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Articles 5131 - 5160 of 7341

Full-Text Articles in Physical Sciences and Mathematics

Ab Initio Study Of Intermolecular Potential Of H2o Trimer, G. Chalasinski, M. M. Szczesniak, P. Cieplak, Steve Scheiner Jan 1991

Ab Initio Study Of Intermolecular Potential Of H2o Trimer, G. Chalasinski, M. M. Szczesniak, P. Cieplak, Steve Scheiner

Chemistry and Biochemistry Faculty Publications

Nonadditive contribution to the interaction energy in water trimer is analyzed in terms of Heitler–London exchange, SCF deformation, induction and dispersion nonadditivities. Nonadditivity originates mainly from the SCF deformation effect which is due to electric polarization. However, polarization does not serve as a universal mechanism for nonadditivity in water. In the double‐donor configuration, for example, the Heitler–London exchange contribution is the most important and polarization yields the wrong sign. Correlation effects do not contribute significantly to the nonadditivity. A detailed analysis of the pair potential is also provided. The present two‐body potential and its components are compared to the existing …


Extension Of The Metal Light Pipe Infrared Spectroscopy Technique: Applications To Surface Adsorption And High Tc Superconductors, Torsten Will Dec 1990

Extension Of The Metal Light Pipe Infrared Spectroscopy Technique: Applications To Surface Adsorption And High Tc Superconductors, Torsten Will

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The development of an infrared instrument for the study of surface adsorption and high Tc superconductors is presented and its applicability is discussed. The use of and theoretical background for the metal light pipe multiple-reflection technique are discussed in comparison to other infrared devices. Measurements are carried out to determine its limitations with powdered substrates as well as its sensitivity limitation for thin films. The results of the two test measurements, adsorption of CO on MgO and investigation of the energy gap of high Tc superconductors, are presented. Comparisons of the spectra with the experimental and theoretical literature …


Fresnel And Fraunhofer Diffraction: Development Of An Advanced Laboratory Experiment, Jeff Adams Dec 1990

Fresnel And Fraunhofer Diffraction: Development Of An Advanced Laboratory Experiment, Jeff Adams

Senior Theses and Projects

The purpose of this lab is to help the student become more familiar with, or get a better feel for what is actually occurring, when observing the effects of double slit diffraction patterns. In most sophomore labs dealing with double slit diffraction, the student simply determines the diffraction angle, and slit spacing, from marking the positions of the maxima on the screen. No attempt is made to measure the relative intensity of the interference pattern, and see how the experimental data compare with the theory of interference and diffraction. In an attempt to further clarify this phenomena, we will attempt …


A Loading Device For Fracture Testing Of Compact Tension Specimens In The Scanning Electron Microscope, Jügen Rödel, James F. Kelly, Mark R. Stoudt, Stephen J. Bennison Oct 1990

A Loading Device For Fracture Testing Of Compact Tension Specimens In The Scanning Electron Microscope, Jügen Rödel, James F. Kelly, Mark R. Stoudt, Stephen J. Bennison

Scanning Microscopy

A loading device for performing fracture experiments on compact tension specimens in the SEM has been designed. Its key elements are a piezoelectric translator for applying controlled displacements to the loading points on the specimen and a load cell to measure applied loads. The effective transmission of displacement from the piezoelectric driver to the specimen was found to be the major mechanical design problem. The peripheral equipment includes a function generator and a high voltage amplifier that drives the piezoelectric translator as well as a video overlay and standard video equipment to record the image continuously during the course of …


Superfund Record Of Decision: Monticello Mill Tailings (Doe), Ut First Remedial Action, U.S. Environmental Protection Agency, Office Of Emergency And Remedial Response Aug 1990

Superfund Record Of Decision: Monticello Mill Tailings (Doe), Ut First Remedial Action, U.S. Environmental Protection Agency, Office Of Emergency And Remedial Response

All U.S. Government Documents (Utah Regional Depository)

The 300-acre Monticello Mill Tailings site is comprised of a 7S-acre inactive uranium and vanadium milling operation and affected peripheral properties in Monticello, San Juan County, Utah. Surrounding land use is rural residential and agricultural. The site overlies a shallow alluvial aquifer, and part of the site lies within the floodplain of Montezuma Creek. Approximately IS-acres of wetlands adjacent to Montezuma Creek also have been contaminated by tailings. In 1940, the site was operated as a vanadium ore-buying station. Milling of ore began in 1942, and a vanadium/uranium sludge product was produced onsite from 1943 to 1944. Onsite uranium milling …


