No abstract

The Karpman equation describing the interaction of a longitudinal electric field with the ion-acoustic wave in a two-component plasma, shown to be integrable by Kaup, is solved exactly both on the full-line and on the semi-line for a given (arbitrary) incident electric field in x = −∞ or x = 0. In particular, the method provides the explicit output values of the electric field for a plasma initially neutral. In the full-line case it is proved that the input electrostatic field does not generate solitons, while it does so when the problem is on the semi-line.

Linear particle transport in stochastic media is key to such relevant applications as neutron diffusion in randomly mixed immiscible materials, light propagation through engineered optical materials, and inertial confinement fusion, only to name a few. We extend the pioneering work by Adams, Larsen and Pomraning Adams et al. (1989) (recently revisited by Brantley Brantley (2011)) by considering a series of benchmark configurations for mono-energetic and isotropic transport through Markov binary mixtures in dimension d. The stochastic media are generated by resorting to Poisson random tessellations in 1d slab, 2d extruded, and full 3d geometry. For each realization, particle transport is performed by resorting to the Monte Carlo simulation. The distributions of the transmission and reflection coefficients on the free surfaces of the geometry are subsequently estimated, and the average values over the ensemble of realizations are computed. Reference solutions for the benchmark have never been provided before for twoand three-dimensional Poisson tessellations, and the results presented in this paper might thus be useful in order to validate fast but approximated models for particle transport in Markov stochastic media, such as the celebrated Chord Length Sampling algorithm.