Relevant bibliographies by topics / Geology, mathematical models

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Geology, mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 July 2024

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Journal articles on the topic "Geology, mathematical models"

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THIERGÄRTNER, HANNES. "HISTORICAL BACKGROUND OF MATHEMATICAL GEOLOGY AS DEFINED BY VISTELIUS." Earth Sciences History 42, no. 1 (January 1, 2023): 233–45. http://dx.doi.org/10.17704/1944-6187-42.1.233.

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ABSTRACT This paper is dedicated to Andrey Borisovich Vistelius for his contribution to the development of the mathematical geosciences and to his formulation of the term ‘mathematical geology’. The mathematical geosciences as a scientific subdiscipline were independently developed in several countries. J. C. Griffiths, W. C. Krumbein, and A. B. Vistelius are the most commonly recognized founders of mathematical geology. The term ‘mathematical geology’ is generally attributed to Vistelius. He began applying mathematical algorithms to solve practical geological problems in the 1940s. This new discipline was explicitly defined in his standard work Principles of Mathematical Geology published in Russian in 1980 and translated into English in 1992. Vistelius’ definition is focused on two main aspects: (1) Mathematical models developed and applied in geology in a broad sense must be conceptual, that is, they must be based on geoscientific ideas of the studied object; (2) Suitable mathematical models have to be probabilistic because most geological properties and events show a stochastic character. Modern definitions of the term ‘mathematical geosciences’ remain similar to Vistelius’ version.
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Saldaña, Manuel, Edelmira Gálvez, Pedro Robles, Jonathan Castillo, and Norman Toro. "Copper Mineral Leaching Mathematical Models—A Review." Materials 15, no. 5 (February 25, 2022): 1757. http://dx.doi.org/10.3390/ma15051757.

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Mineral leaching is the key unit operation in metallurgical processes and corresponds to the dissolution of metals. The study of leaching is carried out in many areas, such as geology, agriculture and metallurgy. This paper provides an introduction to the theoretical background regarding the mathematical modelling of the leaching process of copper minerals, establishing an overall picture of the scientific literature on technological developments and the generation of representative mathematical and theoretical models, and indicating the challenges and potential contributions of comprehensive models representing the dynamics of copper mineral leaching.
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Gorodilov, L. V. "Mathematical Models of Hydraulic Percussion Systems." Journal of Mining Science 41, no. 5 (September 2005): 475–89. http://dx.doi.org/10.1007/s10913-006-0010-2.

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Revuzhenko, A. F. "Multi-Scale Mathematical Models of Geomedia." Journal of Mining Science 58, no. 3 (June 2022): 347–56. http://dx.doi.org/10.1134/s1062739122030012.

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Revuzhenko, A. F. "Multi-Scale Mathematical Models of Geomedium." Физико-технические проблемы разработки полезных ископаемых, no. 3 (2022): 3–12. http://dx.doi.org/10.15372/ftprpi20220301.

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Thomsen, Rene O. "Dynamical Models in Geology: Sensitivity Analysis and Scientific Risk." Energy Exploration & Exploitation 11, no. 3-4 (July 1993): 329–56. http://dx.doi.org/10.1177/0144598793011003-406.

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Dynamical models are used routinely throughout various branches of geology and decisions are often based on the results of such models. Awareness of some fundamental limitations of any model used is therefore vital in order to avoid decision making based on highly uncertain results. Computer models are based on mathematical models which describe essential features of processes or system behaviour and a systematic approach to investigate and understand model limitations can therefore be applied. Sensitivity analysis provides a feel for the system response to uncertainties in both assumptions and observations. However, sensitivity analyses do not provide a feel for the level of confidence one should assign modelling results. A probabilistic approach to evaluation of uncertainties and modelling results is therefore demonstrated. Two cases are used as examples for the method and it is demonstrated how the combined sensitivity analyses and probabilistic evaluation greatly improve the use of even uncertain modelling results.
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Бикмухаметова, Дильбар Наиловна, Алсу Рафаэлевна Миндубаева, and Евгения Михайловна Нуриева. "Multi-Level Mathematical Training of University Students." Russian Digital Libraries Journal 22, no. 6 (December 15, 2019): 531–41. http://dx.doi.org/10.26907/1562-5419-2019-22-6-531-541.

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An important role for the purposeful development of the motivational component of the formed competences among students of engineering and natural-science (geological) specialties is played by the demonstration of the application of mathematical methods of calculations in engineering and geology. At the same time, the solution of practice-oriented tasks is of great importance.It is necessary to teach the student to master the material not only at the knowledge level, but also at the level of mastery of mathematical methods and models, interpolation and extrapolation not only in mathematics, but also in solving professional and life problems.
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Buryakovskiy, Leonid A., and George V. Chilingarian. "Time factor in mathematical models of geologic and technical processes." Journal of Petroleum Science and Engineering 6, no. 4 (January 1992): 341–47. http://dx.doi.org/10.1016/0920-4105(92)90060-e.

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Tonkin, R. A., M. J. O'Sullivan, and J. P. O'Sullivan. "A review of mathematical models for geothermal wellbore simulation." Geothermics 97 (December 2021): 102255. http://dx.doi.org/10.1016/j.geothermics.2021.102255.

