*David R. Steward*

- Published in print:
- 2020
- Published Online:
- November 2020
- ISBN:
- 9780198856788
- eISBN:
- 9780191890031
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198856788.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces the philosophical perspective for solving problems with the Analytic Element Method, organized within three common types of problems: gradient driven flow and conduction, ...
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This chapter introduces the philosophical perspective for solving problems with the Analytic Element Method, organized within three common types of problems: gradient driven flow and conduction, waves, and deformation by forces. These problems are illustrated by classic, well known solutions to problems with a single isolated element, along with their extension to complicated interactions occurring amongst collections of elements. Analytic elements are presented within fields of study to demonstrate their capacity to represent important processes and properties across a broad range of applications, and to provide a template for transcending solutions across the wide range of conditions occurring along boundaries and interfaces. While the mathematical and computational developments necessary to solve each problem are developed in later chapters, each figure documents where its solutions are presented.Less

This chapter introduces the philosophical perspective for solving problems with the Analytic Element Method, organized within three common types of problems: gradient driven flow and conduction, waves, and deformation by forces. These problems are illustrated by classic, well known solutions to problems with a single isolated element, along with their extension to complicated interactions occurring amongst collections of elements. Analytic elements are presented within fields of study to demonstrate their capacity to represent important processes and properties across a broad range of applications, and to provide a template for transcending solutions across the wide range of conditions occurring along boundaries and interfaces. While the mathematical and computational developments necessary to solve each problem are developed in later chapters, each figure documents where its solutions are presented.

*David C. Culver and Tanja Pipan*

- Published in print:
- 2019
- Published Online:
- June 2019
- ISBN:
- 9780198820765
- eISBN:
- 9780191860485
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198820765.003.0001
- Subject:
- Biology, Ecology, Biodiversity / Conservation Biology

The main subterranean habitats are: small cavities—interstitial spaces beneath surface waters; large cavities—caves; and shallow subterranean habitats—voids of various sizes close to the surface. The ...
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The main subterranean habitats are: small cavities—interstitial spaces beneath surface waters; large cavities—caves; and shallow subterranean habitats—voids of various sizes close to the surface. The defining feature of all these habitats is the absence of light. Environmental variation is also reduced and most subterranean habitats rely on nutrients transported from the surface. The aquatic component of caves includes water percolating from the surface (including epikarst), streams, and resurgences. Terrestrial habitats include epikarst, and the vadose zone. The aquatic interstitial habitat is comprised of the water-filled spaces between grains of unconsolidated sediments. Shallow subterranean habitats are ones close to the surface. They include the hypotelminorheic, interstitial, epikarst, MSS, soil, lava tubes, calcrete aquifers, and iron-ore caves. They share an absence of light, close surface connections, relatively high nutrient levels relative to other subterranean habitats, and the presence of species highly modified for subterranean life.Less

The main subterranean habitats are: small cavities—interstitial spaces beneath surface waters; large cavities—caves; and shallow subterranean habitats—voids of various sizes close to the surface. The defining feature of all these habitats is the absence of light. Environmental variation is also reduced and most subterranean habitats rely on nutrients transported from the surface. The aquatic component of caves includes water percolating from the surface (including epikarst), streams, and resurgences. Terrestrial habitats include epikarst, and the vadose zone. The aquatic interstitial habitat is comprised of the water-filled spaces between grains of unconsolidated sediments. Shallow subterranean habitats are ones close to the surface. They include the hypotelminorheic, interstitial, epikarst, MSS, soil, lava tubes, calcrete aquifers, and iron-ore caves. They share an absence of light, close surface connections, relatively high nutrient levels relative to other subterranean habitats, and the presence of species highly modified for subterranean life.

*Garrison Sposito*

- Published in print:
- 1999
- Published Online:
- November 2020
- ISBN:
- 9780195109900
- eISBN:
- 9780197561058
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195109900.003.0007
- Subject:
- Earth Sciences and Geography, Oceanography and Hydrology

