USGS Science⌕ Search

SEARCH · USGS Science

Results for “Journal of Mathematical Analysis and Applications”

Search indexed USGS publications on groundwater, aquifers, geologic maps, mineral resources and earthquakes. Explore source records by subject and place.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

11 recordsLinked to original sources
USGS2021

Periodic oscillation and tri-stability in mutualism systems with two consumers

This paper considers mutualistic interactions between two consumers, in which one consumer can consume a resource only by exchange of service for service with the other. By rigorous analysis on the one-resource and two-consumer model with Holling-type I response, we show periodic oscillations and tri-stability in the mutualism system: when their initial densities decrease, the consumers' interaction outcomes would change from coexistence in periodic oscillation, to persistence at a steady state, and to extinction. Under certain conditions, we also show two types of bi-stability in the system: the consumers would change from coexisting in periodic oscillation (resp. at a steady state) to going to extinction when their initial densities decrease. Then we analyze a modified system with Holling-type II response. Based on theoretical analysis and numerical computation, we show that there also exist tri-stability and two types of bi-stability in this system. Moreover, it is shown that varying the degree of obligation can lead to transition of interaction outcomes between coexistence in periodic oscillation (resp. at a steady state) and extinction of both consumers. These results are important in understanding complexity in mutualism.

Journal of Mathematical Analysis and Applications↗
USGS1970

Correction of bias in belt transect studies of immotile objects

Unless a correction is made, population estimates derived from a sample of belt transects will be biased if a fraction of, the individuals on the sample transects are not counted. An approach, useful for correcting this bias when sampling immotile populations using transects of a fixed width, is presented. The method assumes that a searcher's ability to find objects near the center of the transect is nearly perfect. The method utilizes a mathematical equation, estimated from the data, to represent the searcher's inability to find all objects at increasing distances from the center of the transect. An example of the analysis of data, formation of the equation, and application is presented using waterfowl nesting data collected in Colorado.

Colorado↗
USGS1989

Removing volatile contaminants from the unsaturated zone by inducing advective air-phase transport

Organic liquids inadvertently spilled and then distributed in the unsaturated zone can pose a long-term threat to ground water. Many of these substances have significant volatility, and thereby establish a premise for contaminant removal from the unsaturated zone by inducing advective air-phase transport with wells screened in the unsaturated zone. In order to focus attention on the rates of mass transfer from liquid to vapour phases, sand columns were partially saturated with gasoline and vented under steady air-flow conditions. The ability of an equilibrium-based transport model to predict the hydrocarbon vapor flux from the columns implies an efficient rate of local phase transfer for reasonably high air-phase velocities. Thus the success of venting remediations will depend primarily on the ability to induce an air-flow field in a heterogeneous unsaturated zone that will intersect the distributed contaminant. To analyze this aspect of the technique, a mathematical model was developed to predict radially symmetric air flow induced by venting from a single well. This model allows for in-situ determinations of air-phase permeability, which is the fundamental design parameter, and for the analysis of the limitations of a single well design. A successful application of the technique at a site once contaminated by gasoline supports the optimism derived from the experimental and modeliing phases of this study, and illustrates the well construction and field methods used to document the volatile contaminant recovery.

Journal of Contaminant Hydrology↗
USGS2002

Of bugs and birds: Markov Chain Monte Carlo for hierarchical modeling in wildlife research

Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more complex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scientific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathematical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors governing individual heterogeneity in breeding and survival rates of kittiwakes ( Rissa tridactyla ). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.

