504 research outputs found
Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates
The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q)
for the numerical solution of initial value problems for ordinary differential
equations are based on piecewise polynomial approximation of degree q on
partitions in time with time steps which may vary for different components of
the computed solution. In this paper, we prove general order a priori error
estimates for the mcG(q) and mdG(q) methods. To prove the error estimates, we
represent the error in terms of a discrete dual solution and the residual of an
interpolant of the exact solution. The estimates then follow from interpolation
estimates, together with stability estimates for the discrete dual solution
Explicit Time-Stepping for Stiff ODEs
We present a new strategy for solving stiff ODEs with explicit methods. By
adaptively taking a small number of stabilizing small explicit time steps when
necessary, a stiff ODE system can be stabilized enough to allow for time steps
much larger than what is indicated by classical stability analysis. For many
stiff problems the cost of the stabilizing small time steps is small, so the
improvement is large. We illustrate the technique on a number of well-known
stiff test problems
A palaeoenvironmental analysis of the archaean moodies group, Barberton mountain land, South Africa.
Near-Infrared Classification Spectroscopy: H-band Spectra of Fundamental MK Standards
We present a catalogue of H-band spectra for 85 stars of approximately solar
abundance observed at a resolving power of 3000 with the KPNO Mayall 4m FTS.
The atlas covers spectral types O7-M5 and luminosity classes I-V as defined on
the MK system. We identify both atomic and molecular indices and line-ratios
which are temperature and luminosity sensitive allowing spectral classification
to be carried out in the H-band. The line ratios permit spectral classification
in the presence of continuum excess emission, which is commonly found in
pre-main sequence and evolved stars. We demonstrate that with spectra of R =
1000 obtained at SNR > 50 it is possible to derive spectral types within +- 2
subclasses for late-type stars. These data are available electronically through
the Astronomical Data Center in addition to being served on the World-Wide-Web.Comment: To appear in the November 20, 1998 issue of ApJ (Volume 508, #1
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Quantum Simulators: Architectures and Opportunities
Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behavior to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the National Science Foundation workshop on “Programmable Quantum Simulators,” that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multidisciplinary collaborations with resources for quantum simulator software, hardware, and education.This document is a summary from a U.S. National Science Foundation supported workshop held on 16–17 September 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum simulators over the next 2–5 years
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