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Utah State University

1992

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Articles 31 - 60 of 70

Full-Text Articles in Physical Sciences and Mathematics

Coverage Dependence Of K Adsorption On Si(100)—2× 1 By Core-Level Photoemission, D. Mark Riffe, G. K. Wertheim, P. H. Citrin, J. E. Rowe Feb 1992

Coverage Dependence Of K Adsorption On Si(100)—2× 1 By Core-Level Photoemission, D. Mark Riffe, G. K. Wertheim, P. H. Citrin, J. E. Rowe

All Physics Faculty Publications

Using core-level photoemission, a coverage-dependent transition in the adsorption of K on Si(100)2×1 is observed. Below ∼0.25 monolayers, a single adsorption is occupied, the asymmetry of the Si-dimer reconstruction is enhanced, and no more than ∼0.05e is transferred from K to Si. Above this coverage, multiple sites are occupied, the dimer configuration becomes more symmetric, and the K overlayer becomes increasingly metallic. These findings resolve a number of conflicting studies of this system.


Finite Thermal Diffusivity At Onset Of Convection In Autocatalytic Systems: Continuous Fluid Density, J. W. Wilder, Boyd F. Edwards, D. A. Vasquez Feb 1992

Finite Thermal Diffusivity At Onset Of Convection In Autocatalytic Systems: Continuous Fluid Density, J. W. Wilder, Boyd F. Edwards, D. A. Vasquez

All Physics Faculty Publications

The linear stability of exothermic autocatalytic reaction fronts is considered using the viscous thermohydrodynamic equations for a fluid with finite thermal diffusivity. For upward front propagation and a thin front, the vertical thermal gradient near the front is reminiscent of the Rayleigh-Bénard problem of a fluid layer heated from below. The problem is also similar to flame propagation, except that here the front propagation speed is limited by catalyst diffusion rather than by activation kinetics. For small density changes in a laterally unbounded system, the curvature dependence of the front propagation speed stabilizes perturbations with short wavelengths λ<λc, …


Dolores River Basin Water Quality Study, Department Of Interior; Bureau Of Reclamation, Technical Service Center; Denver, Co Jan 1992

Dolores River Basin Water Quality Study, Department Of Interior; Bureau Of Reclamation, Technical Service Center; Denver, Co

Elusive Documents

No abstract provided.


A Trophic Gradient Analysis Of Lake Powell During Spring Runnoff 1992, Wayne A. Wurtsbaugh, Clyde Lay, Darren Carlise, Corey Huxol, Craig Schaugaard, Beau Clements, David Beauchamp Jan 1992

A Trophic Gradient Analysis Of Lake Powell During Spring Runnoff 1992, Wayne A. Wurtsbaugh, Clyde Lay, Darren Carlise, Corey Huxol, Craig Schaugaard, Beau Clements, David Beauchamp

Watershed Sciences Faculty Publications

Between 26 April and 2 May 1992, students in a utah state university aquatic ecology class visited Lake Powell to do a study of trophic gradients of the reservoir. The main axis of the reservoir was surveyed, as well as less detailed analyses of Moki and Escalante Canyons. The work was conducted in collaboration with personnel from the u.s. Bureau of Reclamation headed by Bill Vernieu, and from the u.s. Geological Survey (Dick Marzolf). Some of their data appear in the physical-chemical section of this report.

Each student was responsible for compiling a report on one of the following specific …


Visual Feeding By Juvenile Bear Lake Sculpin, D. Neverman, Wayne A. Wurtsbaugh Jan 1992

Visual Feeding By Juvenile Bear Lake Sculpin, D. Neverman, Wayne A. Wurtsbaugh

Watershed Sciences Faculty Publications

Young-of-the-year Bear Lake sculpin Cottus extensus feed throughout the day on benthic invertebrates and cease feeding at night when they migrate to the metalimnion. We investigated their reliance on vision by conducting feeding trials at different light levels in the laboratory. Feeding rate reached a maximum at intermediate light levels (near 10^16 photons sm^–2 ss^–1; approximately 1 lux) but decreased as light intensity increased beyond this range. At this maximum rate, the fish fed nine times faster than they were able to feed in the dark, showing that young Bear Lake sculpin rely heavily upon vision to feed. The light …