Chemical And Reconstruction Induced Surface Core-Level Shifts: H On Low-Index W Surfaces, D. Mark Riffe, G. K. Wertheim, P. H. Citrin Jul 1990

Chemical And Reconstruction Induced Surface Core-Level Shifts: H On Low-Index W Surfaces, D. Mark Riffe, G. K. Wertheim, P. H. Citrin

All Physics Faculty Publications

The H-induced shift of the surface-atom core-level binding energy in W(110) is shown to arise from two distinct effects, one chemical in nature and the other structural. The structural shift supports a recently proposed (1p×1) reconstruction that turns on at ∼0.5 monolayer coverage. These new findings are used to provide a self-consistent interpretation of previously reported shifts from H-covered W(111) and W(100) surfaces.


Research Project Summaries (July 1989-December 1990), Utah Water Research Laboratory Jul 1990

Research Project Summaries (July 1989-December 1990), Utah Water Research Laboratory

Reports

From every side we hear of new threats to our water supply. Carcinogens, droughts, dam failures, global warming, hazardous wastes, deforestation, overpopulation, liability, and an aging infrastructure become household fears; this list grows longer and more foreboding to the average citizen. Some of these threats are real, while others are imaginary. Some we know how to overcome and others we can find ways to overcome, yet, for some, we are still helpless. The strength of a university lies in its success in stimulating inquisitive minds in critical examination of the problems of the world. People sense hope as experts find …


The Daytime Wind In Valleys Adjacent To The Great Salt Lake, G. L. Stone, D. Hoard Jun 1990

The Daytime Wind In Valleys Adjacent To The Great Salt Lake, G. L. Stone, D. Hoard

All U.S. Government Documents (Utah Regional Depository)

In 1986 Los Alamos National Laboratory was engaged by the US Army to study the meteorological aspects of emergency preparedness at several sites where toxic materials are stored and handled. The project included a series of tracer and meteorological field experiments in the vicinity of the Tooele Army Depot, 60 km southwest of Salt Lake City, Utah. These experiments generated a large data set for validating numerical simulations and for empiracal analyses of the local meteorology. This paper discusses the main characteristics of the daytime, up-valley flow at the Utah site, including frequency of occurrence, horizontal and vertical structure, and …


Mars And Beyond: The Solar System Beckons, Frank J. Redd May 1990

Mars And Beyond: The Solar System Beckons, Frank J. Redd

Faculty Honor Lectures

To space zealots, 1989 was the year the drought ended. The space shuttle was operational again; Voyager's grand reconnaissance of the Solar System climaxed with the glorious encounter with the planet Neptune and its startling moon, Triton; the launches of the Magellan spacecraft to Venus and the Gallileo to Jupiter broke a decade long hiatus in the launch of U.S. planetary missions; and, for the first time in over twenty years, a U.S. president announced a daring new initiative in human exploration with the goal of first returning humans to the Moon, then going on to Mars.


Laramide Deformation In Precambrian Granitic Rocks, Northeastern Wind River Range, Wyoming, Mark A. Dubois May 1990

Laramide Deformation In Precambrian Granitic Rocks, Northeastern Wind River Range, Wyoming, Mark A. Dubois

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Fractures and faults in the Jakey's Fork area, northeastern Wind River Range, Wyoming, caused by brittle Laramide deformation in the Precambrian granitic basement have been studied in detail at airphoto, outcrop, and thin-section scales. The study area is bounded on the south by the approximately east-west and vertical Jakey's Fork Fault and on the east by the approximately northwest-southeast and vertical Ross Lakes Fault. Both were active during Laramide deformation. Four distinct structural domains, defined by fracture pat terns and proximity to the two major faults nave emerged in this study. The areas are: 1) Along Ross Lakes Fault granite …


The Effects Of Disease, Prey Fluctuation, And Clear-Cutting On American Marten In Newfoundland, Canada, Richard J. Fredrickson May 1990

The Effects Of Disease, Prey Fluctuation, And Clear-Cutting On American Marten In Newfoundland, Canada, Richard J. Fredrickson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Individual variation in survival and behavior of American marten (Martes americana) was studied in relation to disease, prey fluctuation, and clear-cutting from 10 January 1986 through 20 August 1987 in Newfoundland, Canada. Thirty-seven of forty marten captured on the study area were telemetered and monitored for part or all of the study.

