An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.Comment: 13 pages, 4 figure

Radioheliograph observations of microwave bursts with zebra structures

The so-called zebra structures in radio dynamic spectra, specifically their frequencies and frequency drifts of emission stripes, contain information on the plasma parameters in the coronal part of flare loops. This paper presents observations of zebra structures in a microwave range. Dynamic spectra were recorded by Chinese spectro-polarimeters in the frequency band close to the working frequencies of the Siberian Solar Radio Telescope. The emission sources are localized in the flare regions, and we are able to estimate the plasma parameters in the generation sites using X-ray data. The interpretation of the zebra structures in terms of the existing theories is discussed. The conclusion has been arrived that the preferred generation mechanism of zebra structures in the microwave range is the conversion of plasma waves to electromagnetic emission on the double plasma resonance surfaces distributed across a flare loop.Comment: 18 pages, 7 figure

Chaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated using the following PO formulas: (a) The curvature expansion of the Ruelle zeta function. (b) The average of the PO winding-number squared, $w^{2}$, weighted by a stability factor. (c) The uniform (nonweighted) average of $w^{2}$. The results from formulas (a) and (b) agree very well with those obtained by standard methods, for all the perturbation parameters considered. Formula (c) gives reasonably accurate results for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to {\em uniformity sum rules} satisfied by the PO Lyapunov eigenvalues at {\em fixed} $w$. These sum rules follow from general arguments and are supported by much numerical evidence.Comment: 6 Tables, 2 Figures (postscript); To appear in Physical Review