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Li, Songyan, Zhaomin Li, and Riyi Lin. "Mathematical models for foam-diverted acidizing and their applications." Petroleum Science 5, no. 2 (May 2008): 145–52. http://dx.doi.org/10.1007/s12182-008-0022-4.

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Dissertations / Theses on the topic "Geology, mathematical models"

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Ho, Chau-man, and 何秋文. "Idealisation for mathematical modelling in geotechnical practice." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B45014280.

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Zhao, Qian, and 赵倩. "A thermomechanical approach to constitutive modeling of geomaterials." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B47166836.

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Modeling of the mechanical behavior of geomaterials is a fundamental yet very difficult problem in geotechnical engineering. The difficulty lies in that the engineering behavior of geomaterials is strongly nonlinear and anisotropic, depending on confining pressure, void ratio, stress history, and drainage conditions. A traditional approach to the modeling of geomaterials is to formulate empirical equations to fit experimental data. Generally, this approach is not able to provide physical insights into the diverse responses observed in the soil mechanics laboratories. Another conventional approach is to make use of the classical plasticity theory, established mainly for metals, to develop constitutive models for geomaterials. While this approach is capable of shedding light on the mechanisms involved, it has been recognized that such models may violate the basic laws of physics. The objective of this thesis is to apply a new approach to constructing constitutive models for geomaterials, by making use of thermomechanical principles. The essence of the new approach is that the constitutive behavior of geomaterials can be completely determined once two thermomechanical potentials, i.e. the free energy and dissipation rate functions, are specified. The yield function and flow rule in the classical plasticity theory can be established from the two potentials, and the models so derived satisfy the basic laws of physics automatically. In this thesis, the theoretical framework for constructing thermomechanical models is introduced. Several concepts in relation to plastic work, dissipated and stored energy are discussed. Both the isotropic and anisotropic models are formulated and realized in this framework and the generated predictions are compared with the test data of a series of triaxial compression tests on sand. To address the important density- and pressure-dependent behaviors of sand in the framework, a state-dependent thermomechanical model is developed, by introducing the state parameter into the dissipation rate function such that a unique set of model parameters is able to predict the behaviors of sand for a wide variation of densities and pressures. Finally, a thermomechanical model for predicting the complex unloading and reloading behaviors of sand is developed by modifying the hardening laws, and the performance of this model is investigated.
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Krantz, Robert Warren, and Robert Warren Krantz. "THE ODD-AXIS MODEL: ORTHORHOMBIC FAULT PATTERNS AND THREE-DIMENSIONAL STRAIN FIELDS." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/187542.

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Recent observations have highlighted the shortcomings of traditional thinking about faults and fault patterns. The slip model of faulting, developed by Ze'ev Reches, suggests that four sets of faults, arranged in orthorhombic symmetry about the principal strain axes, can accommodate general, three-dimensional strain. Classic conjugate faults are simply a special case of plane strain. Careful analysis of orthorhombic fault patterns and the tenets of the slip model has led to the development of a practical method for decoding the strain significance of fault systems developed in three-dimensional strain fields. The methods are implicit in a model here called the odd-axis model. This new model calls special attention to the odd axis: the one principal strain with sign opposite the other two, assuming a constant volume deformation. Odd-axis medel equations relate fault set geometry to principal strain magnitudes or ratios, the internal friction angle, φ, and the ratio of average fault slip to average spacing between faults of the same set, R. For systems where R < 0.1, the three principal strain ratios are given by tan²α, -sin²α, and -COS²α, where α is the strike of the fault set(s) measured in the plane perpendicular to the odd axis. The model also predicts slip vector orientations as functions of principal strain ratios and orientations. The kinematic implications of the odd-axis model are compatible with those of the slip model. In this first quantitative field test, both fault models are applied to the Chimney Rock array, a system of orthorhombic faults in the northern San Rafael Swell of central Utah. The odd-axis model uses fault plane and slip vector data from Chimney Rock to predict principal strain ratios (ε(y)/ε(x), ε(y)/ε(z), and ε(x)/ε(z)) of .20, -.16, and -.84. These compare extremely well with the observed values, based on fault separation measurements, of .17, -.15, and -.85. The value of ε(y)/ε(z) predicted by the slip model, -.16, matches exactly the value predicted by the odd-axis model and nearly matches the observed value, which is -.15. The success of the field test at Chimney Rock, and the conceptual agreement of both models, suggest that the new theory can accurately relate orthorhombic fault geometries and three-dimensional strain fields. Furthermore, the results underscore how important it is for geologists to recognize the sensitivity of fault geometry and kinematics to three-dimensional strain.
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Camp, Nicholas Julian. "A model for the time dependent behaviour of rock joints." Master's thesis, University of Cape Town, 1989. http://hdl.handle.net/11427/21138.

