Physics Commons^™

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.

Geometrization Conditions For Perfect Fluids, Scalar Fields, And Electromagnetic Fields, Charles G. Torre, Dionisios Krongos

Charles G. Torre

Rainich-type conditions giving a spacetime “geometrization” of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and electromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equations are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Geometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einstein-scalar field equations and formulas for constructing the scalar field from …

A Solution In Weyl Gravity With Planar Symmetry, James Thomas Wheeler

James Thomas Wheeler

We solve the Bach equation for Weyl gravity for the case of a static metric with planar symmetry. The solution is not conformal to the solution to the corresponding Einstein equation.

The Spacetime Co-Torsion In Torsion-Free Biconformal Spaces, James Thomas Wheeler

James Thomas Wheeler

In preceding studies, [TR Gamma minus, TR Gamma plus] we showed that the solution for the connection of flat biconformal space also solves the curved space field equations for the torsion and co-torsion. We continued this investigation with an attempt to solve the full set of torsion and co-torsion field equations, with only the assumption of vanishing torsion and the known form of the metric. We successfully reduced the torsion equations to a single equation. Here, we reduce that equation to its essential degrees of freedom. We find that the spacetime co-torsion is entirely determined by the scale vector and …

Variation Of The Weyl Action, James Thomas Wheeler

James Thomas Wheeler

We show how to vary the fourth order Weyl gravity action to derive the Bach equation.

Torsion Free Biconformal Spaces: Reducing The Torsion Field Equations, James Thomas Wheeler

James Thomas Wheeler

Our goal is to solve the full set of torsion and co-torsion field equations of Euclidean biconformal space, with only the assumption of vanishing torsion. Here we begin by resolving the involution constraints, symmetry conditions and torsion field equation into a single equation for further study.

Gauge Theories Of General Relativity, James Thomas Wheeler

James Thomas Wheeler

General relativity can be seen as a gauge theory of the Lorentz, Poincaré, Weyl, de Sitter, or conformal groups. In most of these, there is little or no difference from the standard formulation in Riemannian geometry, but the higher symmetries — de Sitter and conformal — introduce new features and explain old ones. The potential presence of a cosmological constant, the spacetime metric, cosmological dust, symplectic structure, Kähler structure and even the existence of a timelike direction can all be seen to arise from the underlying group structure.

Weyl Gravity As General Relativity, James Thomas Wheeler

James Thomas Wheeler

When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.

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 …

The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre

Charles G. Torre

We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …

Effect Of Sudden Stratospheric Warmingon Lunar Tidal Modulation Of The Equatorial Electrojet, J. Park, H. Luhr, M. Kunze, Bela G. Fejer, K. W. Min

Bela G. Fejer

[1] Using the equatorial electrojet (EEJ) peak current intensity as deduced from CHAMP magnetic observations from the years 2001 through 2009, we investigated the relationship between sudden stratospheric warming (SSW) and lunitidal signatures in the tropical ionosphere. There is a practically one-to-one correspondence between midwinter SSW periods and the strongest 13 day modulation of the EEJ strength as observed by CHAMP. That is, all the midwinter SSW periods from December 2001 to August 2009 were accompanied by an enhanced 13 day modulation of the EEJ strength. No other geophysical phenomenon brought about as strong a 13 day modulation as those …

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 …

The Density Factor In The Synthesis Of Carbon Nanotube Forest By Injection Chemical Vapor Deposition, R. W. Call, C. G. Read, C. Mart, T. -C. Shen

T. -C. Shen

Beneath the seeming straight-forwardness of growing carbon nanotube(CNT) forests by the injection chemical vapor deposition(CVD) method, control of the forest morphology on various substrates is yet to be achieved. Using ferrocene dissolved in xylene as the precursor, we demonstrate that the concentration of ferrocene and the injection rate of the precursor dictate the CNT density of these forests. However, CNT density will also be affected by the substrates and the growth temperature which determine the diffusion of the catalyst adatoms. The CNT growth rate is controlled by the temperature and chemical composition of the gases in the CVD reactor. We …

