Memory difference control of unknown unstable fixed points: Drifting parameter conditions and delayed measurement

Difference control schemes for controlling unstable fixed points become important if the exact position of the fixed point is unavailable or moving due to drifting parameters. We propose a memory difference control method for stabilization of a priori unknown unstable fixed points by introducing a memory term. If the amplitude of the control applied in the previous time step is added to the present control signal, fixed points with arbitrary Lyapunov numbers can be controlled. This method is also extended to compensate arbitrary time steps of measurement delay. We show that our method stabilizes orbits of the Chua circuit where ordinary difference control fails.Comment: 5 pages, 8 figures. See also chao-dyn/9810029 (Phys. Rev. E 70, 056225) and nlin.CD/0204031 (Phys. Rev. E 70, 046205

Control of gradient-driven instabilities using shear Alfv\'en beat waves

A new technique for manipulation and control of gradient-driven instabilities through nonlinear interaction with Alfv\'en waves in a laboratory plasma is presented. A narrow field-aligned density depletion is created in the Large Plasma Device (LAPD), resulting in coherent unstable fluctuations on the periphery of the depletion. Two independent kinetic Alfv\'en waves are launched along the depletion at separate frequencies, creating a nonlinear beat-wave response at or near the frequency of the original instability. When the beat-wave has sufficient amplitude, the original unstable mode is suppressed, leaving only the beat-wave response at a different frequency, generally at lower amplitude.Comment: Submitted for Publication in Physical Review Letters. Revision 2 reflects changes suggested by referees for PRL submission. One figure removed, several major changes to another figure, and a number of major and minor changes to the tex

Avalanches in a Bose-Einstein condensate

Collisional avalanches are identified to be responsible for an 8-fold increase of the initial loss rate of a large 87-Rb condensate. We show that the collisional opacity of an ultra-cold gas exhibits a critical value. When exceeded, losses due to inelastic collisions are substantially enhanced. Under these circumstances, reaching the hydrodynamic regime in conventional BEC experiments is highly questionable.Comment: 4 pages, 2 figures, 1 tabl

Rubidium in Metal-Deficient Disk and Halo Stars

We report the first extensive study of stellar Rb abundances. High-resolution spectra have been used to determine, or set upper limits on, the abundances of this heavy element and the associated elements Y, Zr, and Ba in 44 dwarfs and giants with metallicities spanning the range -2.0 <[Fe/H] < 0.0. In metal-deficient stars Rb is systematically overabundant relative to Fe; we find an average [Rb/Fe] of +0.21 for the 32 stars with [Fe/H] < -0.5 and measured Rb. This behavior contrasts with that of Y, Zr, and Ba, which, with the exception of three new CH stars (HD 23439A and B and BD +5 3640), are consistently slightly deficient relative to Fe in the same stars; excluding the three CH stars, we find the stars with [Fe/H] < -0.5 have average [Y/Fe], [Zr/Fe], and [Ba/Fe] of --0.19 (24 stars), --0.12 (28 stars), and --0.06 (29 stars), respectively. The different behavior of Rb on the one hand and Y, Zr, and Ba on the other can be attributed in part to the fact that in the Sun and in these stars Rb has a large r-process component while Y, Zr, and Ba are mostly s-process elements with only small r-process components. In addition, the Rb s-process abundance is dependent on the neutron density at the s-processing site. Published observations of Rb in s-process enriched red giants indicate a higher neutron density in the metal-poor giants. These observations imply a higher s-process abundance for Rb in metal-poor stars. The calculated combination of the Rb r-process abundance, as estimated for the stellar Eu abundances, and the s-process abundance as estimated for red giants accounts satisfactorily for the observed run of [Rb/Fe] with [Fe/H].Comment: 23 pages, 5 tables, 7 figure