Snake River Sockeye Salmon (Oncorhynchus Nerka) Habitat/Limnologic Research, Scott Spaulding, Wayne A. Wurtsbaugh, Shoshone-Bannock Tribe Jan 1992

Snake River Sockeye Salmon (Oncorhynchus Nerka) Habitat/Limnologic Research, Scott Spaulding, Wayne A. Wurtsbaugh, Shoshone-Bannock Tribe

Watershed Sciences Faculty Publications

This report outlines long-term planning and monitoring activities that occurred in 1991 and 1992 in the Stanley Basin Lakes of the upper Salmon River, Idaho for the purpose of sockeye salmon (Oncorhynchus nerka) recovery. Limnological monitoring and experimental sampling protocol, designed to establish a limnological baseline and to evaluate sockeye salmon production capability of the lakes, are present:ed. Also presented are recommended passage improvements for current fish passage barriers/impediments on migratory routes to the lakes. We initiated O. Nerka population evaluations for Redfish and Alturas lakes; this included population estimates of emerging kokanee fry entering each lake in the spring …


Lake Trout Spawning In Lake Tahoe: Egg Incubation In Deepwater Macrophyte Beds, D. A. Beauchamp, B. C. Allen, R. C. Richards, Wayne A. Wurtsbaugh, C. R. Goldman Jan 1992

Lake Trout Spawning In Lake Tahoe: Egg Incubation In Deepwater Macrophyte Beds, D. A. Beauchamp, B. C. Allen, R. C. Richards, Wayne A. Wurtsbaugh, C. R. Goldman

Watershed Sciences Faculty Publications

Although most populations of lake trout Salvelinus namaycush spawn over rocky shoals, use of these substrates by lake trout has not yet been found in Lake Tahoe. Large cobble substrate exists at depths less than 20 m, and steep, fractured, rocky substrate can be found in isolated areas from the surface down to at least 100 m, but no evidence of spawning activity in these areas has been found. Instead, at least a portion of the population spawns on deepwater mounds (40–60 m deep) over beds of the macrophyte Chara delicatula. This is the first known report of lake trout …


Soil Nitrogen Dynamics Following Harvesting And Conversion Of Red Alder And Douglas-Fir Stands, H. Van Miegroet, P. S. Homann, D. W. Cole Jan 1992

Soil Nitrogen Dynamics Following Harvesting And Conversion Of Red Alder And Douglas-Fir Stands, H. Van Miegroet, P. S. Homann, D. W. Cole

Watershed Sciences Faculty Publications

Drastic reductions in NO3- leaching have been observed after harvesting of mature red alder (Alnus rubra Bong.) stands. Our objective was to examine whether these reduction were linked to changes in soil N dynamics. Adjacent alder and Douglas fir [Pseudotsuga menziessii (Mirbel.) Franco] stands on young glacial soils (Alderwood; a loamy-skeletal, mixed, mesic, ortstein Aquic Haplorthod) in western Washington were harvested and replanted with either alder or Douglas fir seedlings; reference plots were established in nearby undisturbed stands. Three years after site conversion, when NO3- leaching declined most drastically in the harvested alder plots, net N mineralization and net nitrification …


Soil Chemistry And Nutrition Of North American Red Spruce-Fir Stands: Evidence For Recent Change, J. D. Joslin, J. M. Kelly, H. Van Miegroet Jan 1992

Soil Chemistry And Nutrition Of North American Red Spruce-Fir Stands: Evidence For Recent Change, J. D. Joslin, J. M. Kelly, H. Van Miegroet

Watershed Sciences Faculty Publications

One set of hypotheses offered to explain the decline of red spruce (Picea rubens Sarg.) in eastern North America focuses on the effect of acidic deposition on soil chemistry changes that may affect nutrient availability and root function. Long-term soils data suggest that soil acidification has occurred in some spruce stands over the past 50 yr, with plant uptake and cation leaching both contributing to the loss of cations. Studies of tree ring chemistry also have indicated changes in Ca/Al and Mg/Al ratios in red spruce wood, suggesting increases in the ionic strength of soil solution. Irrigation studies using strong …


Fragmentation Of Percolation Clusters At The Percolation Threshold, M. F. Gyure, Boyd F. Edwards Jan 1992

Fragmentation Of Percolation Clusters At The Percolation Threshold, M. F. Gyure, Boyd F. Edwards

All Physics Faculty Publications

A scaling theory and simulation results are presented for fragmentation of percolation clusters by random bond dilution. At the percolation threshold, scaling forms describe the average number of fragmenting bonds and the distribution of cluster masses produced by fragmentation. A relationship between the scaling exponents and standard percolation exponents is verified in one dimension, on the Bethe lattice, and for Monte Carlo simulations on a square lattice. These results further describe the structure of percolation clusters and provide kernels relevant to rate equations for fragmentation.