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This thesis is a theoretical investigation into the time-dependent behaviour of rock joints. Much of the research work that has been conducted to date in the area of finite element analysis has been involved with the development of special elements to deal with these discontinuities. A comprehensive literature survey is undertaken highlighting some of the significant contributions to the modelling of joints. It is then shown how internal variables can be used to model discontinuities in the rock mass. A finite element formulation is described resulting in a system of equations which can easily be adapted to cope with various constitutive behaviours on the discontinuities. In particular, a viscoplastic relationship; which uses a homogeneous, hyperbolic yield function is adopted. The viscoplastic relationship can be used for both time-dependent (creep) or quasi-static (elasto-plastic) problems. Time-dependent behaviour requires a time integration scheme and therefore a generalised explicit/implicit scheme is chosen. The resulting numerical algorithms are all implemented in the finite element program, NOSTRUM. Various examples are presented to illustrate certain features of both the formulation and the numerical algorithm. Jointed rock beams and a jointed infinite rock mass are modelled assuming plane strain conditions. Reasons are proposed to explain the predicted behaviour. The results of the analysis shows that the internal variable formulation successfully models time-dependent joint movements in a continuous media. The method gives good, qualitative results which agree with observations in deep level mines. It is recommended that quantitative mine observations be used to calibrate the model so that usable predictions of joint movement can be made. This would enable any new developments to be implemented in the model. Further work on implicit methods might allow greater modelling flexibility by reducing computer run times.
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Biesiada, Veronica Catherine. "A Characterization of Structures Across the Hurricane Ridge Fault in the Southeastern Olympic Peninsula, WA, Hamma Hamma River Transect." PDXScholar, 2019. https://pdxscholar.library.pdx.edu/open_access_etds/4883.

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The Olympic Mountains in northwestern Washington, USA are defined by the arcuate shape of the basaltic Crescent Formation (Fm.) that wraps a faulted and folded meta-sedimentary core. This area was developed through accretion and exhumation by subduction-related processes, but how this relates to the deformational history of the area is not fully understood. The region has been mapped geologically, however little focus has been placed on interpreting meso-scale structures. This study investigates structures along a transect where the Hamma Hamma River crosses the Hurricane Ridge Fault, which juxtaposes the meta-sedimentary core (west) and the basaltic Crescent Fm. (east). In the study area, the meta-sedimentary unit is characterized by outcrop scale folding with a calculated fold axis of 69-->342 and a penetrative foliation with a representative orientation of (178, 75). The folds and foliation are crosscut by two fracture populations with representative orientations of (115, 61) and (303, 76). The pillow basalts of the Crescent Fm. are near vertical, N-S striking beds that are cut by four fault groups. Fault Groups A and B have representative orientations of (304, 37) and (207, 59), respectively, and are associated with similarly oriented fracture populations. Fault Group C crosscuts Groups A and B and has a representative orientation of (031, 61). Fault Group D runs subparallel to the outcrop, cuts all other faults, and has a representative orientation of (087, 50). From an interpretation of this data, a deformation model is presented that proposes three distinct periods of deformation under three different states of stress. The first period was dominated by E-W or ENE-WSW oriented compression, followed by a period of N-S or NNW-SSE oriented compression, followed by vertical compression.
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Wijns, Christopher P. "Exploring conceptual geodynamic models : numerical method and application to tectonics and fluid flow." University of Western Australia. School of Earth and Geographical Sciences, 2005. http://theses.library.uwa.edu.au/adt-WU2005.0068.

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Geodynamic modelling, via computer simulations, offers an easily controllable method for investigating the behaviour of an Earth system and providing feedback to conceptual models of geological evolution. However, most available computer codes have been developed for engineering or hydrological applications, where strains are small and post-failure deformation is not studied. Such codes cannot simultaneously model large deformation and porous fluid flow. To remedy this situation in the face of tectonic modelling, a numerical approach was developed to incorporate porous fluid flow into an existing high-deformation code called Ellipsis. The resulting software, with these twin capabilities, simulates the evolution of highly deformed tectonic regimes where fluid flow is important, such as in mineral provinces. A realistic description of deformation depends on the accurate characterisation of material properties and the laws governing material behaviour. Aside from the development of appropriate physics, it can be a difficult task to find a set of model parameters, including material properties and initial geometries, that can reproduce some conceptual target. In this context, an interactive system for the rapid exploration of model parameter space, and for the evaluation of all model results, replaces the traditional but time-consuming approach of finding a result via trial and error. The visualisation of all solutions in such a search of parameter space, through simple graphical tools, adds a new degree of understanding to the effects of variations in the parameters, the importance of each parameter in controlling a solution, and the degree of coverage of the parameter space. Two final applications of the software code and interactive parameter search illustrate the power of numerical modelling within the feedback loop to field observations. In the first example, vertical rheological contrasts between the upper and lower crust, most easily related to thermal profiles and mineralogy, exert a greater control over the mode of crustal extension than any other parameters. A weak lower crust promotes large fault spacing with high displacements, often overriding initial close fault spacing, to lead eventually to metamorphic core complex formation. In the second case, specifically tied to the history of compressional orogenies in northern Nevada, exploration of model parameters shows that the natural reactivation of early normal faults in the Proterozoic basement, regardless of basement topography or rheological contrasts, would explain the subsequent elevation and gravitationally-induced thrusting of sedimentary layers over the Carlin gold trend, providing pathways and ponding sites for mineral-bearing fluids.
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Burgess, Peter Mark. "A quantitative forward modelling analysis of the controls on passive rift-margin stratigraphy." Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:1249833d-ef11-4327-bdbd-5d0c40faa29e.

