Applied Mathematics Commons^™

Foundations Of Wave Phenomena: Complete Version, Charles G. Torre

Foundations of Wave Phenomena

This is the complete version of Foundations of Wave Phenomena. Version 8.3.1.

Please click here to explore the components of this work.

Introduction To Classical Field Theory, Charles G. Torre

All Complete Monographs

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

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.

Installation instructions

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 …

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.

Foundations Of Wave Phenomena, Charles G. Torre

Charles G. Torre

This is an undergraduate text on the mathematical foundations of wave phenomena. Version 8.2.

On The Propagation Of Atmospheric Gravity Waves In A Non-Uniform Wind Field: Introducing A Modified Acoustic-Gravity Wave Equation, Ahmad Talaei

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Atmospheric gravity waves play fundamental roles in a broad-range of dynamical processes extending throughout the Earth’s neutral atmosphere and ionosphere. In this paper, we present a modified form for the acoustic-gravity wave equation and its dispersion relationships for a compressible and non-stationary atmosphere in hydrostatic balance. Importantly, the solutions have been achieved without the use of the well-known Boussinesq approximation which have been used extensively in previous studies.

We utilize the complete set of governing equations for a compressible atmosphere with non-uniform airflows to determine an equation for vertical velocity of possible atmospheric waves. This intricate wave equation is simplified …

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.

Vector Spaces (Appendix B), Charles G. Torre

Foundations of Wave Phenomena

Throughout this text we have noted that various objects of interest form a vector space. Here we outline the basic structure of a vector space. You may find it useful to refer to this Appendix when you encounter this concept in the text.

Taylor’S Theorem And Taylor Series (Appendix A), Charles G. Torre

Foundations of Wave Phenomena

Taylor’s theorem and Taylor’s series constitute one of the more important tools used by mathematicians, physicists and engineers. They provides a means of approximating a function in terms of polynomials.

References And Suggestions For Further Reading (Appendix C), Charles G. Torre

Foundations of Wave Phenomena

References and Suggestions for Further Reading (Appendix C)

Perihelion Precession In General Relativity, Charles G. Torre

Charles G. Torre

This is a Maple worksheet providing 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 will derive this result. My analysis aligns with that found in the old text "Introduction to General Relativity", by Adler, Bazin and Schiffer. The plan of the analysis is as follows. * Model the planetary orbits as geodesics in the (exterior) Schwarzschild spacetime. * Compute the geodesic equations. * Simplify them using symmetries and first integrals. * Isolate the differential equation expressing the radial coordinate as a function of …

Schematics Of A Water Balloon Launcher Design And Reproducible Water-Balloon-Filling Procedures Used For A Middle School Summer Science Camp, Mike A. Christiansen, Boyd F. Edwards, David D. Sam

USU Uintah Basin Faculty Publications

We recently held a Science Summer Camp for middle school students, designed to infuse young people with increased excitement for STEM (Science, Technology, Engineering, and Math) subjects. Our efforts, which received nationally-syndicated news coverage, included the invention of a versatile water balloon launcher.

This document contains:

(1) detailed construction schematics and user operation guidelines for our balloon launcher;

(2) data and instructions for reproducibly filling water balloons to specific volumes and weights, within used by students during the summer camp.

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.

How To Create A Two-Component Spinor, Charles G. Torre

How to... in 10 minutes or less

Let (M, g) be a spacetime, i.e., a 4-dimensional manifold M and Lorentz signature metric g. The key ingredients needed for constructing spinor fields on the spacetime are: a complex vector bundle E -> M ; an orthonormal frame on TM ; and a solder form relating sections of E to sections of TM (and tensor products thereof). We show how to create a two-component spinor field on the Schwarzschild spacetime using the DifferentialGeometry package in Maple. PDF and Maple worksheets can be downloaded from the links below.

Investigating Mountain Waves In Mtm Image Data At Cerro Pachon, Chile, Neal R. Criddle, M. J. Taylor, P.-D. Pautet, Y. Zhao, G. Swenson, A. Liu

Neal R Criddle

Gravity waves are important drivers of chemical species mixing, energy and momentum transfer into the MLT (~80 - 100 km) region. As part of a collaborative program involving instruments from several institutions Utah State University has operated a Mesospheric Temperature Mapper (MTM) at the new Andes Lidar Observatory (ALO) on Cerro Pachon (30.2°S, 70.7°W) Since August 2009. A primary goal of this program is to quantify the impact of mountain waves on the MLT region. The Andes region is an excellent natural laboratory for investigating gravity wave influences on the MLT region, especially the study of mountain waves, created by …

Seasonal Variability And Dynamics Of Mesospheric Gravity Waves Over The Andes, Neal R. Criddle, M. J. Taylor, P.-D. Pautet, Y. Zhao

Neal R Criddle

The ALO is a new facility developed for atmospheric research, located at the foot of the Andes mountain range in Cerro Pachon, Chile (30.2°S, 70.7°W). As part of a collaborative program, Utah State has a Mesospheric Temperature Mapper (MTM) on site, which is used to study short period gravity wave dynamics and temperature variations in the mesosphere-lower thermosphere region. The MTM began taking measurements of the OH(6,2) and O2(0,1) spectral bands in August 2009 and a complete profile of seasonal variation in gravity wave characteristics has been created for August 2009 through August 2010 using the OH(6,2) Band. The primary …