Journal of Wildlife Management↗
USGS2002

A bibliography of terrain modeling (geomorphometry), the quantitative representation of topography: Supplement 4.0

Terrain modeling, the practice of ground-surface quantification, is an amalgam of Earth science, mathematics, engineering, and computer science. The discipline is known variously as geomorphometry (or simply morphometry), terrain analysis, and quantitative geomorphology. It continues to grow through myriad applications to hydrology, geohazards mapping, tectonics, sea-floor and planetary exploration, and other fields. Dating nominally to the co-founders of academic geography, Alexander von Humboldt (1808, 1817) and Carl Ritter (1826, 1828), the field was revolutionized late in the 20th Century by the computer manipulation of spatial arrays of terrain heights, or digital elevation models (DEMs), which can quantify and portray ground-surface form over large areas (Maune, 2001). Morphometric procedures are implemented routinely by commercial geographic information systems (GIS) as well as specialized software (Harvey and Eash, 1996; Köthe and others, 1996; ESRI, 1997; Drzewiecki et al., 1999; Dikau and Saurer, 1999; Djokic and Maidment, 2000; Wilson and Gallant, 2000; Breuer, 2001; Guth, 2001; Eastman, 2002). The new Earth Surface edition of the Journal of Geophysical Research, specializing in surficial processes, is the latest of many publication venues for terrain modeling. This is the fourth update of a bibliography and introduction to terrain modeling (Pike, 1993, 1995, 1996, 1999) designed to collect the diverse, scattered literature on surface measurement as a resource for the research community. The use of DEMs in science and technology continues to accelerate and diversify (Pike, 2000a). New work appears so frequently that a sampling must suffice to represent the vast literature. This report adds 1636 entries to the 4374 in the four earlier publications1. Forty-eight additional entries correct dead Internet links and other errors found in the prior listings. Chronicling the history of terrain modeling, many entries in this report predate the 1999 supplement. Coverage is representative from about 1800 through early–mid 2002. Papers increasingly are published exclusively or in duplicate on the Internet's World Wide Web; the dates given here for Web addresses (URLs) that lack a print publication indicate a Web site's last update or my last access of it. The bibliography is arranged alphabetically and thus is not readily summarized. This introduction cites about 500 entries, a third of them grouped under 24 morphometric topics, as a guide to the listing's contents. Continuing the practice of previous bibliographies in the series to provide more information on a few applications (see summary of past topics in Pike, 2000a), this report elaborates further on topographic data, putative new parameters, tectonic geomorphology/neo-orometry, biogeography, ice-cap morphometry, results from the Mars Global DEM, landslide-hazard mapping, terrain modeling as physics, Hack's law, and broad-scale computer visualization. The literature of some of these subjects is large, and none of the summaries is intended to more than introduce the topic and comment on some of the current contributions of terrain modeling. Closing the essay is a discussion of pre-1900 papers that trace the evolution of ridge-line and watercourse quantification by descriptive geometry, as well as comments on some new books and an on-line bulletin board.

Open-File Report↗
USGS1983

Characteristic analysis-1981: Final program and a possible discovery

The latest ornewest version of thecharacteristicanalysis (NCHARAN)computer program offers the exploration geologist a wide variety of options for integrating regionalized multivariate data. The options include the selection of regional cells for characterizing deposit models, the selection of variables that constitute the models, and the choice of logical combinations of variables that best represent these models. Moreover, the program provides for the display of results which, in turn, makes possible review, reselection, and refinement of a model. Most important, the performance of the above-mentioned steps in an interactive computing mode can result in a timely and meaningful interpretation of the data available to the exploration geologist. The most recent application of characteristic analysis has resulted in the possible discovery of economic sulfide mineralization in the Grong area in central Norway. Exploration data for 27 geophysical, geological, and geochemical variables were used to construct a mineralized and a lithogeochemical model for an area that contained a known massive sulfide deposit. The models were applied to exploration data collected from the Gjersvik area in the Grong mining district and resulted in the identification of two localities of possible mineralization. Detailed field examination revealed the presence of a sulfide vein system and a partially inverted stratigraphic sequence indicating the possible presence of a massive sulfide deposit at depth. ?? 1983 Plenum Publishing Corporation.