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A quantitative forward model has been developed to investigate the controls on the deposition, erosion, and preservation of passive rift margin stratigraphy. The model includes thermal subsidence, variable absolute sealevel, flexural isostasy, subaerial and submarine deposition on fluvial and marine equilibrium profiles, and the facility to vary sediment supply through time. Results from the quantitative model can be used to reproduce elements of the sequence stratigraphic depositional model. Conducting sensitivity tests demonstrates that variables such as sediment supply and fluvial profile behaviour are likely to be of equal importance to thermal subsidence and eustasy in passive margin stratigraphy. Sensitivity tests with the quantitative model also demonstrate the problems associated with attempting to use a discretised stratigraphic model to investigate unforced cyclicty resulting from complex interactions in stratigraphic systems. Although the model appears capable of producing such unforced cyclical behaviour, this cyclicity is shown to be due to a numerical instability within the model which occurs with certain initial conditions and assumptions. The applicability of the model to observed stratigraphy is tested by comparing specific model output to patterns of stratigraphy from the North American Atlantic margin. The results from this test demonstrate that although the model is in many respects simplistic when compared to the complexities of natural systems, it is nevertheless capable of reproducing some of the basic elements of the observed stratigraphic patterns.
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Linde, Tamara Causer. "Relational Database Analysis of Dated Prehistoric Shorelines to Establish Sand Partitioning in Late Holocene Barriers and Beach Plains of the Columbia River Littoral Cell, Washington and Oregon, USA." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/1696.

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Studies of episodic shoreline accretion of the Columbia River Littoral Cell (CRLC) have been ongoing since 1964. In this study, the sediment volumes in the late Holocene barriers and beach plains are compiled and formatted in GIS compatible databases for the four sub-cells of the CRLC. Initial evaluation involved the creation of a geodatabase of 160 dated retreat scarp positions, that were identified on across-shore GPR and borehole profiles. Ten primary timelines were identified throughout the CRLC (0-4700 ybp) and those were used to develop polygon cells. Elevation, distance measurements, and position information were all linked to the polygon through a centroid location within the geodatabase. Once the geodatabase was completed, data was imported into MSAccessTM to create a relational database that would allow for examination of the littoral cell in its entirety or of the individual sub-cells. Within the database, sediment volumes, ages, accretion rates, sediment thicknesses, and timeline relationships were calculated and recorded. Using the database, the accretion history of the Columbia River Littoral Cell was evaluated and this examination illustrated the complexity of the system. Northern littoral transport was shown to be an important factor in the development of the littoral cell as a whole. Total sediment volume in the littoral cell was calculated to be 1.74 x 109 m3, with a mean accretion rate of 1.90 x 104 m3/yr, which is significantly less than some previous studies. This is due to a more detailed analysis of the beach and foredune facies themselves. This is likely the result of the higher precision of beach and foredune surface information using LiDAR. The database shows that the developmental history of the CRLC is dependent on temporal and spatial constraints that can be coupled with reverse modeling to predict shoreline erosion trends from impounded river sediments and potential global sea level rise. The North Beaches and Grayland Plains sub-cells have the greatest potential for future erosion; followed by the Clatsop Plains sub-cell.
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Waibel, Michael Scott. "A Numerical Model Investigation of the Role of the Glacier Bed in Regulating Grounding Line Retreat of Thwaites Glacier, West Antarctica." Thesis, Portland State University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10259298.

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I examine how two different realizations of bed morphology affect Thwaites Glacier response to ocean warming through the initiation of marine ice sheet instability and associated grounding line retreat. A state of the art numerical ice sheet model is used for this purpose. The bed configurations used are the 1-km resolution interpolated BEDMAP2 bed and a higher-resolution conditional simulation produced by John Goff at the University of Texas using the same underlying data. The model is forced using a slow ramp approach, where melt of ice on the floating side of the grounding line is increased over time, which gently nudges the glacier toward instability. Once an instability is initiated, the anomalous forcing is turned off, and further grounding line retreat is tracked.

Two model experiments are conducted. The first experiment examines the effect of different anomalous forcing magnitudes over the same bed. The second experiment compares the generation and progress of instabilities over different beds. Two fundamental conclusions emerge from these experiments. First, different bed geometries require different ocean forcings to generate a genuine instability, where ice dynamics lead to a positive feedback and grounding line retreat becomes unstable. Second, slightly different forcings produce different retreat rates, even after the anomalous forcing is shut off, because different forcing magnitudes produce different driving stresses at the time the instability is initiated. While variability in the retreat rate over time depends on bed topography, the rate itself is set by the magnitude of the forcing. This signals the importance of correct knowledge of both bed shape and ocean circulation under floating portions of Antarctic ice sheets. The experiments also imply that different ocean warming rates delivered by different global warming scenarios directly affects the rate of Antarctic contribution to sea level rise.

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Hiester, Justin. "Investigations into the Regional and Local Timescale Variations of Subglacial Drainage Networks." PDXScholar, 2013. https://pdxscholar.library.pdx.edu/open_access_etds/1022.