Marten mortality was concentrated in two intervals, fall 1986 and late winter 1987. Mortality during fall 1986 was attributable to encephalitis, while marten deaths during late winter 1987 resulted from predation and starvation attributable to the prey decline. Nonsuppurative encephalitis was first detected 7 October 1986; …


The Effect Of Seasonal Cattle Grazing On California Bighorn Sheep Habitat Use, Melanie J. Steinkamp May 1990

The Effect Of Seasonal Cattle Grazing On California Bighorn Sheep Habitat Use, Melanie J. Steinkamp

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The effect of seasonal cattle grazing on a newly reintroduced population of California bighorn sheep (Ovis canadensis californiana) in Big Cottonwood Canyon, Idaho, was studied. The hypothesis that bighorn sheep avoid cattle was tested. The issue of avoidance between bighorn sheep and livestock is arguable. Some studies have found that bighorn sheep avoid cattle while others have found no response of bighorn sheep to cattle.

Evidence was found to document the avoidance of cattle by bighorn sheep. The size of the bighorn's home range and core area decreased with the movement of cattle into areas of high bighorn …


Pair-Correlation Kinetics And The Reversible Diffusion-Controlled Reaction, David Peak, D C. Greenlaw, L A. Schick May 1990

Pair-Correlation Kinetics And The Reversible Diffusion-Controlled Reaction, David Peak, D C. Greenlaw, L A. Schick

All Physics Faculty Publications

It has long been known that the time course of a bimolecular reaction occurring in a condensed host depends on the behavior of the nonequilibrium pair-correlation function for reactant pairs. The classical analysis of such reactions has led to a kind of standard rule: The association rate constant for a diffusion-controlled reaction is 4πDR and this rate constant produces the fastest possible kinetics. This result is only (approximately) true for the case of an irreversible reaction, however. Here, we reexamine this old problem, looking closely at the reversible case. We report a result that challenges the standard wisdom: When the …


Rate Equation And Scaling For Fragmentation With Mass Loss, Boyd F. Edwards, M. Cai, H. Han May 1990

Rate Equation And Scaling For Fragmentation With Mass Loss, Boyd F. Edwards, M. Cai, H. Han

All Physics Faculty Publications

A linear rate equation describes fragmentation with continuous and discrete mass loss typified by consumption of porous reactive solids and two-phase heterogeneous solids. For a mass-dependent fragmentation rate xα and a continuous-mass-loss rate εxγ,σ=γ-α-1<0 yields a>‘‘recession regime’’ where small particles lose mass continuously without breaking, σ>0 yields a ‘‘fragmentation regime’’ where all particles break, and σ=0 yields scaling for α>0. Shattering for α<0 and>σ≥0 is runaway fragmentation producing an infinte number of particles in a finite time, Exact and asymptotic solutions, exponent relations, and connections with static percolation are found.


A Descriptive Study Of Range Livestock Operations In The Somali Central Rangelands, Abdinasir M. Abdulle May 1990

A Descriptive Study Of Range Livestock Operations In The Somali Central Rangelands, Abdinasir M. Abdulle

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Information on livestock operations, particularly what kind of livestock operations are practiced in the Somali central rangelands, and how these operations differ for different herders in different vegetation types and farming systems, could serve as a major tool in making management decisions. This study provides a detailed description of range livestock operations in the Somali Central Rangelands. It also answers some important management questions.

