Adopting the MPI-AMRVAC code, we present a 2.5-dimensional magnetohydrodynamic (MHD) simulation, which includes thermal conduction and radiative cooling, to investigate formation evolution of coronal rain phenomenon. We perform simulation in initially linear force-free magnetic fields host chromospheric, transition region, plasma, with turbulent heating localized on their footpoints. Due instab...

Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of walker grows non-linearly with time contrast to diffusive motion described by random walks or Brownian motion. In this paper we study extension LW one dimension introducing correlation among velocities different (flight) steps. Such is absent model. The correlation...

Abstract In this note we examine the following random graph model: for an arbitrary , with quadratic many edges, construct a by randomly adding edges to and coloring of colors. We show that large enough constant every pair vertices in are joined rainbow path, is, is connected high probability. This confirms conjecture Anastos Frieze, who proved statement resolved case when function .