Journal of the International Association for Mathe↗
USGS1979

Mathematics and mallard management

Waterfowl managers can effectively use simple population models to aid in making management decisions. We present a basic model of the change in population size as related to survival and recruitment. A management technique designed to increase survival of mallards (Anas platyrhynchos) by limiting harvest on the Chippewa National Forest, Minnesota, is used to illustrate the application of models in decision making. The analysis suggests that the management technique would be of limited effectiveness. In a 2nd example, the change in mallard population in central North Dakota is related to implementing programs to create dense nesting cover with or without supplementary predator control. The analysis suggests that large tracts of land would be required to achieve a hypothetical management objective of increasing harvest by 50% while maintaining a stable population. Less land would be required if predator reduction were used in combination with cover management, but questions about effectiveness and ecological implications of large scale predator reduction remain unresolved. The use of models as a guide to planning research responsive to the needs of management is illustrated.

Journal of Wildlife Management↗
USGS2007

Yellowstone grizzly bear investigations: Annual report of the Interagency Grizzly Bear Study Team, 2006

The contents of this Annual Report summarize results of monitoring and research from the 2006 field season. The report also contains a summary of nuisance grizzly bear ( Ursus arctos horribilis ) management actions. The Interagency Grizzly Bear Study Team (IGBST) continues to work on issues associated with counts of unduplicated females with cubs-of- the-year (COY). These counts are used to establish a minimum population size, which is then used to establish mortality thresholds for the Recovery Plan (U.S. Fish and Wildlife Service [USFWS] 1993). After considerable delays due to programming issues, a computer program that defines the rule set used by Knight et al. (1995) to differentiate unique family groups was development and tested in 2005 and 2006. Simulations using observations of collared females with COY were randomly sampled to generate datasets of observations of random females with COY. These datasets were then run though the simulations program to test the accuracy of the rules. Data are currently being summarized. This project has been completed and a manuscript was submitted to the Journal of Wildlife Management. The grizzly bear recovery plan (USFWS 1993) established human-caused mortality quotas. We used the latest information on reproduction and survival to estimate population trajectory in the same simulation model originally used by Harris (1984). A Wildlife Monographs was published in 2006. Additionally, the study team, in cooperation with several quantitative experts, reassessed how population size is indexed and how sustainable mortality rates are established. A draft report was presented to the Yellowstone Ecosystem Subcommittee in spring 2005. It was published as part of the USFWS Delisting Rule (Federal Register Vol. 70, No. 221, Nov. 17, 2005, 69853–69884) and subjected to public comment. This workshop document can be found at http://www.fws.gov/mountain-prairie/species/mammals/grizzly/yellowstone.htm. During the summer of 2006, a second workshop was held to address public comment and professional peer review. The result of this workshop was a supplement to the 2005 workshop document. This supplement can be found at http://www.fws.gov/mountain-prairie/species/mammals/grizzly/yellowstone.htm under the link Revised Methods to Estimate Population Size and Sustainable Mortality Limits. Results of those estimates are provided in Appendix A. Our project addressing the potential application of stable isotopes and trace elements to quantify consumption rates of whitebark pine ( Pinus albicaulis ) and cutthroat trout ( Oncorhynchus clarki ) by grizzly bears was completed. Our manuscript on consumption rates of whitebark pine was published in the Canadian Journal of Zoology 81:763-770. Results of the mercury studies were also published in the Canadian Journal of Zoology 82:493–501. Copies can be found on the IGBST website http://www.nrmsc.usgs.gov/research/igbst-home.htm. Based upon this work, we submitted a proposal to analyze all historic tissue samples from grizzly bears in the ecosystem. That proposal was funded and samples have been sent to a lab for isotopic analysis. We hope to have those results in early 2008. Results of DNA hair snaring work conducted on Yellowstone Lake were submitted and published in the Journal Ursus (Haroldson et al. 2005). Results of this study conducted from 1997–2000 showed a decline in fish use by grizzly bears when compared to earlier work conducted by Reinhart (1990) in 1985–1987. As a consequence, the IGBST submitted a proposal to the National Park Service and received 3 years funding to repeat that work. This project began in 2007. There are 2 graduate students and several field technicians working on the program. We completed the final field season in Grand Teton National Park evaluating habitat use both temporally and spatially between grizzly and black bears ( Ursus americanus ). We continue to use GPS technology that incorporates a spread spectrum communication system. Spread spectrum allows for transfer of stored GPS locations from the collar to a remote receiving station. Results of the 2006 field season are reported here. We plan to complete the final report in late 2007. We continued to monitor the health of whitebark pine in the Greater Yellowstone Ecosystem (GYE) in cooperation with the Greater Yellowstone Whitebark Pine Monitoring Working Group. A summary of the 2006 monitoring is also presented (Appendix B). The IGBST uses counts of winter-killed ungulates to index spring carcass abundance for grizzly bears. Likewise, we use wier counts and stream surveys to index cutthroat trout abundance. We ask Dr. Steve Cherry, Department of Mathematical Sciences, Montana State University-Bozeman, to review the protocols and make recommendations for improving them. That review and recommendations are presented in Appendix C. Finally, the state of Wyoming, following recommendations from the Yellowstone Ecosystem Subcommittee and the IGBST, launched the Bear Wise Community Effort. The focus is to minimize human/bear conflicts, minimize human-caused bear mortalities associated with conflicts, and safeguard the human community. Results of these efforts are detailed in Appendix D. The annual reports of the IGBST summarize annual data collection. Because additional information can be obtained after publication, data summaries are subject to change. For that reason, data analyses and summaries presented in this report supersede all previously published data. The study area and sampling techniques are reported by Blanchard (1985), Mattson et al. (1991 a), and Haroldson et al. (1998).