Su(3) X Su(2) X U(1)Su(3): The Residual Symmetry Of Conformal Gravity, James Thomas Wheeler Jan 1992

Su(3) X Su(2) X U(1)Su(3): The Residual Symmetry Of Conformal Gravity, James Thomas Wheeler

All Physics Faculty Publications

SUe 4) x SU(2) is shown to characterize the possible choices of spacetime metric constructible from the gauge fields of the conformal group. When this symmetry is broken by the choice of metric, exactly the SU(3) x SU(2) x U(l) symmetry of the standard model remains. The conformal group consists of Lorentz transformations, translations, inverse translations and dilations. Treated in the standard way, conformal symmetry fails as a unifying gauge group: dilations make the mass spectrum continuous, and the inverse translational gauge field is auxiliary. The theory reduces back to the Poincare group.


Analysis Of Experiments In Helium Microbeam Mixing, J B. Davis, R E. Benenson, David Peak Jan 1992

Analysis Of Experiments In Helium Microbeam Mixing, J B. Davis, R E. Benenson, David Peak

All Physics Faculty Publications

We have continued to investigate ion-beam mixing in bilay-er targets irradiated by 2-MeV He+ microbeams at room temperature. Although we have previously reported a linear dependence of interface width on dose for Cu/Al targets 1, more extensive results have not supported this conclusion, within statistical uncertainty, it appears that the interface width in Cu/Al (1) is proportional to the square root of dose, at constant dose rate, (2) is larger in Al than in Cu, for the same dose, (3) is proportional to the 1/4 power of dose rate, and (4) is absent at liquid nitrogen temperature. Calculations …


Ionospheric Simulation Compared With Dynamics Explorer Observations For November 22, 1981, Jan Josef Sojka, M. D. Bowline, Robert W. Schunk, J. D. Craven, L. A. Frank, J. R. Sharber, J. D. Winningham, L. H. Brace Jan 1992

Ionospheric Simulation Compared With Dynamics Explorer Observations For November 22, 1981, Jan Josef Sojka, M. D. Bowline, Robert W. Schunk, J. D. Craven, L. A. Frank, J. R. Sharber, J. D. Winningham, L. H. Brace

All Physics Faculty Publications

Dynamics Explorer (DE) 2 electric field and particle data have been used to constrain the inputs of a time-dependent ionospheric model (TDIM) for a simulation of the ionosphere on November 22, 1981. The simulated densities have then been critically compared with the DE 2 electron density observations. This comparison uncovers a model-data disagreement in the morning sector trough, generally good agreement of the background density in the polar cap and evening sector trough, and a difficulty in modelling the observed polar F layer patches. From this comparison, the consequences of structure in the electric field and precipitation inputs can be …


Solar Cycle Dependence Of Spacecraft Charging In Low Earth Orbit, T. B. Frooninckx, Jan Josef Sojka Jan 1992

Solar Cycle Dependence Of Spacecraft Charging In Low Earth Orbit, T. B. Frooninckx, Jan Josef Sojka

All Physics Faculty Publications

Recent experimental evidence has shown that Defense Meteorological Satellite Program (DMSP) polar orbiting spacecraft at 840 km can develop electric potentials as severe as −1430 V while at high magnetic latitudes. To explore this charging region, an analysis of DMSP F6, F7, F8, and F9 satellite precipitating particle and ambient plasma measurements taken during periods of high, medium, and low solar flux is performed. One hundred eighty-four charging events ranging from −46 to −1430 V are identified, and an extreme solar cycle dependence is found as charging is most frequent and severe during solar minimum. Satellite measurements and time-dependent ionospheric …


Is General Relativity An "Already Parametrized" Theory?, Charles G. Torre Jan 1992