Observations Of The Vertical Ion Drift In The Equatorial Ionosphere During The Solar Minimum Period Of 2009, R. A. Stoneback, R. A. Heelis, A. G. Burrell, W. R. Coley, Bela G. Fejer, E. Pacheco

Bela G. Fejer

[1] The extended solar minimum conditions in 2008 and 2009 presented an opportunity to investigate the ionosphere at lower solar activity levels than previously observed. The Coupled Ion Neutral Dynamics Investigation (CINDI) Ion Velocity Meter (IVM) instrument onboard the Communication/Navigation Outage Forecasting System is used to construct the median meridional (vertical) ion drifts, ion densities, and O+ concentrations during periods of low geomagnetic activity for four characteristic seasons each year spanning late 2008 to 2010. The presence of a large semidiurnal component in the ion drift variation at the equator produced significant differences from typical ionospheric conditions. Instead of upward …

Enhanced Lunar Semidiurnal Equatorial Vertical Plasma Drifts During Sudden Stratospheric Warmings, Bela G. Fejer, B. D. Tracy, J. L. Chau

Bela G. Fejer

[1] Large scale electrodynamic and plasma density variations in the low latitude ionosphere have recently been associated with sudden stratospheric warming (SSW) events. We present average patterns of largely enhanced lunar semidiurnal equatorial vertical plasma drift perturbations during arctic winter low and high solar flux SSW events. These perturbations play a dominant role in the electrodynamic response of the low latitude ionosphere to SSWs. Our models indicate that the amplitudes of the enhanced lunar semidiurnal drifts are strongly local time and solar flux dependent, with largest values during early morning low solar flux SSW periods. These results suggest that ionospheric …

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 …

New Symbolic Tools For Differential Geometry, Gravitation, And Field Theory (Extended Version), Charles G. Torre, Ian M. Anderson

Charles G. Torre

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors and other tensorial invariants, algebraic classification of curvature, and …

Symmetric Criticality In Classical Field Theory, Charles G. Torre

Charles G. Torre

This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais’ Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group-invariant Lagrangian by the symmetry group yields the correct symmetry-reduced Euler-Lagrange equations.

Duskside F-Region Dynamo Currents: Itsrelationship With Prereversal Enhancement Of Vertical Plasma Drift, P. Park, H. Luhr, Bela G. Fejer, K. W. Mim

Bela G. Fejer

From magnetic field observations by CHAMP we estimate F-region dynamo current densities near the sunset terminator during solar maximum years from 2001 to 2002. The dynamo currents are compared with the pre-reversal enhancement (PRE) of vertical plasma drift as observed by ROCSAT-1. The seasonal-longitudinal variation of PRE can be largely related to the F-region dynamo current density, with the correlation coefficient reaching 0.74. The correlation can be further improved if we consider a zonal gradient of the E-region Pedersen conductivity, which also depends on season and longitude. It is widely accepted that the Fregion dynamo drives PRE near sunset. For …

Lunar Dependent Equatorial Ionospheric Effects During Sudden Stratosphericwarmings, Bela G. Fejer, M. E. Olson, J. L. Chau, C. Stolle, H. Luhr, L. P. Goncharenko, K. Yumoto, T. Nagatsuma

Bela G. Fejer

[1] We have used plasma drift and magnetic field measurements during the 2001–2009 December solstices to study, for the first time, the longitudinal dependence of equatorial ionospheric electrodynamic perturbations during sudden stratospheric warmings. Jicamarca radar measurements during these events show large dayside downward drift (westward electric field) perturbations followed by large morning upward and afternoon downward drifts that systematically shift to later local times. Ground-based magnetometer measurements in the American, Indian, and Pacific equatorial regions show strongly enhanced electrojet currents in the morning sector and large reversed currents (i.e., counterelectrojets) in the afternoon sector with onsets near new and full …

Quiet Variability Of Equatorial E × B Drifts During A Sudden Stratospheric Warning Event, J. L. Chau, Bela G. Fejer, L. P. Goncharenko

