Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- General Relativity (5)
- Differential Geometry (4)
- Computer Algebra (3)
- Einstein Field Equations (2)
- Algebraic computing (1)
-
- Computer Algebran (1)
- Correction (1)
- DifferentialGeometry (1)
- Einstein Maxwell equations (1)
- Einstein equations (1)
- Einstein-Maxwell Equations (1)
- Electrovacuum (1)
- Field Theory (1)
- Forecasting (1)
- Geo land sat (1)
- Gravitation (1)
- HWM14 (1)
- Image noise (1)
- Ionosphere (1)
- Isometry (1)
- K-meaning clusters (1)
- Killing Vector (1)
- Lie Algebra (1)
- Lie Algebras (1)
- Lie Groups (1)
- Lie algebras (1)
- Lorentzian Geometry (1)
- Maple (1)
- Mla (1)
- Modeling (1)
Articles 1 - 20 of 20
Full-Text Articles in Physical Sciences and Mathematics
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre
Downloads
This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.
A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre
A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre
Research Vignettes
No abstract provided.
What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre
What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre
Tutorials on... in 1 hour or less
This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.
Standard Non-Uniform Noise Dataset, Andres Imperial, John M. Edwards
Standard Non-Uniform Noise Dataset, Andres Imperial, John M. Edwards
Browse all Datasets
Fixed Pattern Noise Non-Uniformity Correction through K-Means Clustering
Fixed pattern noise removal from imagery by software correction is a practical approach compared to a physical hardware correction because it allows for correction post-capture of the imagery. Fixed pattern noise presents a unique challenge for de-noising techniques as the noise does not present itself where large number statistics are effective. Traditional noise removal techniques such as blurring or despeckling produce poor correction results because of a lack of noise identification. Other correction methods developed for fixed pattern noise can often present another problem of misidentification of noise. This problem can result …
Meps Data Assimilation System, Robert W. Schunk, Larry Gardner
Meps Data Assimilation System, Robert W. Schunk, Larry Gardner
Browse all Datasets
For the current funding opportunity we propose to develop a master system that will enhance the user interface to the MEPS model and enable the scientific community to efficiently use the model. Furthermore, we will build and automate validation tools and improve the efficiency and robustness of the MEPS ensemble averaging scheme. Finally, we will explore the nest step toward a major advancement in MEPS b significantly improving the spatial resolution of one of the data assimilation models to explore meso- and small-scale features.
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Publications
A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …
Data From: Polar Topside Ionosphere During Geomagnetic Storms: Comparison Of Isis-Ii With Tdim, Jan J. Sojka, Dan Rice, Michael David, Robert W. Schunk, Robert Benson, H. G. James
Data From: Polar Topside Ionosphere During Geomagnetic Storms: Comparison Of Isis-Ii With Tdim, Jan J. Sojka, Dan Rice, Michael David, Robert W. Schunk, Robert Benson, H. G. James
Browse all Datasets
Output files from runs of the TDIM ionospheric model used for calculations and electron density profiles from ISIS-II and TDIM used in figures in the article in Radio Science.
How To Make Tetrads, Charles G. Torre
How To Make Tetrads, Charles G. Torre
How to... in 10 minutes or less
This is a worksheet which demonstrates tools for creating orthonormal and null tetrads for a given spacetime.
Symmetric Criticality In General Relativity, Charles G. Torre
Symmetric Criticality In General Relativity, Charles G. Torre
Research Vignettes
In this worksheet I explore the local Lagrangian version of the Principle of Symmetric Criticality (PSC) due to Anderson, Fels, and Torre], which asserts the commutativity of the processes (i) of symmetry reduction (for finding group-invariant fields) and (ii) forming Euler-Lagrange equations. There are two obstructions to PSC, which I will call the Lie algebra obstruction and the isotropy obstruction. In this worksheet I will illustrate these obstructions in the General Theory of Relativity.
Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre
Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre
Tutorials on... in 1 hour or less
In this worksheet I demonstrate three versions of Birkhoff's theorem, which is a characterization of spherically symmetric solutions of the Einstein equations. The three versions considered here correspond to taking the "Einstein equations" to be: (1) the vacuum Einstein equations; (2) the Einstein equations with a cosmological constant (3) the Einstein-Maxwell equations. I will restrict my attention to 4-dimensional spacetimes.
Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre
Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre
Tutorials on... in 1 hour or less
This is a Maple worksheet providing an introduction to the USU Library of Solutions to the Einstein Field Equations. The library is part of the DifferentialGeometry software project and is a collection of symbolic data and metadata describing solutions to the Einstein equations.
Perihelion Precession In The General Theory Of Relativity, Charles G. Torre
Perihelion Precession In The General Theory Of Relativity, Charles G. Torre
Tutorials on... in 1 hour or less
This is a relatively quick and informal sketch of a demonstration that general relativistic corrections to the bound Kepler orbits introduce a perihelion precession. Any decent textbook on the general theory of relativity will derive this result. My analysis aligns with that found in the good old text "Introduction to General Relativity", by Adler, Bazin and Schiffer.
Data From: How Uncertainty In The Neutral Wind Limits The Accuracy Of Ionospheric Modeling And Forecasting, Michael David, Jan Sojka, Robert W. Schunk
Data From: How Uncertainty In The Neutral Wind Limits The Accuracy Of Ionospheric Modeling And Forecasting, Michael David, Jan Sojka, Robert W. Schunk
Browse all Datasets
Output files from runs of the TDIM ionospheric model used for the figures and calculations in the article in JGR Space Physics.
The Kretschmann Scalar, Charles G. Torre
The Kretschmann Scalar, Charles G. Torre
How to... in 10 minutes or less
On a pseudo-Riemannian manifold with metric g, the "Kretschmann scalar" is a quadratic scalar invariant of the Riemann R tensor of g, defined by contracting all indices with g. In this worksheet we show how to calculate the Kretschmann scalar from a metric.
Differentialgeometry In Brno, Ian M. Anderson
Differentialgeometry In Brno, Ian M. Anderson
Presentations
This page will provide files supporting Ian Anderson's presentations in Brno, December 2015. The files can be found and downloaded from "Additional Files", below.
The files include:
(1) DifferentialGeometryUSU.mla: This is the Maple Library Archive file which provides all the DifferentialGeometry functionality. Here are Installation Instructions.
(2) DifferentialGeometry.help : this is the latest version of the DifferentialGeometry documentation. Copy this file to the same directory used for DifferentialGeometryUSU.mla (from step (1)).
Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre
Rainich-Type Conditions For Perfect Fluid Spacetimes, Dionisios Krongos, Charles G. Torre
Research Vignettes
In this worksheet we describe and illustrate a relatively simple set of new Rainich-type conditions on an n-dimensional spacetime which are necessary and sufficient for it to define a perfect fluid solution of the Einstein field equations. Procedures are provided which implement these Rainich-type conditions and which reconstruct the perfect fluid from the metric. These results provide an example of the idea of geometrization of matter fields in general relativity, which is a purely geometrical characterization of matter fields via the Einstein field equations.
Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
Research Vignettes
In this second of two worksheets I continue describing local Rainich-type conditions which are necessary and sufficient for the metric to define a null electrovacuum. In other words, these conditions, which I will call the null electrovacuum conditions, guarantee the existence of a null electromagnetic field such that the metric and electromagnetic field satisfy the Einstein-Maxwell equations. When it exists, the electromagnetic field is easily constructed from the metric. In this worksheet I consider the null electrovacuum conditions which apply when a certain null geodesic congruence determined by the metric is twisting. I shall illustrate the these conditions using a …
Gr 20 Workshop, Warsaw, July 2013, Ian M. Anderson, Charles G. Torre
Gr 20 Workshop, Warsaw, July 2013, Ian M. Anderson, Charles G. Torre
Presentations
These are the Maple worksheets used at the Differential Geometry in Maple Workshop, which was held at the 20th International Conference on General Relativity and Gravitation, in Warsaw, July 2013.
There are 6 worksheets which can be downloaded from the list of files below.
Rainich-Type Conditions For Null Electrovacuum Spacetimes I, Charles G. Torre
Rainich-Type Conditions For Null Electrovacuum Spacetimes I, Charles G. Torre
Research Vignettes
In this worksheet I describe local Rainich-type conditions on a spacetime geometry which are necessary and sufficient for the existence of a solution of the Einstein-Maxwell equations with a null electromagnetic field. When it exists, the electromagnetic field is easily constructed.
How To Find Killing Vectors, Charles G. Torre
How To Find Killing Vectors, Charles G. Torre
How to... in 10 minutes or less
We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.