Is General Relativity An "Already Parametrized" Theory?, Charles G. Torre

All Physics Faculty Publications

Beginning with the work of Dirac and of Arnowitt, Deser, and Misner in the late 1950s and early 1960s, and then after subsequent development by Kuchař, the canonical dynamical structure of general relativity has often been viewed as that of a parametrized field theory in which the many-fingered spacetime variables are hidden among the geometrodynamical field variables. This paradigm of general relativity as an "already parametrized" theory forms the basis for one of the most satisfactory resolutions of the problems of time and observables in classical and quantum gravity. However, despite decades of effort, no identification of many-fingered spacetime variables …


Covariant Phase Space Formulation Of Parametrized Field Theories, Charles G. Torre Jan 1992

Covariant Phase Space Formulation Of Parametrized Field Theories, Charles G. Torre

All Physics Faculty Publications

Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical (pre)symplectic structure. Motivated by issues arising in general relativity, we focus on phase space representations of the space‐time diffeomorphism group, construction of observables, and the relationship between the canonical and covariant phase spaces.


Ultrahigh Vacuum Chamber For Synchrotron X-Ray Diffraction From Films Adsorbed On Single-Crystal Surfaces, Jr Dennison, S. K. Wang, S. N. Ehrlich Jan 1992

Ultrahigh Vacuum Chamber For Synchrotron X-Ray Diffraction From Films Adsorbed On Single-Crystal Surfaces, Jr Dennison, S. K. Wang, S. N. Ehrlich

Journal Articles

An ultrahigh vacuum chamber has been developed for structural analysis of adsorbed films and single-crystal surfaces using synchrotron x-ray diffraction. It is particularly well suited for investigations of physisorbed and other weakly bound films. The chamber is small enough to transport and mount directly on a standard four-axis diffractometer and can also be used independently of the x-ray diffractometer. A low-current, pulse-counting, low-energy electron diffraction/Auger spectroscopy system with a position-sensitive detector enables in situ characterization of the film and substrate while the sample is located at the x-ray scattering position. A closed-cycle He refrigerator and electron bombardment heater provide controlled …


Composting Of Explosives Contaminated Soil Using The White Rot Fungus Phanerochaete Chrysosporium, Michael J. Mcfarland, Shashi Kalaskar, Eric Baiden Jan 1992

Composting Of Explosives Contaminated Soil Using The White Rot Fungus Phanerochaete Chrysosporium, Michael J. Mcfarland, Shashi Kalaskar, Eric Baiden

Reports

Bioaugmentation using the white rot fungus Phanerochaete chrysosporium was found to be effective in enhancing TNT removal in lightly (i.e., below 100 mg/kg) contaminated soil. The percent reduction in TNT increased from 15% to 53% when soils were treated with fungal inoculated organic material. Maximum removal rates improved from 0.33 mg TNT/kg-day to 0.76 mg TNT/kg-day during the same treatment. Neither fungal inoculation nor organic amendment addition resulted in improving TNT removal kinetics in highly contaminated soils (i.e., above 1000 mg/kg). Executive Summary: Laboratory scale compost studies were conducted to evaluate the effect of bioaugmentation with the white rot fungus,


A Spatially Distributed Water Balance Based On Physical, Isotropic And Airborne Remotely Sensed Data, C. M.U. Neale, David G. Tarboton, J. J. Mcdonnell Jan 1992

A Spatially Distributed Water Balance Based On Physical, Isotropic And Airborne Remotely Sensed Data, C. M.U. Neale, David G. Tarboton, J. J. Mcdonnell

Reports

Introduction: The objective of this research to develop a spatially distributed water balance model based on the integration of spatially distributed data. Progress this year has consisted of model development, instrument acquisition, installation and development of experimental procedures, and baseline data collection. The original research plan called for detailed observations related to the water balance over the year September 1991 to August 1992. The detailed measurements were to start with accumulation of the snowpack followed by melt and evapotranspiration measurements from March to August. The objective was to measure the energy balance parameters starting with the peak accumulation, through the …


Evaluation Of Mechanisms Of Alteration And Humification Of Pahs For Water Quality Management, Ronald C. Sims, Carolyn K. Abbott Jan 1992

Evaluation Of Mechanisms Of Alteration And Humification Of Pahs For Water Quality Management, Ronald C. Sims, Carolyn K. Abbott