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Subglacial water plays an important role in the regulation of an ice sheet's mass balance. It may be the dominant control on the velocities of ice streams and outlet glaciers on scales of months to millennia. Recent satellite observations of ice surface elevation changes have given researchers new insights into how subglacial water is stored and transported. Localized uplift and settling of the ice surface implies that lakes exist beneath the ice sheet that are being filled and drained on relatively short time scales. %At the base of an ice sheet water can be transported through a variety of drainage networks or stored in subglacial lakes. Here, a numerical investigation of the mechanisms of transport and storage of subglacial water and the associated time scales is presented. Experiments are carried out using a finite element model of coupled ice and water flow. The first experiment seeks to understand the relationship between the depth of a basal depression and the area over which the feature affects basal water flow. It is found that as the perturbation to a topographic depression's depth is increased, water is rerouted in response to the perturbation. Additionally it is found that the relationship between perturbation depth and the extent upstream to which its effects reach is nonlinear. The second experiment examines how the aspect ratio of bed features (prolate, oblate, or equidimensional) influences basal water flow. It is found that the systems that develop and their interactions are mediated by both the topography and the feedbacks taken into account by the coupling of the systems in the model. Features oriented parallel to ice and water flow are associated with distributed fan systems that develop branches which migrate laterally across the domain and interact with one another on monthly and yearly timescales. Laterally oriented features develop laterally extensive ponds. As the ratio of longitudinal to lateral dimension of the topography is increased, a combination of these two water distributions is seen.
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Books on the topic "Geology, mathematical models"

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L, Hunter Regina, and Mann C. John, eds. Techniques for determining probabilities of geologic events and processes. New York: Oxford University Press, 1992.

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Knoring, L. D. Mathematics for geologists. Rotterdam: A.A. Balkema, 1993.

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Computational engineering geology. Upper Saddle River, NJ: Prentice Hall, 1997.

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Cramer, Barton Christopher, and La Pointe P. R, eds. Fractals in the earth sciences. New York: Plenum Press, 1995.

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N, Bondarenko V., and Ovchinnikov Lev Nikolaevich, eds. Matematicheskie modeli zavisimosti geologicheskikh obʺektov. Moskva: "Nauka", 1989.

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N, Dmitriev A., Solovʹev V. A, and Institut geologii i geofiziki (Akademii͡a︡ nauk SSSR), eds. Modelirovanie pri logiko-matematicheskoĭ obrabotke geologicheskikh dannykh: Sbornik nauchnykh trudov. Novosibirsk: Akademii͡a︡ nauk SSSR, Sibirskoe otd-nie, In-t geologii i geofiziki, 1990.

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Snay, Richard A. Project REDEAM: Models for historical horizontal deformation. Rockville, MD: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, Charting and Geodetic Services, 1987.

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Snay, Richard A. Project REDEAM: Models for historical horizontal deformation. Rockville, MD: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, Charting and Geodetic Services, 1987.

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Snay, Richard A. Project REDEAM: Models for historical horizontal deformation. Rockville, MD: U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, Charting and Geodetic Services, 1987.

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Dietrich, Stauffer, and Oliveira, Suzana Moss de, 1955-, eds. Biology, sociology, geology by computational physicists. Amsterdam: Elsevier, 2006.

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Book chapters on the topic "Geology, mathematical models"

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Kistovich, Anatoly. "The Exact Mathematical Models of Nonlinear Surface Waves." In Springer Geology, 305–16. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77788-7_32.

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Juming, Zhang, Liu Chengzou, and Sun Huiwen. "Three Dimensional Mathematical Models of Geological Bodies and Their Graphical Display *." In Mathematical Geology and Geoinformatics, 103–14. London: CRC Press, 2021. http://dx.doi.org/10.1201/9780429070891-11.

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Jia-Hua, Wang, Zhang Tuan-Feng, and Huang Cang-Dian. "The Simulation of Braided Channels in Two Dimensions with Random Walk Model." In Mathematical Geology and Geoinformatics, 115–24. London: CRC Press, 2021. http://dx.doi.org/10.1201/9780429070891-12.

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Dela Haije, Tom, and Aasa Feragen. "Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI." In Mathematics and Visualization, 193–202. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56215-1_9.

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AbstractDiffusion-weighted magnetic resonance imaging (MRI) is sensitive to ensemble-averaged molecular displacements, which provide valuable information on e.g. structural anisotropy in brain tissue. However, a concrete interpretation of diffusion-weighted MRI data in terms of physiological or structural parameters turns out to be extremely challenging. One of the main reasons for this is the multi-scale nature of the diffusion-weighted signal, as it is sensitive to the microscopic motion of particles averaged over macroscopic volumes. In order to analyze the geometrical patterns that occur in (diffusion-weighted measurements of) biological tissue and many other structures, we may invoke tools from the field of stochastic geometry. Stochastic geometry describes statistical methods and models that apply to random geometrical patterns of which we may only know the distribution. Despite its many uses in geology, astronomy, telecommunications, etc., its application in diffusion-weighted MRI has so far remained limited. In this work we review some fundamental results in the field of diffusion-weighted MRI from a stochastic geometrical perspective, and discuss briefly for which other questions stochastic geometry may prove useful. The observations presented in this paper are partly inspired by the Workshop on Diffusion MRI and Stochastic Geometry held at Sandbjerg Estate (Denmark) in 2019, which aimed to foster communication and collaboration between the two fields of research.
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Elena, Debolskaya. "A Mathematical Model of Reservoir and River Bank Deformations in Permafrost Regions Under Simultaneous Effect of the Waves and Warming." In Engineering Geology for Society and Territory - Volume 3, 469–72. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09054-2_96.

