Spectral and spatial observations of microwave spikes and zebra structure in the short radio burst of May 29, 2003

The unusual radio burst of May 29, 2003 connected with the M1.5 flare in AR 10368 has been analyzed. It was observed by the Solar Broadband Radio Spectrometer (SBRS/Huairou station, Beijing) in the 5.2-7.6 GHz range. It proved to be only the third case of a neat zebra structure appearing among all observations at such high frequencies. Despite the short duration of the burst (25 s), it provided a wealth of data for studying the superfine structure with millisecond resolution (5 ms). We localize the site of emission sources in the flare region, estimate plasma parameters in the generation sites, and suggest applicable mechanisms for interpretating spikes and zebra-structure generation. Positions of radio bursts were obtained by the Siberian Solar Radio Telescope (SSRT) (5.7 GHz) and Nobeyama radioheliograph (NoRH) (17 GHz). The sources in intensity gravitated to tops of short loops at 17 GHz, and to long loops at 5.7 GHz. Short pulses at 17 GHz (with a temporal resolution of 100 ms) are registered in the R-polarized source over the N-magnetic polarity (extraordinary mode). Dynamic spectra show that all the emission comprised millisecond pulses (spikes) of 5-10 ms duration in the instantaneous band of 70 to 100 MHz, forming the superfine structure of different bursts, essentially in the form of fast or slow-drift fibers and various zebra-structure stripes. Five scales of zebra structures have been singled out. As the main mechanism for generating spikes (as the initial emission) we suggest the coalescence of plasma waves with whistlers in the pulse regime of interaction between whistlers and ion-sound waves. In this case one can explain the appearance of fibers and sporadic zebra-structure stripes exhibiting the frequency splitting.Comment: 11 pages, 5 figures, in press; A&A 201

Billiards with polynomial mixing rates

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. However, mathematical methods for the analysis of systems with slow mixing rates were developed just recently and are still difficult to apply to realistic models. Here we reduce those methods to a practical scheme that allows us to obtain a nearly optimal bound on mixing rates. We demonstrate how the method works by applying it to several classes of chaotic billiards with slow mixing as well as discuss a few examples where the method, in its present form, fails.Comment: 39pages, 11 figue

Deterministic Walks in Quenched Random Environments of Chaotic Maps

This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The particle motion in both models is chaotic and found to fluctuate about a linear drift. In the proper scaling limit, the cumulative distribution function of the fluctuations converges to a Gaussian one with system dependent variance while the density function shows no convergence to any function. We have verified our analytical results using extreme precision numerical computations.Comment: 18 pages, 9 figure

Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards

The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional billiards without using the Ansatz.Comment: 17 pages, 2 figure

Structure and evolution of strange attractors in non-elastic triangular billiards

We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the boundary is a uniform factor $\lambda < 1$ smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter $\lambda$ is varied. For $\lambda$ in the interval (0, 1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of $\lambda$ the billiard dynamics gives rise to nonaccessible regions in phase space. For $\lambda$ close to 1, the attractor splits into three transitive components, the basins of attraction of which have fractal basin boundaries.Comment: 12 pages, 10 figures; submitted for publication. One video file available at http://sistemas.fciencias.unam.mx/~dsanders

Experimental modelling of lightning interaction phenomena with a free potential conducting objects

Laboratory experiments were conducted to investigate the physical processes of the development of air discharge and its interaction with free potential conducting objects. The space-time development of lightning in gaps was recorded by a motion picture camera and an optoelectronic transducer. The electric field at different points in the gap was measured using a Pockels device both in the leader stage and in the stage of the return stroke. Experimental results of the streamer zone length measurements in the gaps with lengths up to 65 meters are presented. The physical processes occurring during the interaction of positive and negative long sparks with isolated objects were investigated. The striking probability of isolated conducting spheres with different diameters and the dependence of the strike on the location of the gap are investigated

Protein Crystallization

Nucleation, growth and perfection of protein crystals will be overviewed along with crystal mechanical properties. The knowledge is based on experiments using optical and force crystals behave similar to inorganic crystals, though with a difference in orders of magnitude in growing parameters. For example, the low incorporation rate of large biomolecules requires up to 100 times larger supersaturation to grow protein, rather than inorganic crystals. Nucleation is often poorly reproducible, partly because of turbulence accompanying the mixing of precipitant with protein solution. Light scattering reveals fluctuations of molecular cluster size, its growth, surface energies and increased clustering as protein ages. Growth most often occurs layer-by-layer resulting in faceted crystals. New molecular layer on crystal face is terminated by a step where molecular incorporation occurs. Quantitative data on the incorporation rate will be discussed. Rounded crystals with molecularly disordered interfaces will be explained. Defects in crystals compromise the x-ray diffraction resolution crucially needed to find the 3D atomic structure of biomolecules. The defects are immobile so that birth defects stay forever. All lattice defects known for inorganics are revealed in protein crystals. Contribution of molecular conformations to lattice disorder is important, but not studied. This contribution may be enhanced by stress field from other defects. Homologous impurities (e.g., dimers, acetylated molecules) are trapped more willingly by a growing crystal than foreign protein impurities. The trapped impurities induce internal stress eliminated in crystals exceeding a critical size (part of mni for ferritin, lysozyme). Lesser impurities are trapped from stagnant, as compared to the flowing, solution. Freezing may induce much more defects unless quickly amorphysizing intracrystalline water