The kinetic description of a collisionless system of particles in an external stochastic field possessing helicity is examined. The kinetic equation which contains an additional term proportional to the helicity is obtained. The solution describing evolution of the distribution function for...

We investigate two coupled properties of Lévy stable random motions: the first passage times (FPTs) and the first passage leapovers (FPLs). While, in general, the FPT problem has been studied quite extensively, the FPL problem has hardly attracted any attention. Considering a particle that...

The role of Lévy flights on fluctuation-driven transport in time independent periodic potentials with broken spatial symmetry is studied. Two complementary approaches are followed. The first one is based on a generalized Langevin model describing overdamped dynamics in a ratchet type external...

We consider the structure functions S^(q)(T), i.e. the moments of order q of the increments X(t+T)-X(t) of the Foreign Exchange rate X(t) which give clear evidence of scaling (S^(q)(T)~T^z(q)). We demonstrate that the nonlinearity of the observed scaling exponent z(q) is incompatible with...

Scale invariant symmetries are usually restricted to systems involving extremely special types of scale changes; self-similar and self-affine fractals involving isotropy and differential stratification respectively. In contrast, geophysical and astrophysical systems can be scale invariant but...

Over the last twenty years, many studies have been made of radiative transfer in scaling cloud fields, the vast majority of which have been limited to numerical studies in clouds with relatively small optical thickness. An exception to this was the development of a formalism for treating single...

We show that multifractal notions encompass a wider variety of phenomena than often believed. Ranked by increasing highest order of singularities we have geometric, then microcanonical and finally canonical multifractals. They are respectively localized and “calm”, delocalized and...

State-of-the-art airborne lidar data of passive scalars have shown that the spatial stratification of the atmosphere is scaling: the vertical extent (Δz) of structures is typically ≈ΔxHz where Δx is the horizontal extent and Hz is a stratification exponent. Assuming horizontal isotropy, the...

In Part I of this paper, we developed asymptotic approximations for single photon scattering in thick, highly heterogeneous, “Log-Lévy” multifractal clouds. In Part II, theoretical multiple scattering predictions are numerically tested using Monte Carlo techniques, which show that, due to...

Scale-invariant intergalactic dynamics governed by a statistically homogeneous cascade process generically yields multifractal luminosity distributions with highly inhomogeneous realizations (the standard nonfractal and fractal models are special limiting cases). The main obstacles for extending...