Reports

Introduction: Creosote-pentachlorophenol (PCP) is a mixture commonly used as a wood preservative in the U.S. (1). A 1988 survey (2) indicated that 1,397 wood preserving waste contaminated sites exist in the United States consisting of 555 active wood treatment plants and 842 inactive plants. Stinson (3) indentifed 58 wood preserving sites on the National Priorities List, of which 51 have PCP and/or creosote or polycyclic aromatic hydrocarbon (PAH) contamination. Principal classes of organic constituents present in creosote waste are PAHs (~85% by weight) and phenolics. PAHs with less than three fused benzene rings comprise 69% (i.e., naphthalene, anthracene and phenanthrene); …


Nonparametric Stratigraphic Interpretation From Drill Log Data, Upmanu Lall, A. I. Ali Jan 1992

Nonparametric Stratigraphic Interpretation From Drill Log Data, Upmanu Lall, A. I. Ali

Reports

Near surface groundwater contamination is a widespread problem. The potential for contamination of deep aquifers in such areas depends on the vertical hydraulic gradient as well as the extent and location of interconnection between the upper and lower aquifers. In alluvial, sedimentary environment, the geologic units are typically weakly connected lenses or layers of high or low conductivity with variable size, geometry and orientation. Drill logs provide qualitative, local information on such aquifer heterogeneities. A binary (high or low conductivity) indicator function is used to describe the aquifer system. A nonparametric statistical methodology for assessing the probability that a particular …


A Partial Glossary Of Elk Management Terms, United States Department Of Agriculture, Forest Service Jan 1992

A Partial Glossary Of Elk Management Terms, United States Department Of Agriculture, Forest Service

Forestry

This glossary helps define terms that have been misused during forest planning. Terms that were developed from research on the influences of timber sales and roads during the summer months have been used inappropriately when referring to winter range, hunting seasons, and other conditions. The glossary is based on the results of an "Elk Management Terminology Workshop" held at the University of Montana's Lubrecht Experimental Forest on April 3-4, 1990.


Effects Of Seeder Design And Seed Placement On Seedling Size And Cull Rates At Western Forest Nurseries, United States Department Of Agriculture, Forest Service Jan 1992

Effects Of Seeder Design And Seed Placement On Seedling Size And Cull Rates At Western Forest Nurseries, United States Department Of Agriculture, Forest Service

Forestry

Nursery plots sown with the Summit Precision Seeder and the Oyjord Seeder were compared with plots oversown and hand thinned to desired spacings. We studied 26 seedlots of nine conifer species at five Forest Service, U.S. Department of Agriculture, nurseries. Results varied with nursery, species, and seed characteristics. Thinned plots produced less clumping and fewer gaps between seedlings, but showed little or no difference in seedling size, nor in the number of acceptable seedlings.


Plant Community Diversity After Herbicide Control Of Spotted Knapweed, United States Department Of Agriculture, Forest Service Jan 1992

Plant Community Diversity After Herbicide Control Of Spotted Knapweed, United States Department Of Agriculture, Forest Service

Herbicides and Pesticides

Herbicides were applied to four west-central Montana sites with light to moderate spotted knapweed (Centaurea maculosa Lam.) infestations. Althought knapweed suppression was high, 2 years after the spraying the communities were not converted to grass monocultures. No large declines in plant diversity were caused by the herbicides, and small depressions were probably transitory. By the third year, diversity had increased.


Final Environmental Impact Statement Stanley Basin C & H Allotment Management Plan Sawtooth National Recreation Area, United States Forest Service Jan 1992

Final Environmental Impact Statement Stanley Basin C & H Allotment Management Plan Sawtooth National Recreation Area, United States Forest Service

Final Environmental Impact Statements (ID)

This Final Environmental Impact Statement (FEIS) documents the analysis conducted for the Stanley Basin Cattle and Horse Allotment Management Plan. The allotment management plan involves National Forest System lands within the Sawtooth and Challis National Forests. The analysis of the current condition of the Stanley Basin Allotment has found that the existing grazing system does not comply with the direction, standards and guidelines of the Sawtooth and Challis Forest Land and Resource Management Plans (FLRMP). The proposed action of this Final Environmental Impact Statement is to bring management of the allotment into compliance with the FLRMPs. The FEIS describes five …


Final Environmental Impact Statement For Salt Lake City International Airport Expansion, Salt Lake City, Utah, United States Department Of Transportation Federal Aviation Administration Jan 1992