Range livestock operations were inventoried through personal interviews with the owners and herders. Data are supplemented by previous nation-wide and regional survey statistics. Herd productivity data which include herd structures, age, age-related sales, slaughters, gifts, and …


Survival Of Trout Strains As Affected By Limnological Parameters, Wayne A. Wurtsbaugh, Timothy Modde, Chris Luecke, Cheryl Courtney Mar 1990

Survival Of Trout Strains As Affected By Limnological Parameters, Wayne A. Wurtsbaugh, Timothy Modde, Chris Luecke, Cheryl Courtney

Watershed Sciences Faculty Publications

Juvenile rainbow trout Oncorhynchus mykiss. (ca. 80 mm S.L.) stocked into mid-elevation reservoirs in Utah are vulnerable to predation from piscivorous fish and birds. I determined how effectively juvenile trout used cover to avoid these predators by using direct observations (snorkel transects) on habitat selection in two reservoirs. Observations of juvenile trout were conducted within five weeks of stocking in 1988 and 1989. During the day juvenile trout were abundant in complex inshore habitats. Juvenile trout actively fed during the day but the time of peak feeding was variable. Large Daphnia made of > 95% of the diet of juvenile trout. …


Trophic Interactions Between Fish And Invertebrates In Bear Lake, Utah-Idaho, Wayne A. Wurtsbaugh, Charles P. Hawkins Mar 1990

Trophic Interactions Between Fish And Invertebrates In Bear Lake, Utah-Idaho, Wayne A. Wurtsbaugh, Charles P. Hawkins

Watershed Sciences Faculty Publications

An intensive study of the limnology, invertebrates and fishes of Bear Lake was conducted in 1987 in order to define the productivity and food web of the community. Limno10gica1 parameters and invertebrates were measured at approximately monthly intervals while fish distribution and feeding was analyzed in February, June, August, and October. Samples were collected at three to eight stations along a transect running from the shallow littoral area on the west side of the lake, to the deep profundal zone.


Lowand Mid-Latitude Ionospheric Electric Fields During The January 1984 Gismos Campaign, Bela G. Fejer, M. C. Kelley, C. Senior, O. De La Beaujardiere, J. A. Holt, C. A. Tepley, R. Burnside, M. A. Abdu, J. H.A. Sobral, R. F. Woodman, Y. Kamide, R. Lepping Mar 1990

Lowand Mid-Latitude Ionospheric Electric Fields During The January 1984 Gismos Campaign, Bela G. Fejer, M. C. Kelley, C. Senior, O. De La Beaujardiere, J. A. Holt, C. A. Tepley, R. Burnside, M. A. Abdu, J. H.A. Sobral, R. F. Woodman, Y. Kamide, R. Lepping

Bela G. Fejer

This paper examines in detail the electrical coupling between the high-, middle-, and low-latitude ionospheres during January 17–19, 1984, using interplanetary and high-latitude magnetic field data together with F region plasma drift measurements from the EISCAT, Sondre Stromfjord, Millstone Hill, Saint-Santin, Arecibo, and Jicamarca incoherent scatter radars. We study the penetration of both the zonal and meridional electric field components of high-latitude origin into the low-latitude and the equatorial ionospheres. In the dusk sector, a large perturbation of the zonal equatorial electric field was observed in the absence of similar changes at low and middle latitudes in the same longitudinal …


Hydrogen Adsorption On The Β N-Covered W(100) Surface: An Infrared Study Of The W–Hstretch, D. Mark Riffe, A. J. Sievers Feb 1990

Hydrogen Adsorption On The Β N-Covered W(100) Surface: An Infrared Study Of The W–Hstretch, D. Mark Riffe, A. J. Sievers

All Physics Faculty Publications

The adsorption of hydrogen on the c(2×2) β-N-covered W(100) surface has been studied with infrared and thermal-desorption spectroscopies. A new dipole-active vibrational absorption due to chemisorbed hydrogen has been discovered. Its center frequency (1738 cm-1 for minimal H2 adsorption), isotopic dependence (1252 cm-1 for D2 adsorption and the existence of both lines for HD adsorption), absorption strength versus β-N coverage, and effective dynamic charge e*≥0.12e lead to the assignment of the W-H stretch associated with a top-bonded H species. The vibration has been studied in detail on the highly ordered surface characterized …


Corrugation In The Nitrogen-Graphite Potential Probed By Inelastic Neutron Scattering, F. Y. Hansen, L. W. Bruch, H. Taub, V. L. Frank, H. J. Lauter, John R. Dennison Feb 1990

Corrugation In The Nitrogen-Graphite Potential Probed By Inelastic Neutron Scattering, F. Y. Hansen, L. W. Bruch, H. Taub, V. L. Frank, H. J. Lauter, John R. Dennison

All Physics Faculty Publications

Inelastic neutron spectra of the commensurate √3 ×3 herringbone monolayer phase of nitrogen physisorbed on the graphite (002) surface at low temperature have been compared with lattice dynamics calculations of the polycrystalline-averaged one-phonon coherent neutron cross section. The observed zone-center energy gap of ∼0.4 THz in the acoustic-phonon branches is a factor of 2 larger than calculated from central atom-atom potentials. We conclude that current models of the corrugation in the adatom substrate potential greatly underestimate the lateral restoring forces in this relatively simple molecular film.