Idaho, Montana, Wyoming↗
USGS2013

Whole-coal versus ash basis in coal geochemistry: a mathematical approach to consistent interpretations

Several standard methods require coal to be ashed prior to geochemical analysis. Researchers, however, are commonly interested in the compositional nature of the whole-coal, not its ash. Coal geochemical data for any given sample can, therefore, be reported in the ash basis on which it is analyzed or the whole-coal basis to which the ash basis data are back calculated. Basic univariate (mean, variance, distribution, etc.) and bivariate (correlation coefficients, etc.) measures of the same suite of samples can be very different depending which reporting basis the researcher uses. These differences are not real, but an artifact resulting from the compositional nature of most geochemical data. The technical term for this artifact is subcompositional incoherence. Since compositional data are forced to a constant sum, such as 100% or 1,000,000 ppm, they possess curvilinear properties which make the Euclidean principles on which most statistical tests rely inappropriate, leading to erroneous results. Applying the isometric logratio (ilr) transformation to compositional data allows them to be represented in Euclidean space and evaluated using traditional tests without fear of producing mathematically inconsistent results. When applied to coal geochemical data, the issues related to differences between the two reporting bases are resolved as demonstrated in this paper using major oxide and trace metal data from the Pennsylvanian-age Pond Creek coal of eastern Kentucky, USA. Following ilr transformation, univariate statistics, such as mean and variance, still differ between the ash basis and whole-coal basis, but in predictable and calculated manners. Further, the stability between two different components, a bivariate measure, is identical, regardless of the reporting basis. The application of ilr transformations addresses both the erroneous results of Euclidean-based measurements on compositional data as well as the inconsistencies observed on coal geochemical data reported on different bases.