Stability borders of feedback control of delayed measured systems

When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi and Yorke (OGY) has to be based on a measurement delayed by $\tau$ orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Ljapunov number of $\lambda_{max}=1+\frac{1}{\tau}$. In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions have to be considered if one wants to stabilize fixed points with Ljapunov numbers above $\lambda_{max}$.Comment: 5 pages LaTeX using revtex and epsfig (4 figs included). Revised versio

Solid state television camera system Patent

Solid state television camera system consisting of monolithic semiconductor mosaic sensor and molecular digital readout system

Triggering up states in all-to-all coupled neurons

Slow-wave sleep in mammalians is characterized by a change of large-scale cortical activity currently paraphrased as cortical Up/Down states. A recent experiment demonstrated a bistable collective behaviour in ferret slices, with the remarkable property that the Up states can be switched on and off with pulses, or excitations, of same polarity; whereby the effect of the second pulse significantly depends on the time interval between the pulses. Here we present a simple time discrete model of a neural network that exhibits this type of behaviour, as well as quantitatively reproduces the time-dependence found in the experiments.Comment: epl Europhysics Letters, accepted (2010

Extremely Metal-Poor Stars. VII. The Most Metal-Poor Dwarf, CS 22876-032

We report high-resolution, high-signal-to-noise, observations of the extremely metal-poor double-lined spectroscopic binary CS 22876-032. The system has a long period : P = 424.7 $\pm$ 0.6 days. It comprises two main sequence stars having effective temperatures 6300 K and 5600 K, with a ratio of secondary to primary mass of 0.89 $\pm$ 0.04. The metallicity of the system is [Fe/H] = -3.71 $\pm$ 0.11 $\pm$ 0.12 (random and systematic errors) -- somewhat higher than previous estimates. We find [Mg/Fe] = 0.50, typical of values of less extreme halo material. [Si/Fe], [Ca/Fe], and [Ti/Fe], however, all have significantly lower values, ~ 0.0-0.1, suggesting that the heavier elements might have been underproduced relative to Mg in the material from which this object formed. In the context of the hypothesis that the abundance patterns of extremely metal-poor stars are driven by individual enrichment events and the models of Woosley and Weaver (1995), the data for CS 22876-032 are consistent with its having been enriched by a zero-metallicity supernova of mass 30 M$_{\odot}$. As the most metal-poor near-main-sequence-turnoff star currently known, the primary of the system has the potential to strongly constrain the primordial lithium abundance. We find A(Li) (= log(N(Li)/N(H)) + 12.00) = 2.03 $\pm$ 0.07, which is consistent with the finding of Ryan et al. (1999) that for stars of extremely low metallicity A(Li) is a function of [Fe/H].Comment: 27 pages, 9 figures, accepted for publication in The Astrophysical Journal, Sept. 1, 2000 issu

New Lithium Measurements in Metal-Poor Stars

We provide *lambda*6708 Li 1 measurements in 37 metal-poor stars, most of which are poorly-studied or have no previous measurements, from high-resolution and high-S/N spectroscopy obtained with the McDonald Observatory 2.1m and 2.7m telescopes. The typical line strength and abundance uncertainties, confirmed by the thinness of the Spite plateau manifested by our data and by comparison with previous measurements, are <=4 mAng and <=0.07-0.10 dex respectively. Two rare moderately metal-poor solar-Teff dwarfs, HIP 36491 and 40613, with significantly depleted but still detectable Li are identified; future light element determinations in the more heavily depeleted HIP 40613 may provide constraints on the Li depletion mechanism acting in this star. We note two moderately metal-poor and slightly evolved stars, HIP 105888 and G265-39, that appear to be analogs of the low-Li moderately metal-poor subgiant HD 201889. Preliminary abundance analysis of G 265-39 finds no abnormalities that suggest the low Li content is associated with AGB mass-transfer or deep mixing and p-capture. We also detect line doubling in HIP 4754, heretofore classified as SB1.Comment: Accepted for publication in PASP, volume 912 (Feb 2012) 15 pages, 3 figures, 2 table