Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries

We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional map when lambda=0 and the classical Hamiltonian case of elastic collisions when lambda=1. For all lambda<1, the dynamics is dissipative, and thus gives rise to attractors, which may be periodic or chaotic. Motivated by recent rigorous results of Markarian, Pujals and Sambarino, we numerically investigate and characterise the bifurcations of the resulting attractors as the contraction parameter is varied. Some billiards exhibit only periodic attractors, some only chaotic attractors, and others have coexistence of the two types.Comment: 30 pages, 17 figures. v2: Minor changes after referee comments. Version with some higher-quality figures available at http://sistemas.fciencias.unam.mx/~dsanders/publications.htm

Review of current interest and research in water hyacinth-based wastewater treatment

The status of activity in the user community for water hyacinth-based wastewater treatment was evaluated. The principal technique used was that of interviewing people who either (1) were known to be engaged in hyacinth research or development or (2) had made inquiry to NASA about hyacinth systems. About 40 non-research organizations and a similar number of research organizations were contacted. As a result of the interviews and a review of the relevant literature, it was concluded that hyacinth systems have the potential for providing a lower cost way for small cities to meet increasingly stringent effluent requirements. A limited amount of full-scale demonstration of hyacinth systems has been carried out during the past two years, but the yield of design data has been small. Several organizations are currently planning construction of experimental full-scale hyacinth-based wastewater treatment systems during 1977-1978

A new proof of the Herman-Avila-Bochi formula for Lyapunov exponents of SL(2,R)-cocycles

We study the geometry of the action of SL(2,R) on the projective line in order to present a new and simpler proof of the Herman-Avila-Bochi formula. This formula gives the average Lyapunov exponent of a class of 1-families of SL(2,R)-cocycles.Comment: 13 pages, 2 figure

Exponential speed of mixing for skew-products with singularities

Let $f: [0,1]\times [0,1] \setminus {1/2} \to [0,1]\times [0,1]$ be the $C^\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is topologically mixing and if $c>1/4$ then $f$ is mixing with respect to Lebesgue measure. Furthermore we prove that the speed of mixing is exponential.Comment: 23 pages, 3 figure

Stochastic perturbations of convex billiards

We consider a strictly convex billiard table with C 2 boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation distribution corresponds to the physical situation where either the scale of the surface irregularities is smaller than but comparable to the diameter of the reflected object, or the billiard ball is not perfectly rigid. We prove that for a large class of such perturbations the resulting Markov chain is uniformly ergodic, although this is not true in general.Fil: Markarian, R.. Universidad de la Republica. Facultad de Ingeniería; UruguayFil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Sidoravicius, V.. Jardim Botânico; BrasilFil: Tal, F. A.. Universidade de Sao Paulo; BrasilFil: Vares, M. E.. Universidade Federal do Rio de Janeiro; Brasi

Chaos and stability in a two-parameter family of convex billiard tables

We study, by numerical simulations and semi-rigorous arguments, a two-parameter family of convex, two-dimensional billiard tables, generalizing the one-parameter class of oval billiards of Benettin--Strelcyn [Phys. Rev. A 17, 773 (1978)]. We observe interesting dynamical phenomena when the billiard tables are continuously deformed from the integrable circular billiard to different versions of completely-chaotic stadia. In particular, we conjecture that a new class of ergodic billiard tables is obtained in certain regions of the two-dimensional parameter space, when the billiards are close to skewed stadia. We provide heuristic arguments supporting this conjecture, and give numerical confirmation using the powerful method of Lyapunov-weighted dynamics.Comment: 19 pages, 13 figures. Submitted for publication. Supplementary video available at http://sistemas.fciencias.unam.mx/~dsanders

