New Enhanced Chaotic Number Generators

We introduce new families of enhanced chaotic number generators in order to compute very fast long series of pseudorandom numbers. The key feature of these generators being the use of chaotic numbers themselves for sampling chaotic subsequence of chaotic numbers in order to hide the generating function. We explore numerically the properties of these new families and underline their very high qualities and usefulness as CPRNG when series are computed up to 10 trillions iterations.Comment: 42 pages, 17 figures, to be published in Proceeding 8th International Conference of Indian Soc. of Indust. and Appl. Math., Jammu,India, 31st March - 3rd April 2007, Invited conferenc

Diffraction-limited polarimetric imaging of protoplanetary disks and mass-loss shells with VAMPIRES

Both the birth and death of a stellar system are areas of key scientific importance. Whether it's understanding the process of planetary formation in a star's early years, or uncovering the cause of the enormous mass-loss that takes place during a star's dying moments, a key to scientific understanding lies in the inner few AU of the circumstellar environment. Corresponding to scales of 10s of milli-arcseconds, these observations pose a huge technical challenge due to the high angular-resolutions and contrasts required. A major stumbling block is the problem of the Earth's own atmospheric turbulence. The other difficulty is that precise calibration is required to combat the extremely high contrast ratios and high resolutions faced. By taking advantage of the fact that starlight scattered by dust in the circumstellar region is polarized, differential polarimetry can help achieve this calibration. Spectral features can also be utilized

Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size

The behavior of a family of dissipative dynamical systems representing transformations of two-dimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying dissipative dynamical systems to generation of pseudorandom numbers is shown to be advantageous and equidistribution of probabilities for the sequences of bits can be achieved. A new algorithm for generating uniform pseudorandom numbers is proposed. The theory of the generator, which includes proofs of periodic properties and of statistical independence of bits at distances up to logarithm of mesh size, is presented. Extensive statistical testing using available test packages demonstrates excellent results, while the speed of the generator is comparable to other modern generators.Comment: 6 pages, 3 figures, 3 table

Phase-induced amplitude apodization complex mask coronagraph tolerancing and analysis

Phase-Induced Amplitude Apodization Complex Mask Coronagraphs (PIAACMC) offer high-contrast performance at a small inner-working angle ($\approx$ 1 $\lambda$/D) with high planet throughput ($>$ 70%). The complex mask is a multi-zone, phase-shifting mask comprised of tiled hexagons which vary in depth. Complex masks can be difficult to fabricate as there are many micron-scale hexagonal zones ($>$ 500 on average) with continuous depths ranging over a few microns. Ensuring the broadband PIAACMC design performance carries through to fabricated devices requires that these complex masks are manufactured to within well-defined tolerances. We report on a simulated tolerance analysis of a "toy" PIAACMC design which characterizes the effect of common microfabrication errors on on-axis contrast performance using a simple Monte Carlo method. Moreover, the tolerance analysis provides crucial information for choosing a fabrication process which yields working devices while potentially reducing process complexity. The common fabrication errors investigated are zone depth discretization, zone depth errors, and edge artifacts between zones.Comment: 8 pages, 6 figures, SPIE Astronomical Telescopes + Instrumentatio

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

Diffraction-limited polarimetric imaging of protoplanetary disks and mass-loss shells with VAMPIRES

Both the birth and death of a stellar system are areas of key scientific importance. Whether it's understanding the process of planetary formation in a star's early years, or uncovering the cause of the enormous mass-loss that takes place during a star's dying moments, a key to scientific understanding lies in the inner few AU of the circumstellar environment. Corresponding to scales of 10s of milli-arcseconds, these observations pose a huge technical challenge due to the high angular-resolutions and contrasts required. A major stumbling block is the problem of the Earth's own atmospheric turbulence. The other difficulty is that precise calibration is required to combat the extremely high contrast ratios and high resolutions faced. By taking advantage of the fact that starlight scattered by dust in the circumstellar region is polarized, differential polarimetry can help achieve this calibration. Spectral features can also be utilized