D MD model. The simulations show that the pulse mainly moves in longitudinal direction with small fluctuations in vertical direction. The pulse shapes in our numerical simulations were depicted by every 0.1 seconds separation and compared with experimental results.