Bela G. Fejer

[1] We present strong evidence that during the January 2008 minor sudden stratospheric warming (SSW) event, the equatorial vertical E × B drifts exhibit a unique and distinctive daytime pattern. We do not think one event causes the other, however both events might be related through the global effects of planetary waves. The drifts were measured by the Jicamarca Incoherent scatter radar located under the magnetic equator. We have observed an anomalous temporal variation of the vertical E × B drifts during the minor SSW event, showing a semidiurnal variation with very large amplitudes lasting for several days. Large differences …

Climatology Of Early Night Equatorial Spread F Over Jicamarca, N. P. Chapagain, Bela G. Fejer

Bela G. Fejer

[1] We use radar observations from 1996 to 2006 to study the climatology of postsunset equatorial 3-m spread F irregularities over Jicamarca during all seasons. We show that the spread F onset times do not change with solar flux and that their onset heights, which occur near the altitude of the evening F region velocity vortex, increase linearly from about 260 to 400 km from solar minimum to solar maximum. Higher onset heights generally lead to stronger radar echoes. During the equinox, spread F onset occurs near vertical drift evening reversal times, while during the December solstice, they occur near …

Overviewand Summary Of The Spread F Experiment (Spreadfex), D. C. Fritts, M. A. Abdu, B. R. Batista, I. S. Batista, P. P. Batista, R. Buritii, B. R. Clemesha, J. Comberiate, T. Dautermann, E. De Paula, B. J. Fechine, Bela G. Fejer, D. Gobbi, J. Haase, F. Kalamabadi, B. Laughman, P. P. Lima, H. L. Liu, A. Medeiros, D. Pautet, F. Sao Sabbas, J. H.A. Sobral, P. Stamus, H. Takahashi, M. J. Taylor, S. L. Vadas, C. Wrasse

Bela G. Fejer

We provide here an overview of, and a summary of results arising from, an extensive experimental campaign (the Spread F Experiment, or SpreadFEx) performed from September to November 2005, with primary measurements in Brazil. The motivation was to define the potential role of neutral atmosphere dynamics, specifically gravity wave motions propagating upward from the lower atmosphere, in seeding Rayleigh-Taylor instability (RTI) and plasma bubbles extending to higher altitudes. Campaign measurements focused on the Brazilian sector and included ground-based optical, radar, digisonde, and GPS measurements at a number of fixed and temporary sites. Related data on convection and plasma bubble structures …

Gathering Leadership Momentum Across Great Distances: Creating An Online Community Of Practice, Erin L. Davis, Danielle Theiss-White

Erin Davis

At the 2007 Mountain Plains Library Association Leadership (MPLA) Institute, held in New Mexico, USA, eight academic librarians formed an online multi-state, multigenerational community of practice. MPLA is a twelve-state library association within the United States. Using Google Groups™, the members formed an online environment called the MPLA Community of Practice for continuing development of the leadership skills presented at the Institute. These early-career librarians represent diverse educational backgrounds and work in libraries serving varied populations with differing disciplinary emphases.

The group meets monthly with each member preparing and facilitating online discussions, complete with personal assessments, topical readings, and questions. …

Seasonal And Longitudinal Dependence Of Equatorialdisturbance Vertical Plasma Drifts, Bela G. Fejer, J. W. Jensen, S. Y. Su

Bela G. Fejer

[1] We used equatorial measurements from the ROCSAT-1 satellite to determine the seasonal and longitudinal dependent equatorial F region disturbance vertical plasma drifts. Following sudden increases in geomagnetic activity, the prompt penetration vertical drifts are upward during the day and downward at night, and have strong local time dependence at all seasons. The largest prompt penetration drifts near dusk and dawn occur during June solstice. The daytime disturbance dynamo drifts are small at all seasons. They are downward near dusk with largest (smallest) values during equinox (June solstice); the nighttime drifts are upward with the largest magnitudes in the postmidnight …

