Pressure and energy of compressional shocks in two-dimensional Yukawa systems

Fast particles overtaking shock front in two-dimensional Yukawa solids

High-speed particles overtaking the shock front during the propagation of compressional shocks in two-dimensional (2D) Yukawa solids are investigated using molecular dynamical simulations. When the compressional speed is lower, all particles around the shock front are almost accelerated synchronously. However, when the compressional speed is much higher, some particles penetrate the shock front to enter the preshock region. Around the shock front, it is found that the particle velocity profile at the first peak of the dispersive shock wave (DSW) is able to be described using the Gaussian distribution, so that the amplitudes of the DSW can be well characterized. As the compressional speed increases, the particle velocity corresponding to these DSW's amplitudes increase more substantially than the shock front speed. These amplitudes of the DSW are found to be able to predict the occurrence of the fast particles. Combined with the previous study of the DSW's period, it is demonstrated that the properties of the DSW are nearly not affected by the conditions of the 2D Yukawa systems, but only related to the compressional speed.

Reflection and transmission of an incident solitary wave at an interface of a binary complex plasma in a microgravity condition

Theoretical results are given in the present paper, which can well explain the experimental observations performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station about the propagation of a solitary wave across an interface in a binary complex plasma. By using the traditional reductive perturbation method and the continuity conditions of both the electric potential and the momentum at the interface, we obtain the equivalent "initial conditions" for both the transmitted wave and the reflected waves from the incident wave. Then we obtain the numbers of the reflected and the transmitted solitary waves as well as all the wave amplitudes by using the inverse scattering method. The ripples of both reflection and transmission have also been given by using the Fourier series. The number of the reflected and the transmitted solitary waves produced by interface, as well as all the solitary wave amplitudes, depend on the system parameters such as the number density, electric charge, mass of the dust particles, and the effective temperature in both regions. The analytical results agree with observations in the experiments.

Head-on collision of compressional shocks in two-dimensional Yukawa systems

The head-on collision of compressional shocks in two-dimensional dusty plasmas is investigated using both molecular dynamical and Langevin simulations. Two compressional shocks are generated from the inward compressional boundaries in simulations. It is found that, during the collision of shocks, there is a generally existing time delay of shocks τ, which diminishes monotonically with the increasing compressional speed of boundaries, corresponding to the time resolution of the studied system. Dispersive shock waves (DSWs) are generated around the shock front for some conditions. It is also found that the period of the DSW decreases monotonically with the inward compressional speed of boundaries, more substantially than the time delay of shocks τ. When the inward compressional speed of boundaries increases further, the DSWs gradually vanish. We speculate that, for these high compressional speeds of boundaries, the period of the DSW might be reduced to a comparable timescale of the time delay of shocks τ, i.e., the time resolution of our studied system, or even shorter, thus the DSW reasonably vanishes.

Determination of viscosity in shear-induced melting two-dimensional dusty plasmas using Green-Kubo relation

Langevin dynamical simulations of shear-induced melting two-dimensional (2D) dusty plasmas are performed to study the determination of the shear viscosity of this system. It is found that the viscosity calculated from the Green-Kubo relation, after removing the drift motion, well agrees with the viscosity definition, i.e., the ratio of the shear stress to the shear rate in the sheared region, even the shear rate is magnified ten times higher than that in experiments. The behaviors of shear stress and its autocorrelation function of shear-induced melting 2D dusty plasmas are compared with those of uniform liquids at the same temperatures, leading to the conclusion that the Green-Kubo relation is still applicable to determine the viscosity for shear-induced melting dusty plasmas.

Rotating vortices in two-dimensional inhomogeneous strongly coupled dusty plasmas: Shear and spiral density waves

Dusty plasma experiments can be performed quite easily in a strong coupling regime. In our previous work [V. S. Dharodi, S. K. Tiwari, and A. Das, Physics of Plasmas 21, 073705 (2014)]PHPAEN1070-664X10.1063/1.4888882, we numerically explored such plasmas with constant density and observed the transverse shear (TS) waves from the rotating vortex. Laboratory dusty plasmas are good examples of homogeneous plasmas; however, heterogeneity (e.g., density, temperature, and charge) may be due to the existence of voids, different domains with different orientations, presence of external forces like magnetic and/or electric, size or charge imbalance, etc. Here, we examine how the density heterogeneity in dusty plasmas responds to the circularly rotating vortex monopoles, specifically, smooth and sharp cutoff. For this purpose, we have carried out a series of two-dimensional fluid simulations in the framework of the incompressible generalized hydrodynamics fluid model. The rotating vortices are placed at the interface of two incompressible fluids with different densities. The smooth rotating vortex causes two effects: First, the regions are stretched to form the spiral density waves; second, there is a shear in flows which consequently induces the TS waves. The TS waves move slower in the denser side than in the lighter side. The difference in speeds of the waves induces the net flow of the medium towards the lower density side. We notice that the spiral density arms are distinguishable in the early time while later they get smeared out. In sharp flows, the interplay between the TS waves and the vortices of Kelvin-Helmholtz instability distorts the formation of the regular spiral density arms around the rotor.

Experimental determination of shock speed versus exciter speed in a two-dimensional dusty plasma

A shock that is continuously driven by a moving exciter will propagate at a speed that depends on the exciter speed. We obtained this dependence experimentally, in a strongly coupled dusty plasma that was prepared as a single two-dimensional layer of charged microparticles. Attaining this result required an experimental advance, developing a method of driving a shock continuously, which we did using an exciter moving at a constant supersonic speed, analogous to a piston in a cylinder. The resulting compressional pulse was a shock that propagated steadily without weakening, ahead of the moving exciter. We compare our experimental results to an empirical form M_{shock}=1+sM_{exciter}, and to the prediction of a recent simulation.

Universal relationship of compression shocks in two-dimensional Yukawa systems

Using molecular dynamical simulations, compressional shocks in two-dimensional (2D) dusty plasmas are quantitatively investigated under various conditions. A universal relationship between the thermal and the drift velocities after shocks is discovered in 2D Yukawa systems. Using the equation of state of 2D Yukawa liquids, and the obtained pressure from the Rankine-Hugoniot relation, an analytical relation between the thermal and the drift velocities is derived, which well agrees with the discovered universal relationship for various conditions.