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

Dynamics towards the Feigenbaum attractor

We expose at a previously unknown level of detail the features of the dynamics of trajectories that either evolve towards the Feigenbaum attractor or are captured by its matching repellor. Amongst these features are the following: i) The set of preimages of the attractor and of the repellor are embedded (dense) into each other. ii) The preimage layout is obtained as the limiting form of the rank structure of the fractal boundaries between attractor and repellor positions for the family of supercycle attractors. iii) The joint set of preimages for each case form an infinite number of families of well-defined phase-space gaps in the attractor or in the repellor. iv) The gaps in each of these families can be ordered with decreasing width in accord to power laws and are seen to appear sequentially in the dynamics generated by uniform distributions of initial conditions. v) The power law with log-periodic modulation associated to the rate of approach of trajectories towards the attractor (and to the repellor) is explained in terms of the progression of gap formation. vi) The relationship between the law of rate of convergence to the attractor and the inexhaustible hierarchy feature of the preimage structure is elucidated.Comment: 8 pages, 12 figure

Discrete soliton ratchets driven by biharmonic fields

Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform unidirectional motion. The phenomenon resembles the well known effects of ratchet transport and nonlinear harmonic mixing. Direction of the motion and its velocity depends on the shape of the AC drive. Necessary conditions for the occurrence of the effect are formulated. In comparison with the previously studied continuum case, the discrete case shows a number of new features: non-zero depinning threshold for the driving amplitude, locking to the rational fractions of the driving frequency, and diffusive ratchet motion in the case of weak intersite coupling.Comment: 13 pages, 13 figure

Preliminary design and cost of a 1-megawatt solar-pumped iodide laser space-to-space transmission station

A preliminary conceptual design of a space-based solar pumped iodide laser emitting 1 megawatt of laser power for space-to-space power transmission is described. A near parabolic solar collector focuses sunlight onto the t-C4F9I (perfluoro-t butyl iodide) lasant within a transverse flow optical cavity. Using waste heat, a thermal system was designed to supply compressor and auxiliary power. System components were designed with weight and cost estimates assigned. Although cost is very approximate, the cost comparison of individual system components leads to valuable insights for future research. In particular, it was found that laser efficiency was not a dominant cost or weight factor, the dominant factor being the laser cavity and laser transmission optics. The manufacturing cost was approx. two thirds of the total cost with transportation to orbit the remainder. The flowing nonrenewable lasant comprised 20% of the total life cycle cost of the system and thus was not a major cost factor. The station mass was 92,000 kg without lasant, requiring approx. four shuttle flights to low Earth orbit where an orbital transfer vehicle will transport it to the final altitude of 6378 km

Brachial plexus injury mimicking a spinal-cord injury.

Objective High-energy impact to the head, neck, and shoulder can result in cervical spine as well as brachial plexus injuries. Because cervical spine injuries are more common, this tends to be the initial focus for management. We present a case in which the initial magnetic resonance imaging (MRI) was somewhat misleading and a detailed neurological exam lead to the correct diagnosis.Clinical presentation A 19-year-old man presented to the hospital following a shoulder injury during football practice. The patient immediately complained of significant pain in his neck, shoulder, and right arm and the inability to move his right arm. He was stabilized in the field for a presumed cervical-spine injury and transported to the emergency department.Intervention Initial radiographic assessment (C-spine CT, right shoulder x-ray) showed no bony abnormality. MRI of the cervical-spine showed T2 signal change and cord swelling thought to be consistent with a cord contusion. With adequate pain control, a detailed neurological examination was possible and was consistent with an upper brachial plexus avulsion injury that was confirmed by CT myelogram. The patient failed to make significant neurological recovery and he underwent spinal accessory nerve grafting to the suprascapular nerve to restore shoulder abduction and external rotation, while the phrenic nerve was grafted to the musculocutaneous nerve to restore elbow flexion.Conclusion Cervical spinal-cord injuries and brachial plexus injuries can occur by the same high energy mechanisms and can occur simultaneously. As in this case, MRI findings can be misleading and a detailed physical examination is the key to diagnosis. However, this can be difficult in polytrauma patients with upper extremity injuries, head injuries or concomitant spinal-cord injury. Finally, prompt diagnosis and early surgical renerveration have been associated with better long-term recovery with certain types of injury

The role of inhibitory feedback for information processing in thalamocortical circuits

The information transfer in the thalamus is blocked dynamically during sleep, in conjunction with the occurence of spindle waves. As the theoretical understanding of the mechanism remains incomplete, we analyze two modeling approaches for a recent experiment by Le Masson {\sl et al}. on the thalamocortical loop. In a first step, we use a conductance-based neuron model to reproduce the experiment computationally. In a second step, we model the same system by using an extended Hindmarsh-Rose model, and compare the results with the conductance-based model. In the framework of both models, we investigate the influence of inhibitory feedback on the information transfer in a typical thalamocortical oscillator. We find that our extended Hindmarsh-Rose neuron model, which is computationally less costly and thus siutable for large-scale simulations, reproduces the experiment better than the conductance-based model. Further, in agreement with the experiment of Le Masson {\sl et al}., inhibitory feedback leads to stable self-sustained oscillations which mask the incoming input, and thereby reduce the information transfer significantly.Comment: 16 pages, 15eps figures included. To appear in Physical Review

Electrochemical machining of stainless steel microelements with ultrashort voltage pulses

An electrochemical pulse technique enables the fabrication of three-dimensional microelements from stainless steel. The method is based on the application of ultrashort (nanosecond) voltage pulses, whereupon electrochemical reactions are locally confined with submicrometer precision. Employing properly shaped tool electrodes enables the machining of freestanding cantilevers or microstructures directly to a metal sheet. Due to gentle removal of the material, the grain structure of the material is revealed without any chemical or mechanical modifications. This is demonstrated by measuring the vibration frequency of a cantilever, and agrees well with the value derived from the bulk material properties

New Low-Mass Stars and Brown Dwarfs with Disks in Lupus

Using the Infrared Array Camera and the Multiband Imaging Photometer aboard the {\it Spitzer Space Telescope}, we have obtained images of the Lupus 3 star-forming cloud at 3.6, 4.5, 5.8, 8.0, and 24 \micron. We present photometry in these bands for the 41 previously known members that are within our images. In addition, we have identified 19 possible new members of the cloud based on red 3.6-8.0 \micron colors that are indicative of circumstellar disks. We have performed optical spectroscopy on 6 of these candidates, all of which are confirmed as young low-mass members of Lupus 3. The spectral types of these new members range from M4.75 to M8, corresponding to masses of 0.2-0.03 $M_\odot$ for ages of $\sim1$ Myr according to theoretical evolutionary models. We also present optical spectroscopy of a candidate disk-bearing object in the vicinity of the Lupus 1 cloud, 2M 1541-3345, which Jayawardhana & Ivanov recently classified as a young brown dwarf ($M\sim0.03$ $M_\odot$) with a spectral type of M8. In contrast to their results, we measure an earlier spectral type of M5.75$\pm$0.25 for this object, indicating that it is probably a low-mass star ($M\sim0.1$ $M_\odot$). In fact, according to its gravity-sensitive absorption lines and its luminosity, 2M 1541-3345 is older than members of the Lupus clouds ($\tau\sim1$ Myr) and instead is probably a more evolved pre-main-sequence star that is not directly related to the current generation of star formation in Lupus.Comment: 18 pages, 3 tables, 6 figure

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