Final Environmental Impact Statement For Salt Lake City International Airport Expansion, Salt Lake City, Utah, United States Department Of Transportation Federal Aviation Administration

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

Expansion of the Salt Lake City International Airport is proposed to meet the existing and future travel demands of the public and air carriers using the airport. Specifically, it is proposed to increase the safety and efficiency of the airport by reducing congestion and delays. The expansion of the airport has been planned for over 12 years including 2 Master Planning efforts, a FAR Part 150 document (an airport noise compatability planning study), a Capacity Task Force Document, and the Draft Environmental Assessment and Expanded Environmental Assessment efforts in addition to numerous smaller studies and documents.


Environmental Assessment, Carter Mountain-Thermopolis 230-Kv Transmission Line Project, Hot Springs County, Wyoming, U.S. Department Of Energy Jan 1992

Environmental Assessment, Carter Mountain-Thermopolis 230-Kv Transmission Line Project, Hot Springs County, Wyoming, U.S. Department Of Energy

Environmental Assessments (WY)

The Western Area Power Administration (Western) is proposing to construct, operate, and maintain a new 230-kV transmission line between the Carter Mountain and Thermopolis Substations in northcentral Wyoming (Hot Springs County). The project area is shown on Map 2-1. This environmental assessment was prepared in compliance with the National Environmental Policy Act (NEPA) and the regulations of the Council on Environmental Quality and the Department of Energy, which is responsible for approval of the proposed action. The Bureau of Land Management (BLM) is a cooperating agency on the project and is also the Federal review agency responsible for granting rights-of-way …


Oil And Gas Leasing On The Thunder Basin National Grassland Final Environmental Impact Statement, United States Forest Service Jan 1992

Oil And Gas Leasing On The Thunder Basin National Grassland Final Environmental Impact Statement, United States Forest Service

Final Environmental Impact Statements (WY)

This Final Environmental Impact Statement was conducted to analyze what lands on the Medicine Bow National Forest, Thunder Basin National Grassland in northeast Wyoming could be available for leasing and what conditions could be attached to future leases. Seven alternatives are described, and potential effects are disclosed and evaluated. These alternatives represent possible ways to manage oil and gas leasing on 520,000 acres that are available for leasing. The alternatives are: ALTERNATIVE 1, Leasing consistent with the Forest Plan (No Action); ALTERNATIVE 2, Leasing with standard and special stipulations, consistent with the Forest Plan; ALTERNATIVE 3, Leasing with standard and …


Proton–Donor Properties Of Water And Ammonia In Van Der Waals Complexes With Rare‐Gas Atoms. Kr–H2o And Kr–Nh3, G. Chalasinski, M. M. Szczesniak, Steve Scheiner Jan 1992

Proton–Donor Properties Of Water And Ammonia In Van Der Waals Complexes With Rare‐Gas Atoms. Kr–H2o And Kr–Nh3, G. Chalasinski, M. M. Szczesniak, Steve Scheiner

Chemistry and Biochemistry Faculty Publications

The perturbation theory of intermolecular forces in conjunction with the supermolecular Møller–Plesset perturbation theory is applied to the analysis of the potential‐energy surfaces of Kr–H2O and Kr–NH3 complexes. The valleylike minimum region on the potential‐energy surface of Kr–H2O ranges from the coplanar geometry with the C2 axis of H2O nearly perpendicular to the O–Kr axis (T structure) to the H‐bond structure in which Kr faces the H atom of H2O. Compared to the previously studied Ar–H2O [J. Chem. Phys. 94, 2807 (1991)] the minimum has more …


Introduction To The Variational Bicomplex, Ian M. Anderson Jan 1992

Introduction To The Variational Bicomplex, Ian M. Anderson

Mathematics and Statistics Faculty Publications

The variational bicomplex was first introduced in the mid 1970's as a means of studying the inverse problem of the calculus of variations. This is the problem of characterizing those differential equations which are the Euler-Lagrange equations for a classical, unconstrained variational problem. Since then, the variational bicomplex has emerged as an effective means for studying other formal, differential-geometric aspects of the calculus of variations. Moreover, it has been shown that the basic variational bicomplex constructed to solve the inverse problem can be modified in various ways and that the cohomology groups associated with these modified bicomplexes are relevant to …