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Tang, Chuanfeng, Liangquan Ge, Shengliang Guo, Zhipeng Deng, and Jin Li. "Study on a Non-collecting Atmospheric Radon Concentration Measurement System." In Springer Proceedings in Physics, 1002–14. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-1023-6_85.

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AbstractRadon in the atmosphere is an important tracer in meteorology and geology and an important index of environmental radioactivity level evaluation. In this paper, NaI (Tl) scintillator detector was developed to directly measure radon concentration in the atmosphere, and a mathematical model of atmospheric radon gamma measurement was proposed, which solved the technical problem of online real-time monitoring of atmospheric radon concentration. It has important scientific and practical value.In this paper, the characteristic gamma peaks of radon daughters 214Bi (609.31 keV) and 214Pb (351.92 keV) are respectively selected to calculate the radon concentration in the atmosphere. During the measurement period, the variation trend of radon concentration is the same as the theory, which suggests a higher concentration in the morning and a lower in the evening. Finally, the experimental measurement results were compared with the RAD7 radon measuring instrument. The error range of this detection system is 79.73% smaller than that of RAD7 on average, and its detection limit reaches 0.29 Bq/m3 with a 30-min-measurement at room temperature. This paper proves that it is feasible to directly measure the activity concentration of radon in the atmosphere. The atmospheric radon measurement method proposed in this paper can accurately obtain the concentration of atmospheric radon and has the advantages of convenience, large measuring range, low detection limit, and online measurement.
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Buryakovsky, Leonid A., George V. Chilingar, and Fred Aminzadeh. "Mathematical Models in Petroleum Geology." In Petroleum Geology of the South Caspian Basin, 243–47. Elsevier, 2001. http://dx.doi.org/10.1016/b978-088415342-9/50013-8.

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Kacewicz, Marek. "Mathematics Between Source And Trap: Uncertainty In Hydrocarbon Migration Modeling." In Computers in Geology - 25 Years of Progress. Oxford University Press, 1994. http://dx.doi.org/10.1093/oso/9780195085938.003.0011.

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Petroleum geology provides a wide spectrum of data that differs from frontier to mature areas. Data quality and quantity control which mathematical methods and techniques should be applied. In this paper two mathematical methods are shown: fuzzy-set theory and possibility theory as applied to permeability prediction and stochastic modeling of traps and leaks. Both methods are used in the modeling of hydrocarbon migration efficiency. Examples of how data uncertainty may affect final assessment of oil accumulation are presented. The complexity of petroleum geology and its importance to society stimulate research in different scientific areas including mathematical geology, which is becoming steadily more important. Armed with workstations, mainframes, and supercomputers, research laboratories in the petroleum industry investigate sophisticated mathematical techniques and develop complex mathematical models which can speed and improve exploration and lower total exploration costs. Together with classical analysis of geological, geochemical, and seismic data, mathematics provides an additional tool for basin research. The elements of petroleum systems—maturation, expulsion and primary migration, secondary migration, seals, reservoirs, and traps—may be better described by properly applied mathematical techniques. The complexity of petroleum geology and its importance to society stimulate research in different scientific areas including mathematical geology, which is becoming steadily more important. Armed with workstations, mainframes, and supercomputers, research laboratories in the petroleum industry investigate sophisticated mathematical techniques and develop complex mathematical models which can speed and improve exploration and lower total exploration costs. Together with classical analysis of geological, geochemical, and seismic data, mathematics provides an additional tool for basin research. The elements of petroleum systems—maturation, expulsion and primary migration, secondary migration, seals, reservoirs, and traps—may be better described by properly applied mathematical techniques. The applicability of mathematical methods differs in frontier and mature areas and depends upon the quality and quantity of available information. Frontier areas for which data are mostly qualitative require methods which can handle imprecise and limited information easily. Fuzzy-set theory with fuzzy inference algorithms and artificial intelligence are useful approaches. Cokriging and "soft" geostatistical approaches also may be helpful.
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Barron, Eric J. "MATHEMATICAL CLIMATE MODELS: INSIGHTS INTO THE RELATIONSHIP BETWEEN CLIMATE AND ECONOMIC SEDIMENTARY DEPOSITS." In Paleoclimates and Economic Geology, 31–83. SEPM (Society for Sedimentary Geology), 1986. http://dx.doi.org/10.2110/scn.86.18.0031.

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Buryakovsky, Leonid A., George V. Chilingar, and Fred Aminzadeh. "Mathematical Models in Oil and Gas Exploration and Production (Static Geologic Systems)." In Petroleum Geology of the South Caspian Basin, 248–346. Elsevier, 2001. http://dx.doi.org/10.1016/b978-088415342-9/50014-x.

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Conference papers on the topic "Geology, mathematical models"

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Evgrashkina, Galina. "MATHEMATICAL MODELS OF THE VERTICAL SALT TRANSFER AT MINE DUMPS FOR SUBSTANTIATION OF THEIR RECLAMATION METHOD." In 13th SGEM GeoConference on SCIENCE AND TECHNOLOGIES IN GEOLOGY, EXPLORATION AND MINING. Stef92 Technology, 2013. http://dx.doi.org/10.5593/sgem2013/ba1.v1/s03.041.

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Shevelan, John, and Nicholas T. Smith. "Characterisation of the Geology of the UK Low Level Waste Repository." In ASME 2011 14th International Conference on Environmental Remediation and Radioactive Waste Management. ASMEDC, 2011. http://dx.doi.org/10.1115/icem2011-59146.