Quiet Time Equatorial F Region Vertical Plasma Drift Model Derived From Rocsat-1 Observations, Bela G. Fejer, J. W. Jensen, S. Y. Su

Bela G. Fejer

[1] We have used five years of measurements on board the ROCSAT-1 satellite to develop a detailed quiet time global empirical model for equatorial F region vertical plasma drifts. This model describes the local time, seasonal and longitudinal dependence of the vertical drifts for an altitude of 600 km under moderate and high solar flux conditions. The model results are in excellent agreement with measurements from the Jicamarca radar and also from other ground-based and in situ probes. We show that the longitudinal dependence of the daytime and nighttime vertical drifts is much stronger than reported earlier, especially during December …

F3 Layerduring Penetration Electric Field, N. Balan, H. Alleyne, S. V. Thampi, K. Lynn, Y. Otsuka, Bela G. Fejer, M. A. Abdu

Bela G. Fejer

[1] The occurrence of an additional layer, called F3 layer, in the equatorial ionosphere at American, Indian, and Australian longitudes during the super double geomagnetic storm of 7–11 November 2004 is presented using observations and modeling. The observations show the occurrence, reoccurrence, and quick ascent to the topside ionosphere of unusually strong F3 layer in Australian longitude during the first super storm (8 November) and in Indian longitude during the second super storm (10 November), all with large reductions in peak electron density (Nmax) and total electron content (GPS-TEC). The unusual F3 layers can arise mainly from unusually strong fluctuations …

Relation Between The Occurrence Rate Of Esf And The Verticalplasma Drift Velocity At Sunset Derived Form Global Observations, C. Stolle, H. Luhr, Bela G. Fejer

Bela G. Fejer

In this study, we investigate two global climatological data sets; the occurrence rate of Equatorial Spread- F (ESF), associated with equatorial plasma irregularities, at 400 km altitude obtained from CHAMP observations, and the evening equatorial vertical plasma drift, vz, from ROCSAT-1 measurements. First, as retrieved for a solar flux level of F10.7=150, the longitudinal variation of the two independently derived quantities correlates between 84% and 93% in the seasons December solstice, equinox and June solstice. The highest correlation is found for the solstice seasons when vz is integrated over local time around the prereversal enhancement (PRE) and displaced 6 towards …

Gravity Wave And Tidalinfluences On Equatorial Spread F Based On Observations During The Spread F Experiment(Spreadfex), D. C. Fritts, S. L. Vadas, D. M. Riggin, M. A. Abdu, I. S. Batista, H. Takahashi, A. Medeiros, F. Kalamabadi, H. L. Liu, Bela G. Fejer, M. J. Taylor, F. Vargas

Bela G. Fejer

The Spread F Experiment, or SpreadFEx, was performed from September to November 2005 to define the potential role of neutral atmosphere dynamics, primarily gravity waves propagating upward from the lower atmosphere, in seeding equatorial spread F (ESF) and plasma bubbles extending to higher altitudes. A description of the SpreadFEx campaign motivations, goals, instrumentation, and structure, and an overview of the results presented in this special issue, are provided by Fritts et al. (2008a). The various analyses of neutral atmosphere and ionosphere dynamics and structure described in this special issue provide enticing evidence of gravity waves arising from deep convection in …

Equatorial Ionospheric Electric Fields During The November 2004 Magnetic Storm, Bela G. Fejer, J. W. Jensen, T. Kikuchi, M. A. Abdu, J. L. Chau

Bela G. Fejer

[1] We use radar measurements from the Jicamarca Radio Observatory, magnetometer observations from the Pacific sector and ionosonde data from Brazil to study equatorial ionospheric electric fields during the November 2004 geomagnetic storm. Our data show very large eastward and westward daytime electrojet current perturbations with lifetimes of about an hour (indicative of undershielding and overshielding prompt penetration electric fields) in the Pacific equatorial region during the November 7 main phase of the storm, when the southward IMF, the solar wind and reconnection electric fields, and the polar cap potential drops had very large and nearly steady values. This result …