The first detailed study of solute movement through the vadose zone at field scales of space and time was performed by Biggar and Nielsen (1976). Their experiment was ...
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The first detailed study of solute movement through the vadose zone at field scales of space and time was performed by Biggar and Nielsen (1976). Their experiment was conducted on a 150-ha agricultural site located at the West Side Field Station of the University of California, where the soil (Panoche series) exhibits a broad range of textures. Twenty well-separated, 6.5-m-square plots, previously instrumented to monitor matric potential and withdraw soil solution for chemical analysis, were ponded with water containing low concentrations of the tracer anions chloride and nitrate. After about 1 week, steady-state infiltration conditions were established, and 0.075 m of water containing the two anions at concentrations between 0.1 and 0.2 mol L-1 was leached through each plot at the local infiltration rate, which varied widely from 0.054 to 0.46 m day-1, depending on plot location. Once this solute pulse had infiltrated (< 1.5 days), leaching under ponded conditions was recommenced with the water low in chloride and nitrate. Solution samples were extracted before and after the solute pulse input at six depths up to 1.83 m below the land surface in each plot. Analyses of these samples for chloride and nitrate produced a broad range of concentration data which nonetheless showed an excellent linear correlation between the concentrations of the two anions (R2= 0.975), with a proportionality coefficient equal to that expected on the basis of the composition of the input pulse. Values of the measured solute concentrations at each sampling depth were tabulated as functions of the leaching time. Biggar and Nielsen (1976) decided to fit their very large concentration-depth-time database to a finite-pulsc-input solution of the one-dimensional advection-dispersion equation, leaving both the dispersion coefficient D and advection velocity u as adjustable parameters. The 359 field-wide values of u obtained in this way were highly variable (CV ≈ 200%), but also highly correlated (R2 = 0.84) and proportional to values of the advection velocity calculated directly as the ratio of water flux density to water content in each field plot (Biggar and Nielsen, 1976, figure 4).
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The first detailed study of solute movement through the vadose zone at field scales of space and time was performed by Biggar and Nielsen (1976). Their experiment was conducted on a 150-ha agricultural site located at the West Side Field Station of the University of California, where the soil (Panoche series) exhibits a broad range of textures. Twenty well-separated, 6.5-m-square plots, previously instrumented to monitor matric potential and withdraw soil solution for chemical analysis, were ponded with water containing low concentrations of the tracer anions chloride and nitrate. After about 1 week, steady-state infiltration conditions were established, and 0.075 m of water containing the two anions at concentrations between 0.1 and 0.2 mol L-1 was leached through each plot at the local infiltration rate, which varied widely from 0.054 to 0.46 m day-1, depending on plot location. Once this solute pulse had infiltrated (< 1.5 days), leaching under ponded conditions was recommenced with the water low in chloride and nitrate. Solution samples were extracted before and after the solute pulse input at six depths up to 1.83 m below the land surface in each plot. Analyses of these samples for chloride and nitrate produced a broad range of concentration data which nonetheless showed an excellent linear correlation between the concentrations of the two anions (R2= 0.975), with a proportionality coefficient equal to that expected on the basis of the composition of the input pulse. Values of the measured solute concentrations at each sampling depth were tabulated as functions of the leaching time. Biggar and Nielsen (1976) decided to fit their very large concentration-depth-time database to a finite-pulsc-input solution of the one-dimensional advection-dispersion equation, leaving both the dispersion coefficient D and advection velocity u as adjustable parameters. The 359 field-wide values of u obtained in this way were highly variable (CV ≈ 200%), but also highly correlated (R2 = 0.84) and proportional to values of the advection velocity calculated directly as the ratio of water flux density to water content in each field plot (Biggar and Nielsen, 1976, figure 4).

*David R. Steward*

- Published in print:
- 2020
- Published Online:
- November 2020
- ISBN:
- 9780198856788
- eISBN:
- 9780191890031
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198856788.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science. The goals are: to introduce readers to the basic principles of the ...
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The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science. The goals are: to introduce readers to the basic principles of the AEM, to provide a template for those interested in pursuing these methods, and to empower readers to extend the AEM paradigm to an even broader range of problems. A comprehensive paradigm: place an element within its landscape, formulate its interactions with other elements using linear series of influence functions, and then solve for its coefficients to match its boundary and interface conditions with nearly exact precision. Collectively, sets of elements interact to transform their environment, and these synergistic interactions are expanded upon for three common types of problems. The first problem studies a vector field that is directed from high to low values of a function, and applications include: groundwater flow, vadose zone seepage, incompressible fluid flow, thermal conduction and electrostatics. A second type of problem studies the interactions of elements with waves, with applications including water waves and acoustics. A third type of problem studies the interactions of elements with stresses and displacements, with applications in elasticity for structures and geomechanics. The Analytic Element Method paradigm comprehensively employs a background of existing methodology using complex functions, separation of variables and singular integral equations. This text puts forth new methods to solving important problems across engineering and science, and has a tremendous potential to broaden perspective and change the way problems are formulated.Less

The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science. The goals are: to introduce readers to the basic principles of the AEM, to provide a template for those interested in pursuing these methods, and to empower readers to extend the AEM paradigm to an even broader range of problems. A comprehensive paradigm: place an element within its landscape, formulate its interactions with other elements using linear series of influence functions, and then solve for its coefficients to match its boundary and interface conditions with nearly exact precision. Collectively, sets of elements interact to transform their environment, and these synergistic interactions are expanded upon for three common types of problems. The first problem studies a vector field that is directed from high to low values of a function, and applications include: groundwater flow, vadose zone seepage, incompressible fluid flow, thermal conduction and electrostatics. A second type of problem studies the interactions of elements with waves, with applications including water waves and acoustics. A third type of problem studies the interactions of elements with stresses and displacements, with applications in elasticity for structures and geomechanics. The Analytic Element Method paradigm comprehensively employs a background of existing methodology using complex functions, separation of variables and singular integral equations. This text puts forth new methods to solving important problems across engineering and science, and has a tremendous potential to broaden perspective and change the way problems are formulated.