International Journal of Coal Geology↗
USGS2009

Mathematical modelling of anisotropy of illite-rich shale

The estimation of illite-rich shale anisotropy to account for the alignment of clays and gas- or brine-filled cracks is presented via mathematical modelling. Such estimation requires analysis to interpret the dominance of one effect over another. This knowledge can help to evaluate the permeability in the unconventional reservoir, stress orientation, and the seal capacity for the conventional reservoir. Effective media modelling is used to predict the elastic properties of the illite-rich shale and to identify the dominant contributions to the shale anisotropy. We consider two principal reasons of the shale anisotropy: orientation of clay platelets and orientation of fluid-filled cracks. In reality, both of these two factors affect the shale anisotropy. The goal of this study is, first, to separately analyse the effect of these two factors to reveal the specific features in P- and S-wave velocity behaviour typical of each of the factors, and, then, consider a combined effect of the factors when the cracks are horizontally or vertically aligned. To do this, we construct four models of shale. The behaviour of P- and S-wave velocities is analysed when gas- and water-filled cracks embedded in a host matrix are randomly oriented, or horizontally or vertically aligned. The host matrix can be either isotropic or anisotropic (of VTI symmetry). In such a modelling, we use published data on mineralogy and clay platelet alignment along with other micromechanical measurements. In the model, where the host matrix is isotropic, the presence of a singularity point (when the difference V S1 - V S2 changes its sign) in shear wave velocities is an indicator of brine-filled aligned cracks. In the model with the VTI host matrix and horizontally aligned cracks filled with gas, an increase in their volume concentration leads to that the azimuth at which the singularity is observed moves toward the symmetry axis. In this case, if the clay content is small (around 20 per cent), the singularity point may even vanish. The Thomsen parameters are helpful in fluid type indication in shale. An indicator of gas-filled aligned cracks is ?? > ??. If aligned cracks in illite-rich shale are brine-filled, ?? < ??. Negative value of ?? indicates brine-filled cracks in illite-rich shale. A shale with brine-filled cracks exhibits higher V p /V s ratio in the vertical direction as compared to the gas-filled shale. A disorientation of clay platelets and brine-filled cracks may lead to that the singularity point is absent for brine-saturated shale as well. In this case one can also observe ?? > ?? and decreased values of V p /V s in the vertical direction as in the case of gas-filled cracks. In the presence of vertically aligned cracks, shales exhibit distinctly revealed features of orthorhombic symmetry. The results have important applications where seismic measurements are applied to predict the maturity state of the shale. ?? 2009 The Authors Journal compilation ?? 2009 RAS.

Conference Paper↗
USGS2003

The saturated zone at Yucca Mountain: An overview of the characterization and assessment of the saturated zone as a barrier to potential radionuclide migration

The US Department of Energy is pursuing Yucca Mountain, Nevada, for the development of a geologic repository for the disposal of spent nuclear fuel and high-level radioactive waste, if the repository is able to meet applicable radiation protection standards established by the US Nuclear Regulatory Commission and the US Environmental Protection Agency (EPA). Effective performance of such a repository would rely on a number of natural and engineered barriers to isolate radioactive waste from the accessible environment. Groundwater beneath Yucca Mountain is the primary medium through which most radionuclides might move away from the potential repository. The saturated zone (SZ) system is expected to act as a natural barrier to this possible movement of radionuclides both by delaying their transport and by reducing their concentration before they reach the accessible environment. Information obtained from Yucca Mountain Site Characterization Project activities is used to estimate groundwater flow rates through the site-scale SZ flow and transport model area and to constrain general conceptual models of groundwater flow in the site-scale area. The site-scale conceptual model is a synthesis of what is known about flow and transport processes at the scale required for total system performance assessment of the site. This knowledge builds on and is consistent with knowledge that has accumulated at the regional scale but is more detailed because more data are available at the site-scale level. The mathematical basis of the site-scale model and the associated numerical approaches are designed to assist in quantifying the uncertainty in the permeability of rocks in the geologic framework model and to represent accurately the flow and transport processes included in the site-scale conceptual model. Confidence in the results of the mathematical model was obtained by comparing calculated to observed hydraulic heads, estimated to measured permeabilities, and lateral flow rates calculated by the site-scale model to those calculated by the regional-scale flow model. In addition, it was confirmed that the flow paths leaving the region of the potential repository are consistent with those inferred from gradients of measured head and those independently inferred from water-chemistry data. The general approach of the site-scale SZ flow and transport model analysis is to calculate unit breakthrough curves for radionuclides at the interface between the SZ and the biosphere using the three-dimensional site-scale SZ flow and transport model. Uncertainties are explicitly incorporated into the site-scale SZ flow and transport abstractions through key parameters and conceptual models. ?? 2002 Elsevier Science B.V. All rights reserved.

Journal of Contaminant Hydrology↗