Moment evolution and level-crossing statistics in dichotomous and multilevel flows with time-dependent control parameters

Mean density of level crossings whose duration exceeds a certain value for a low-friction nonlinear oscillator

A system that exhibits nonlinear oscillations in the presence of low friction and weak fluctuations is considered. An expression for the mean density of level crossings whose duration exceeds a certain value is derived under the assumption of the high Q factor of the oscillations.

Lattice model of the early stages of the electrification of a cloud

The early stages of the microphysics of the electrification process within a cloud are considered using a two-dimensional lattice model. Using insights generated from Monte Carlo simulations and the theory of finite Markov processes, the mean walk length statistics of the particles, the instantaneous electric potential and electric field profiles, the time evolution of electrostatic energy and their dependence on system size are studied. Some unexpected features of the kinetics of electrification and of the statistics of crossings of the threshold for an electric discharge to occur are brought out.