Physical Dissipation and the Method of Controlled Lagrangians

We describe the effect of physical dissipation on stability of equilibria which have been stabilized, in the absence of damping, using the method of controlled Lagrangians. This method applies to a class of underactuated mechanical systems including “balance” systems such as the pendulum on a cart. Since the method involves modifying a system’s kinetic energy metric through feedback, the effect of dissipation is obscured. In particular, it is not generally true that damping makes a feedback-stabilized equilibrium asymptotically stable. Damping in the unactuated directions does tend to enhance stability, however damping in the controlled directions must be “reversed” through feedback. In this paper, we suggest a choice of feedback dissipation to locally exponentially stabilize a class of controlled Lagrangian systems

Dissipation and Controlled Euler-Poincaré Systems

The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-Poincaré (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-Poincaré systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor

The effect of grading the atomic number at resistive guide element interface on magnetic collimation

Using 3 dimensional numerical simulations, this paper shows that grading the atomic number and thus the resistivity at the interface between an embedded high atomic number guide element and a lower atomic number substrate enhances the growth of a resistive magnetic field. This can lead to a large integrated magnetic flux density, which is fundamental to confining higher energy fast electrons. This results in significant improvements in both magnetic collimation and fast-electron-temperature uniformity across the guiding. The graded interface target provides a method for resistive guiding that is tolerant to laser pointing

Calibrating the relation of low-frequency radio continuum to star formation rate at 1 kpc scale with LOFAR

9 figures, 6 tables and 17 pages. This paper is part of the LOFAR surveys data release 1 and has been accepted for publication in a special edition of A&A that will appear in Feb 2019, volume 622. The catalogues and images from the data release will be publicly available on lofar-surveys.org upon publication of the journal. Reproduced with permission from Astronomy & Astrophysics. © 2018 ESO.Radio continuum (RC) emission in galaxies allows us to measure star formation rates (SFRs) unaffected by extinction due to dust, of which the low-frequency part is uncontaminated from thermal (free-free) emission. We calibrate the conversion from the spatially resolved 140 MHz RC emission to the SFR surface density ($\Sigma_{\rm SFR}$) at 1 kpc scale. We used recent observations of three galaxies (NGC 3184, 4736, and 5055) from the LOFAR Two-metre Sky Survey (LoTSS), and archival LOw-Frequency ARray (LOFAR) data of NGC 5194. Maps were created with the facet calibration technique and converted to radio $\Sigma_{\rm SFR}$ maps using the Condon relation. We compared these maps with hybrid $\Sigma_{\rm SFR}$ maps from a combination of GALEX far-ultraviolet and Spitzer 24 $\mu\rm m$ data using plots tracing the relation at $1.2\times 1.2$-kpc$^2$ resolution. The RC emission is smoothed with respect to the hybrid $\Sigma_{\rm SFR}$ owing to the transport of cosmic-ray electrons (CREs). This results in a sublinear relation $(\Sigma_{\rm SFR})_{\rm RC} \propto [(\Sigma_{\rm SFR})_{\rm hyb}]^{a}$, where $a=0.59\pm 0.13$ (140 MHz) and $a=0.75\pm 0.10$ (1365 MHz). Both relations have a scatter of $\sigma = 0.3~\rm dex$. If we restrict ourselves to areas of young CREs ($\alpha > -0.65$; $I_\nu \propto \nu^\alpha$), the relation becomes almost linear at both frequencies with $a\approx 0.9$ and a reduced scatter of $\sigma = 0.2~\rm dex$. We then simulate the effect of CRE transport by convolving the hybrid $\Sigma_{\rm SFR}$ maps with a Gaussian kernel until the RC-SFR relation is linearised; CRE transport lengths are $l=1$-5 kpc. Solving the CRE diffusion equation, we find diffusion coefficients of $D=(0.13$-$1.5) \times 10^{28} \rm cm^2\,s^{-1}$ at 1 GeV. A RC-SFR relation at $1.4$ GHz can be exploited to measure SFRs at redshift $z \approx 10$ using $140$ MHz observations.Peer reviewe

ACBAR: The Arcminute Cosmology Bolometer Array Receiver

We describe the Arcminute Cosmology Bolometer Array Receiver (ACBAR); a multifrequency millimeter-wave receiver designed for observations of the Cosmic Microwave Background (CMB) and the Sunyaev-Zel'dovich effect in clusters of galaxies. The ACBAR focal plane consists of a 16-pixel, background-limited, 240 mK bolometer array that can be configured to observe simultaneously at 150, 220, 280, and 350 GHz. With 4-5' FWHM Gaussian beam sizes and a 3 degree azimuth chop, ACBAR is sensitive to a wide range of angular scales. ACBAR was installed on the 2 m Viper telescope at the South Pole in January 2001. We describe the design of the instrument and its performance during the 2001 and 2002 observing seasons.Comment: 59 pages, 16 figures -- updated to reflect version published in ApJ

The Robinson Gravitational Wave Background Telescope (BICEP): a bolometric large angular scale CMB polarimeter

The Robinson Telescope (BICEP) is a ground-based millimeter-wave bolometric array designed to study the polarization of the cosmic microwave background radiation (CMB) and galactic foreground emission. Such measurements probe the energy scale of the inflationary epoch, tighten constraints on cosmological parameters, and verify our current understanding of CMB physics. Robinson consists of a 250-mm aperture refractive telescope that provides an instantaneous field-of-view of 17 degrees with angular resolution of 55 and 37 arcminutes at 100 GHz and 150 GHz, respectively. Forty-nine pair of polarization-sensitive bolometers are cooled to 250 mK using a 4He/3He/3He sorption fridge system, and coupled to incoming radiation via corrugated feed horns. The all-refractive optics is cooled to 4 K to minimize polarization systematics and instrument loading. The fully steerable 3-axis mount is capable of continuous boresight rotation or azimuth scanning at speeds up to 5 deg/s. Robinson has begun its first season of observation at the South Pole. Given the measured performance of the instrument along with the excellent observing environment, Robinson will measure the E-mode polarization with high sensitivity, and probe for the B-modes to unprecedented depths. In this paper we discuss aspects of the instrument design and their scientific motivations, scanning and operational strategies, and the results of initial testing and observations.Comment: 18 pages, 11 figures. To appear in Millimeter and Submillimeter Detectors and Instrumentation for Astronomy III, Proceedings of SPIE, 6275, 200

Nonlinear Control of a Novel Two-Link Pendulum

This paper describes nonlinear control of a two degree of freedom mechanical system which models a bird perched on a branch or cable. The primary contribution is the implementation, in a controlled laboratory experiment, of the recently developed C\ adaptive control approach. This technique, which allows fast adaptation with guaranteed stability margins, has been proposed for use in a variety of more sophisticated applications. Experimental results for this simple mechanical control system provide further motivation to pursue those applications. The system being considered is a variation of Spong's "Acrobot", a classic example of an underactuated mechanical control system. In addition to the ℒ_1 controller, a swing-up controller based on Spong's original work on collocated partial feedback linearization is implemented with switching logic