A new class of supersonic nonequilibrium flows is studied on the basis of solving the Boltzmann and model kinetic equations with the aim to consider new non-linear structures in open systems and to study anomalous transfer properties in relaxation zones. The Unified Flow Solver is applied for numerical simulations. Simple gases and gases with inner degrees of freedom are considered. The experimental data related to the influence of the so-called optical lattices on the supersonic molecular beams are considered and numerical analysis of the nonequilibrium states obtained on this basis is made. The nonuniform relaxation problem with these distributions is simulated numerically and anomalous transport is confirmed. The conditions for strong changes of the temperature in the anomalous transfer zones are discussed and are realized in computations.

We study a continuous-time random walk on the d-dimensional lattice, subject to a drift and an attraction to large clusters of a subcritical Bernoulli site percolation. We find two distinct regimes: a ballistic one, and a subballistic one taking place when the attraction is strong enough. We identify the speed in the former case, and the algebraic rate of escape in the latter case. Finally, we discuss the diffusive behavior in the case of zero drift and weak attraction.