Alkali Metal Adsorbates On W(110): Ionic, Covalent, Or Metallic?, D. Mark Riffe, G. K. Wertheim, P. H. Citrin Jan 1990

Alkali Metal Adsorbates On W(110): Ionic, Covalent, Or Metallic?, D. Mark Riffe, G. K. Wertheim, P. H. Citrin

All Physics Faculty Publications

The photoemission signal from the first atomic layer of W(110) is used to assess the nature of the interaction between the surface atoms of the metal substrate and the adsorbates Na, K, and Cs for coverages up to 1 atomic layer. Our results indicate that there is little or no charge transfer from the alkali metal to the W surface, even in the limit of low coverage. The satellite structure of the photoemission lines of the outermost p shell of the alkali metals confirms this conclusion. While contrary to the conventional picture of alkali-metal-charge donation, these findings fully support recent …


Quantum Measurement And Geometry, James Thomas Wheeler Jan 1990

Quantum Measurement And Geometry, James Thomas Wheeler

All Physics Faculty Publications

A model for the interpretation of spacetime as a Weyl geometry is proposed, based on the hypothesis that a system moves on any given path with a probability which is inversely proportional to the resulting change in length of the system. The results of physical measurements are calculated as the product of Weyl-conjugate gauge-dependent probabilities for the detection of conjugate objects. Each probability, expressed as a Wiener integral, is the Green's function for a diffusion equation. If the line integral of the Weyl field equals the action functional divided by ℏ this equation provides the stochastic equivalent of the Schrödinger …


Urban And Community Forestry: A Guide For The Interior Western United States, Craig W. Johnson, Fred A. Baker, Wayne S. Johnson, Richard Fisher, Susan Nordstrom, Gary O. Merrill, Stefan Zeglen Jan 1990

Urban And Community Forestry: A Guide For The Interior Western United States, Craig W. Johnson, Fred A. Baker, Wayne S. Johnson, Richard Fisher, Susan Nordstrom, Gary O. Merrill, Stefan Zeglen

Elusive Documents

No abstract provided.


Anasazi Basketmaker: Papers From The 1990 Wetherill-Grand Gulch Symposium, Victoria M. Atkins, Lisa Mcclanahan Jan 1990

Anasazi Basketmaker: Papers From The 1990 Wetherill-Grand Gulch Symposium, Victoria M. Atkins, Lisa Mcclanahan

Elusive Documents

No abstract provided.


Improved Resolution Of A 6m Torodial Grating Monochromator, G. K. Wertheim, J. E. Rowe, D. Mark Riffe, N. V. Smith Jan 1990

Improved Resolution Of A 6m Torodial Grating Monochromator, G. K. Wertheim, J. E. Rowe, D. Mark Riffe, N. V. Smith

All Physics Faculty Publications

We report a modification of the AT&T Bell Laboratories 6m toroidal grating monochromator at the National Synchrotron Light Source at Brookhaven National Laboratory which provides greatly improved resolution at midrange without the use of a movable exit slit. This modification is based on detailed ray tracing calculation, using the precedures developed by Haber, Howells, and McKinney and Howells, modified to include the holographic correction terms to the focusing equations. To maintain the optimum resolution requires an exit slit assembly movable over a distance of ∼20 cm. However, we show that an additional fixed slit 16.8 cm closer to the grating …


Pep Property Estimation Program And Chemical Property Database, William J. Doucette, Mark S. Holt Jan 1990

Pep Property Estimation Program And Chemical Property Database, William J. Doucette, Mark S. Holt

Reports

PEP Overview

A property Estimation Program (PEP), utilizing MCI-property, TSA-property and property correlations and UNIFAC-derived activity coefficients, has been developed for the Apple Macintosh microcomputer to provide the user with several approaches to estimate S, Kow, Pv, H, Koc, and BCF depending on the information available.