Radio Continuum Emission at 1.4 GHz from KISS Emission-Line Galaxies

We have searched the Faint Images of the Radio Sky at Twenty centimeters (FIRST) and the NRAO VLA Sky Survey (NVSS) 1.4 GHz radio surveys for sources that are coincident with emission-line galaxy (ELG) candidates from the KPNO International Spectroscopic Survey (KISS). A total of 207 of the 2157 KISS ELGs (~10%) in the first two H-alpha-selected survey lists were found to possess radio detections in FIRST and/or NVSS. Follow-up spectra exist for all of the radio detections, allowing us to determine the activity type (star-forming vs. AGN) for the entire sample. We explore the properties of the radio-detected KISS galaxies in order to gain a better insight into the nature of radio-emitting galaxies in the local universe (z < 0.1). No dwarf galaxies were detected, despite the large numbers of low-luminosity galaxies present in KISS, suggesting that lower mass, lower luminosity objects do not possess strong galaxian-scale magnetic fields. Due to the selection technique used for KISS, our radio ELGs represent a quasi-volume-limited sample, which allows us to develop a clearer picture of the radio galaxy population at low redshift. Nearly 2/3rds of the KISS radio galaxies are starburst/star-forming galaxies, which is in stark contrast to the results of flux-limited radio surveys that are dominated by AGNs and elliptical galaxies (i.e., classic radio galaxies). While there are many AGNs among the KISS radio galaxies, there are no objects with large radio powers in our local volume. We derive a radio luminosity function (RLF) for the KISS ELGs that agrees very well with previous RLFs that adequately sample the lower-luminosity radio population.Comment: Accepted for publication in the Astronomical Journal (April 2004); 23 pages, 16 figure

Dust Properties and Star-Formation Rates in Star-Forming Dwarf Galaxies

We have used the Spitzer Space Telescope to study the dust properties of a sample of star-forming dwarf galaxies. The differences in the mid-infrared spectral energy distributions for these galaxies which, in general, are low metallicity systems, indicate differences in the physical properties, heating, and/or distribution of the dust. Specifically, these galaxies have more hot dust and/or very small grains and less PAH emission than either spiral or higher luminosity starburst galaxies. As has been shown in previous studies, there is a gradual decrease in PAH emission as a function of metallicity. Because much of the energy from star formation in galaxies is re-radiated in the mid-infrared, star-formation rate indicators based on both line and continuum measurements in this wavelength range are coming into more common usage. We show that the variations in the interstellar medium properties of galaxies in our sample, as measured in the mid-infrared, result in over an order of magnitude spread in the computed star-formation rates.Comment: 25 pages, 11 figures, 4 tables, ApJ accepte

HST observations of the blue compact dwarf SBS 0335-052: a probable young galaxy

We present HST WFPC2 V and I images and GHRS UV spectrophotometry of the spectral regions around Ly$_alpha$ and OI 1302 of the extremely metal-deficient (Z~Zsun/41) blue compact dwarf (BCD) galaxy SBS 0335-052. All the star formation in the BCD occurs in six super-star clusters (SSC) with ages =< 3-4 Myr. Dust is clearly present and mixed spatially with the SSCs. There is a supershell of radius ~380 pc, delineating a large supernova cavity. The instantaneous star formation rate is ~0.4 Msun yr^-1. Strong narrow Ly$\alpha$ emission is not observed. Rather there is low intensity broad (FWZI = 20 A) Ly$\alpha$ emission superposed on even broader Ly$\alpha$ absorption by the HI envelope. This broad low-intensity emission is probably caused by resonant scattering of Ly$\alpha$ photons. The BCD appears to be a young galaxy, undergoing its very first burst of star formation. This conclusion is based on the following evidence: 1) the underlying extended low-surface-brightness component is very irregular and filamentary, suggesting that a significant part of the emission comes from ionized gas; 2) it has very blue colors (-0.34 =< (V-I)$_0$ =< 0.16), consistent with gaseous emission colors; 3) the OI 1302 line is not detected in absorption in the GHRS spectrum, setting an upper limit for N(O)/N(H) in the HI envelope of the BCD of more than 3000 times smaller than the value in Orion.Comment: 20 pages and 6 Postscript figures. Submitted to Astrophysical Journa