Higher Order Force Gradient Symplectic Algorithms

We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10 and 12, the new algorithms are approximately a factor of $10^3$, $10^4$, $10^4$ and $10^5$ better.Comment: 23 pages, 10 figure

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

Symplectic integrators for trajectory simulations

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references (leaves 34).Issued also on microfiche from Lange Micrographics.For Hamiltonians separable in the form H = T + V, the method of Creutz and Gocksch is used to construct even-order integrative that will preserve the invariants of motion. Several of these symplectic integrators of the same order are compared among themselves and to Runge-Kutta integrative as they are applied to the Kepler problem in celestial mechanics. Error terms indicative of the conservation laws inherent in the motion are derived and it is shown how they may be used to gauge the time- scale needed to achieve a desired precision from the computation. A new sixth- order symplectic integrator is discovered in which the energy error is two orders of magnitude less than existing sixth-order integrators

Symplectic integrators for trajectory simulations

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references (leaves 34).Issued also on microfiche from Lange Micrographics.For Hamiltonians separable in the form H = T + V, the method of Creutz and Gocksch is used to construct even-order integrative that will preserve the invariants of motion. Several of these symplectic integrators of the same order are compared among themselves and to Runge-Kutta integrative as they are applied to the Kepler problem in celestial mechanics. Error terms indicative of the conservation laws inherent in the motion are derived and it is shown how they may be used to gauge the time- scale needed to achieve a desired precision from the computation. A new sixth- order symplectic integrator is discovered in which the energy error is two orders of magnitude less than existing sixth-order integrators

Definition and evaluation of transient ischemic attack: a scientific statement for healthcare professionals from the American Heart Association/American Stroke Association Stroke Council; Council on Cardiovascular Surgery and Anesthesia; Council on Cardiovascular Radiology and Intervention; Council on Cardiovascular Nursing; and the Interdisciplinary Council on Peripheral Vascular Disease. The American Academy of Neurology affirms the value of this statement as an educational tool for neurologis

This scientific statement is intended for use by physicians and allied health personnel caring for patients with transient ischemic attacks. Formal evidence review included a structured literature search of Medline from 1990 to June 2007 and data synthesis employing evidence tables, meta-analyses, and pooled analysis of individual patient-level data. The review supported endorsement of the following, tissue-based definition of transient ischemic attack (TIA): a transient episode of neurological dysfunction caused by focal brain, spinal cord, or retinal ischemia, without acute infarction. Patients with TIAs are at high risk of early stroke, and their risk may be stratified by clinical scale, vessel imaging, and diffusion magnetic resonance imaging. Diagnostic recommendations include: TIA patients should undergo neuroimaging evaluation within 24 hours of symptom onset, preferably with magnetic resonance imaging, including diffusion sequences; noninvasive imaging of the cervical vessels should be performed and noninvasive imaging of intracranial vessels is reasonable; electrocardiography should occur as soon as possible after TIA and prolonged cardiac monitoring and echocardiography are reasonable in patients in whom the vascular etiology is not yet identified; routine blood tests are reasonable; and it is reasonable to hospitalize patients with TIA if they present within 72 hours and have an ABCD(2) score >or=3, indicating high risk of early recurrence, or the evaluation cannot be rapidly completed on an outpatient basis