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The UK Low Level Waste Repository Ltd (LLWR) submitted an Environmental Safety Case (ESC) for the disposal of low-level waste (LLW) to the UK Environment Agency on the 1st of May 2011. As part of the ESC, the LLWR have to demonstrate that a programme of site investigation and site characterisation has been carried out to provide the requisite information for the ESC and support facility design and construction. This paper explains the development of the site investigation programme and how the understanding of the geology of the site has developed. The geological environment in the region of the LLWR consists of Quaternary age deposits overlying older bedrock. The site has been subjected to a series of site investigation programmes from 1939 to the present day. The development of 3-D geological models was necessary to integrate data from boreholes, trial pits, geophysical investigations and beach exposures and data gained from site operations. The understanding of the geology has developed with each new set of data. Early simple interpretations from a few boreholes have been superseded by a series of more complex interpretations each incorporating the increasingly detailed observations. Initial attempts to develop a lithostratigraphic representation of the geology proved difficult. It was also difficult provide a clear link between the geology and the hydrogeology using a lithostratigraphic approach as required for the development of hydrogeological models. A lithofacies approach to characterising the geology was adopted in 2007, which has allowed the grouping of geological units with similar hydraulic properties and the development of a regional 3-D geological model. The 3-D geological model has been used as the framework for the development of a hydrogeological model for the site. The development of the 3-D geological models has been iterative. It was observed that there are differences between models developed using solely mathematical interpolation and those controlled by geological interpretation. The different representations of the geological information have been used to consider the effects of uncertainty in the geological interpretation in the hydrogeological modelling.
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Vlada, Marin. "NONLINEAR MODELS. THEORY, SOFTWARE AND APPLICATIONS." In eLSE 2013. Carol I National Defence University Publishing House, 2013. http://dx.doi.org/10.12753/2066-026x-13-188.

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This paper presents mathematical models that estimate nonlinear evolution processes or phenomena based on parameters that define processes and phenomena in pursuit of calculations and approximations (fitting) of experimental data. It addresses the non-linear model (nonlinear regression), the method of Least Squares (MLS) with examples. Are presented theoretical calculations for logarithmic and exponential models realizing a comparison with results obtained using software. In practice in various scientific, economic, social, etc.. occur most complex problems to be solved. Science and scientific research have developed influenced by the complexity of these issues and human society projects. Treasury of human knowledge is influenced by science and technology, culture and art, and in particular how to solve unsolved problems of human society. Such problems arise in chemistry, biology and medicine, physics and geology, in economics and sociology, etc.. To study and analyze processes and phenomena such activities require valid and effective methods and techniques so that models used to eliminate as many uncertainties and approximations. In practice, the study of various processes and phenomena is a wide variety of nonlinear models. The diversity of these nonlinear models depends on the variety fields of chemistry, physics, medicine, biology, sociology, economics, etc. Mathematics and Computer Science have changed dramatically analiya project on methods and analysis of experimental data. Chemistry, biology, pharmacokinetics are areas / disciplines have greatly benefited from the development of theories, methods and techniques of Mathematics and Computer Science via computer. Today procedures for drug testing include important results obtained in research on drug use in the treatment of various diseases. Bioinformatics, Biostatistics and Biopharmaceutics are disciplines that provide various methods and analysis on the pharmacokinetics.
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Hampton, Thomas J., Mohamed El-Mandouh, Stevan Weber, Tirth Thaker, K. Patel, Barclay Macaul, and Jim Erdle. "Comparing Steam Flood Analytical and Simulation Models ~ Strengths and Limitations." In SPE Western Regional Meeting. SPE, 2021. http://dx.doi.org/10.2118/205369-ms.

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Abstract Mathematical Models are needed to aid in defining, analyzing, and quantifying solutions to design and manage steam floods. This paper discusses two main modeling methods – analytical and numerical simulation. Decisions as to which method to use and when to use them, requires an understanding of assumptions used, strengths, and limitations of each method. This paper presents advantages and disadvantages through comparison of analytical vs simulation when reservoir characterization becomes progressively more complex (dip, layering, heterogeneity between injector/producer, and reservoir thickness).While there are many analytical models, three analytical models are used for this paper:Marx & Langenheim, Modified Neuman, and Jeff Jones.The simulator used was CMG Stars on single pattern on both 5 Spot and 9 Spot patterns and Case 6 of 9 patterns, 5-Spot. Results were obtained using 6 different cases of varying reservoir properties based on Marx & Langenheim, Modified Neuman, and Jeff Jones models.Simulation was also done on each of the 6 cases, using Modified Neuman steam rates and then on Jeff Jones Steam rates using 9-Spot and 5-Spot patterns.This was done on predictive basis on inputs provided, without adjusting or history matching on analog or historical performance.Optimization runs using Particle Swarm Optimization was applied on one case in minimizing SOR and maximize NPV. Conclusion from comparing cases is that simulation is needed for complex geology, heterogeneity, and changes in layering. Also, simulation can be used for maximizing economics using AI based optimization tool. While understanding limitations, the analytical models are good for quick looks such as screening, scoping design, some surveillance, and for conceptual understanding of basic steam flood on uniform geologic properties. This paper is innovative in comparison of analytical models and simulation modeling.Results that quantify differences of oil rate, SOR, and injection rates (Neuman and Jeff Jones) impact on recovery factors is presented.
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Li, R., J. Fu, T. Gao, and P. Zhang. "Application of Deep Neural Network (DNN) in Reservoir Simulation for Hydraulic Fracturing and Production of Unconventional Wells." In International Petroleum Technology Conference. IPTC, 2024. http://dx.doi.org/10.2523/iptc-23759-ms.

