On the ADI method for the Sylvester Equation and the optimal-H2\mathcal{H}_2 points

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal in the sense that for the Lyapunov equation, they yield a residual which is orthogonal to the rational Krylov projection subspace. Via several examples, we show that the pseudo H2-optimal shifts consistently yield nearly optimal low rank approximations to the solutions of the Lyapunov equations

AXIS—an Autonomous Expendable Instrument System

Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Atmospheric and Oceanic Technology 34 (2017): 2673-2682, doi:10.1175/JTECH-D-17-0054.1.Expendable bathythermographs (XBT) to profile upper-ocean temperatures from vessels in motion have been in use for some 50 years now. Developed originally for navy use, they were soon adapted by oceanographers to map out upper-ocean thermal structure and its space–-time variability from both research vessels and merchant marine vessels in regular traffic. These activities continue today. This paper describes a new technology—the Autonomous Expendable Instrument System (AXIS)—that has been developed to provide the capability to deploy XBT probes on a predefined schedule, or adaptively in response to specific events without the presence of an observer on board. AXIS is a completely self-contained system that can hold up to 12 expendable probes [XBTs, XCTDs, expendable sound velocimeter (XSV)] in any combination. A single-board Linux computer keeps track of what probes are available, takes commands from ashore via Iridium satellite on what deployment schedule to follow, and records and forwards the probe data immediately with a time stamp and the GPS position. This paper provides a brief overview of its operation, capabilities, and some examples of how it is improving coverage along two lines in the Atlantic.Initial development of AXIS mechanical design elements wasmade possible by awards from the Cecil H. and Ida M. Green Technology Innovation Fund and the Sealark Foundation to the team of Dave Fratantoni, Keith von der Heydt (WHOI), and Terry Hammar (WHOI). Construction of the first full AXIS prototype was supported by a technology grant from the National Science Foundation (OCE-0926853) and the second one through an NSF-funded (OCE-1061185) subcontract from the University of Rhode Island.2018-06-2

Graphene as an electronic membrane

Experiments are finally revealing intricate facts about graphene which go beyond the ideal picture of relativistic Dirac fermions in pristine two dimensional (2D) space, two years after its first isolation. While observations of rippling added another dimension to the richness of the physics of graphene, scanning single electron transistor images displayed prevalent charge inhomogeneity. The importance of understanding these non-ideal aspects cannot be overstated both from the fundamental research interest since graphene is a unique arena for their interplay, and from the device applications interest since the quality control is a key to applications. We investigate the membrane aspect of graphene and its impact on the electronic properties. We show that curvature generates spatially varying electrochemical potential. Further we show that the charge inhomogeneity in turn stabilizes ripple formation.Comment: 6 pages, 11 figures. Updated version with new results about the re-hybridization of the electronic orbitals due to rippling of the graphene sheet. The re-hybridization adds the next-to-nearest neighbor hopping effect discussed in the previous version. New reference to recent STM experiments that give support to our theor

Low Energy Electron Point Projection Microscopy of Suspended Graphene, the Ultimate "Microscope Slide"

Point Projection Microscopy (PPM) is used to image suspended graphene using low-energy electrons (100-200eV). Because of the low energies used, the graphene is neither damaged or contaminated by the electron beam. The transparency of graphene is measured to be 74%, equivalent to electron transmission through a sheet as thick as twice the covalent radius of sp^2-bonded carbon. Also observed is rippling in the structure of the suspended graphene, with a wavelength of approximately 26 nm. The interference of the electron beam due to the diffraction off the edge of a graphene knife edge is observed and used to calculate a virtual source size of 4.7 +/- 0.6 Angstroms for the electron emitter. It is demonstrated that graphene can be used as both anode and substrate in PPM in order to avoid distortions due to strong field gradients around nano-scale objects. Graphene can be used to image objects suspended on the sheet using PPM, and in the future, electron holography

An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations

We discuss model reduction for a particular class of quadratic-bilinear (QB) descriptor systems. The main goal of this article is to extend the recently studied interpolation-based optimal model reduction framework for QBODEs [Benner et al. '16] to a class of descriptor systems in an efficient and reliable way. Recently, it has been shown in the case of linear or bilinear systems that a direct extension of interpolation-based model reduction techniques to descriptor systems, without any modifications, may lead to poor reduced-order systems. Therefore, for the analysis, we aim at transforming the considered QB descriptor system into an equivalent QBODE system by means of projectors for which standard model reduction techniques for QBODEs can be employed, including aforementioned interpolation scheme. Subsequently, we discuss related computational issues, thus resulting in a modified algorithm that allows us to construct \emph{near}--optimal reduced-order systems without explicitly computing the projectors used in the analysis. The efficiency of the proposed algorithm is illustrated by means of a numerical example, obtained via semi-discretization of the Navier-Stokes equations

UNOLS Establishes SCOAR to Promote Research Aircraft Facilities for U.S. Ocean Sciences

Oceanography, Vol. 17, No. 4, pp. 176-185, December 2004

Buckling Thin Disks and Ribbons with Non-Euclidean Metrics

I consider the problem of a thin membrane on which a metric has been prescribed, for example by lithographically controlling the local swelling properties of a polymer thin film. While any amount of swelling can be accommodated locally, geometry prohibits the existence of a global strain-free configuration. To study this geometrical frustration, I introduce a perturbative approach. I compute the optimal shape of an annular, thin ribbon as a function of its width. The topological constraint of closing the ribbon determines a relationship between the mean curvature and number of wrinkles that prevents a complete relaxation of the compression strain induced by swelling and buckles the ribbon out of the plane. These results are then applied to thin, buckled disks, where the expansion works surprisingly well. I identify a critical radius above which the disk in-plane strain cannot be relaxed completely.Comment: 6 pages, 5 figures; lengthened to clarify previously confusing issues. To appear in EP