Structural information required for the MCi and UNIFAC calculation routines can be entered using either Simplified Molecular Identification and Line Entry System (SMILES) notation or connection tables generated with commercially available two-dimensional drawing programs. The TSA module accepts 3-D atomic coordinates entered manually or directly reads coordinate files generated by molecular modeling software. The …


Perturbations Of Gravitational Instantons, Charles G. Torre Jan 1990

Perturbations Of Gravitational Instantons, Charles G. Torre

All Physics Faculty Publications

Ashtekar's spinorial formulation of general relativity is used to study perturbations of gravitational instantons corresponding to finite-action solutions of the Euclidean Einstein equations (with a nonzero cosmological constant) possessing an anti-self-dual Weyl curvature tensor. It is shown that, with an appropriate "on-shell" form of infinitesimal gauge transformations, the space of solutions to the linearized instanton equation can be described in terms of an elliptic complex; the cohomology of the complex defines gauge-inequivalent perturbations. Using this elliptic complex we prove that there are no nontrivial solutions to the linearized instanton equation on conformally anti-self-dual Einstein spaces with a positive cosmological constant. …


The Longitude Dependence Of The Dayside F Region Trough: A Detailed Model-Observation Comparison, Jan Josef Sojka, Robert W. Schunk, J. A. Whalen Jan 1990

The Longitude Dependence Of The Dayside F Region Trough: A Detailed Model-Observation Comparison, Jan Josef Sojka, Robert W. Schunk, J. A. Whalen

All Physics Faculty Publications

The nighttime main F region trough extends into the sunlit afternoon sector. This trough feature exhibits both a strong magnetic activity dependence and a longitude (UT) dependence. Whalen (1987), using International Geophysical Year (IGY) ionosonde data, showed that both of these effects are readily extracted from ƒoF2 observations. In this study we show that the longitude effect is the same as that contained in the Utah State University time-dependent ionospheric model. It arises from the offset of the geomagnetic axis from the geographic axis. The magnetic activity dependency is associated with the westward convection in the afternoon …


Winds In The Upper Mesosphere At Mid-Latitude: First Results Using An Imaging Fabry-Perot Interferometer, D Rees, A Aruliah, T J. Fuller-Rowell, Vincent B. Wickwar, R J. Sica Jan 1990

Winds In The Upper Mesosphere At Mid-Latitude: First Results Using An Imaging Fabry-Perot Interferometer, D Rees, A Aruliah, T J. Fuller-Rowell, Vincent B. Wickwar, R J. Sica

All Physics Faculty Publications

The first stage of a new midlatitude facility at the Hardware Ranch Observatory near Bear Lake (41.93°N, 111.42°W, 1970 M elevation), for studies of the aeronomy of the middle and upper atmosphere, was completed during early September 1989. An Imaging Fabry‐Perot interferometer (IFPI) (Rees et al., 1982; Rees et al., 1990), was commissioned with a special Imaging Photon Detector (IPD) (McWhirter et al., 1982), equipped with a Gallium Arsenide (GaAs) photocathode. Wind and temperature structure can be deduced from observations of the Doppler shift and Doppler broadening of airglow and auroral emissions from the mesosphere and thermosphere. The near infra‐red …


On The Linearization Stability Of The Conformally (Anti-) Self-Dual Einstein Equations, Charles G. Torre Jan 1990

On The Linearization Stability Of The Conformally (Anti-) Self-Dual Einstein Equations, Charles G. Torre

All Physics Faculty Publications

The Einstein equations with a cosmological constant, when restricted to Euclidean space‐times with anti‐self‐dual Weyl tensor, can be replaced by a quadratic condition on the curvature of an SU(2) (spin) connection. As has been shown elsewhere, when the cosmological constant is positive and the space‐time is compact, the moduli space of gauge‐inequivalent solutions to this equation is discrete, i.e., zero dimensional; when the cosmological constant is negative, the dimension of the moduli space is essentially controlled by the Atiyah–Singer index theorem provided the field equations are linearization stable. It is shown that linearization instability occurs whenever the unperturbed geometry possesses …