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Abstract This study focuses on developing a Deep Neural Network (DNN)-based reservoir simulator aimed at improving the efficiency and precision of hydraulic fracturing and production forecasting. Given the complex and nonlinear nature of reservoir behavior, our goal is to implement an automated, scalable solution to effectively navigate these challenges. The proposed DNN simulator integrates diverse data sources, enhancing a comprehensive understanding of reservoir dynamics and supporting real-time decision-making and operational optimization. Reservoir simulation, a key numerical method for predicting fluid behavior in porous media like oil and gas reservoirs, is vital for crafting and refining production strategies in the oil and gas industry. A swift and accurate simulation is essential for effective field development. The study particularly addresses unconventional wells—horizontal wells fractured to facilitate oil and gas flow—where challenges persist in areas like fracture geometry characterization, fluid dynamics between the matrix and fractures, and pressure variation prediction during field development. The scarcity and diversity of data, encompassing both the volume and variety from sources like geology, geophysics, lab tests, and engineering, add complexity to simulating these wells. We explore the use of Deep Neural Networks, a machine learning algorithm capable of deciphering intricate data relationships, in this context. Recent advancements in machine learning have opened avenues for employing DNNs in reservoir simulation, which is a supplement to traditional time-intensive mathematical algorithms. We constructed and simulated both three-dimensional conceptual models and unconventional field models using this approach. The results validate the deep learning method's accuracy and speed, showcasing its supplementary to conventional numerical reservoir simulators.
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Panzeri, M., E. Della Rossa, L. Dovera, M. Riva, and A. Guadagnini. "Integration of Markov Mesh Models and Ensemble Data Assimilation in Reservoirs with Complex Geology." In ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2014. http://dx.doi.org/10.3997/2214-4609.20141785.

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Wang, Jianguo, and shizhen Zhang. "The Application of Case Teaching in Graduate Course Construction: a Case Study of " Mathematical Geology Theory and Method "." In Proceedings of the 2019 4th International Conference on Modern Management, Education Technology and Social Science (MMETSS 2019). Paris, France: Atlantis Press, 2019. http://dx.doi.org/10.2991/mmetss-19.2019.162.

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Gheorghe Gabriel, Dolea. "CONSIDERATIONS REGARDING THE DEVELOPMENT OF AN ECONOMIC-MATHEMATICAL MODEL FOR OPTIMIZING THE TECHNOLOGICAL VARIANTS IN THE COAL MINE FACES." In 14th SGEM GeoConference on SCIENCE AND TECHNOLOGIES IN GEOLOGY, EXPLORATION AND MINING. Stef92 Technology, 2014. http://dx.doi.org/10.5593/sgem2014/b13/s3.022.

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Evgrashkina, Galina. "MATHEMATICAL MODEL OF CHANGES IN THE HYDROGEOLOGICAL CONDITIONS OF TERRITORIES ADJACENT TO MINE WASTE WATER OF CONTAINMENT PONDS-STORAGE." In 13th SGEM GeoConference on SCIENCE AND TECHNOLOGIES IN GEOLOGY, EXPLORATION AND MINING. Stef92 Technology, 2013. http://dx.doi.org/10.5593/sgem2013/ba1.v2/s02.032.

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Smyslova, Irina S. "The State Rubricator of Sci-tech Information-2022: Updating the subject scope in maths, physics and geology." In Twenty Sixth International Conference and Exhibition «LIBCOM-2022». Russian National Public Library for Science and Technology, 2022. http://dx.doi.org/10.33186/978-5-85638-257-9-2022-166-176.

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The author discusses updating the model STRSTI-2021 version. She analyzes the structure of subject vertices levels in STRSTI-2022. The examples of STRSTI subject and structural contents in the priority disciplines of mathematics, physics and geology, included into the Program of Fundamental Studies in the Russian Federation for the years 2021–2030, are offered. Further vectors for updating are identified. The paper is prepared within the framework of the Government Order No. 1021070112681-2-1.2.1;5.8.3 (FNEG-2022-0006).
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Reports on the topic "Geology, mathematical models"

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Lai, C. H. Mathematical models of thermal and chemical transport in geologic media. Office of Scientific and Technical Information (OSTI), December 1985. http://dx.doi.org/10.2172/5709552.

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Runchal, A. K., and B. Sagar. PORFLO-3: A mathematical model for fluid flow, heat, and mass transport in variably saturated geologic media: Users manual, Version 1. 0. Office of Scientific and Technical Information (OSTI), July 1989. http://dx.doi.org/10.2172/5867308.

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Sagar, B., and A. Runchal. PORFLO-3: A mathematical model for fluid flow, heat, and mass transport in variably saturated geologic media; Theory and numerical methods, Version 1.0. Office of Scientific and Technical Information (OSTI), March 1990. http://dx.doi.org/10.2172/137710.

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