639 research outputs found
On the ADI method for the Sylvester Equation and the optimal- 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
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