A series of numerical simulations is presented, based on a recurrence-free Vlasov kinetic model using kinetic phase point trajectories. All plasma components are modeled kinetically via a Vlasov evolution equation, then coupled through Poisson's equation. The dynamics of ion acoustic waves in an electron-ion and in a dusty (electron-ion-dust) plasma configuration are investigated, focusing on wave decay due to Landau damping and, in particular, on the parametric dependence of the damping rate on the dust concentration and on the electron-to-ion temperature ratio. In the absence of dust, the occurrence of damping was observed, as expected, and its dependence to the relative magnitude of the electron vs ion temperature(s) was investigated. When present, the dust component influences the charge balance, enabling dust-ion acoustic waves to survive Landau damping even in the extreme regime where T e^Ti . The Landau damping rate is shown to be minimized for a strong dust concentration or=and for a high value of the electron-to-ion temperature ratio. Our results confirm earlier theoretical considerations and contribute to the interpretation of experimental observations of dust-ion acoustic wave characteristics.

The quantity and quality of scientific output of the topmost 50 countries in the four basic sciences (agricultural & biological sciences, chemistry, mathematics, and physics & astronomy) are studied in the period of the recent 12 years (1996 -2007). In order to rank the countries, a novel two-dimensional method is proposed, which is inspired by the H-index and other methods based on quality and quantity measures. The countries data are represented in a "quantity-quality diagram", and partitioned by a conventional statistical algorithm (k-means), into three clusters, members of which are rather the same in all of the basic sciences. The results offer a new perspective on the global positions of countries with regards to their scientific output.

The overtaking collisions of ion-acoustic solitons (IASs) in presence of trapping effects of electrons are studied based on a fully kinetic simulation approach. The method is able to provide all the kinetic details of the process alongside the fluid-level quantities self consistently. Solitons are produced naturally by utilizing the chain formation phenomenon, then are arranged in a new simulation box to test different scenarios of overtaking collisions. Three achievements are reported here. Firstly, simulations prove the long-time life span of the ion-acoustic solitons in the presence of trapping effect of electrons (kinetic effects), which serves as the benchmark of the simulation code. Secondly, their stability against overtaking mutual collisions is established by creating collisions between solitons with different number and shapes of trapped electrons, i.e. different trapping parameter. Finally, details of solitons during collisions for both ions and electrons are provided on both fluid and kinetic levels. These results show that on the kinetic level, trapped electron population accompanying each of the solitons are exchanged between the solitons during the collision. Furthermore, the behavior of electron holes accompanying solitons contradicts the theory about the electron holes interaction developed based on kinetic theory. They also show behaviors much different from other electron holes witnessed in processes such as nonlinear Landau damping (Bernstein-Greene-Kruskal -BGKmodes) or beam-plasma interaction (like two-beam instability).

The nonlinear fluid theory developed by Schamel suggests a modified KdV equation to describe the temporal evolution of ion acoustic (IA) solitons in the presence of trapped electrons. The validity of this theory is studied here by verifying solitons' main characteristic, i.e., stability against successive mutual collisions. We have employed a kinetic model as a more comprehensive theory than the fluid one, and utilized a fully kinetic simulation approach (both ions and electrons are treated based on the Vlasov equation). In the simulation approach, these solitons are excited self-consistently by employing the nonlinear process of IA solitons formation from an initial density perturbation (IDP). The effect of the size of IDPs on the chain formation is proved by the simulation code as a benchmark test. It is shown that the IA solitons, in the presence of trapped electrons, can retain their features (both in spatial and velocity direction) after successive mutual collisions. The collisions here include encounters of IA solitons with the same trapping parameter, while differing in size. Kinetic simulation results reveal a complicated behavior during a collision between IA solitons in contrast to the fluid theory predictions and simulations. In the range of parameters considered here, two oppositely propagating solitons rotate around their collective center in the phase space during a collision, independent of their trapping parameters. Furthermore, they exchange some portions of their trapped populations.