Fractal mobile/immobile solute transport
A fractal mobile/immobile model for solute transport assumes power law waiting times in the immobile zone, leading to a fractional time derivative in the model equations. The equations are equivalent to previous models of mobile/immobile transport with power law memory functions and are the limiting...
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Veröffentlicht in: | Water resources research 2003-10, Vol.39 (10), p.n/a |
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description | A fractal mobile/immobile model for solute transport assumes power law waiting times in the immobile zone, leading to a fractional time derivative in the model equations. The equations are equivalent to previous models of mobile/immobile transport with power law memory functions and are the limiting equations that govern continuous time random walks with heavy tailed random waiting times. The solution is gained by performing an integral transform on the solution of any boundary value problem for transport in the absence of an immobile phase. In this regard, the output from a multidimensional numerical model can be transformed to include the effect of a fractal immobile phase. The solutions capture the anomalous behavior of tracer plumes in heterogeneous aquifers, including power law breakthrough curves at late time, and power law decline in the measured mobile mass. The MADE site mobile tritium mass decline is consistent with a fractional time derivative of order γ = 0.33, while Haggerty et al.'s [2002] stream tracer test is well modeled by a fractional time derivative of order γ = 0.3. |
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The equations are equivalent to previous models of mobile/immobile transport with power law memory functions and are the limiting equations that govern continuous time random walks with heavy tailed random waiting times. The solution is gained by performing an integral transform on the solution of any boundary value problem for transport in the absence of an immobile phase. In this regard, the output from a multidimensional numerical model can be transformed to include the effect of a fractal immobile phase. The solutions capture the anomalous behavior of tracer plumes in heterogeneous aquifers, including power law breakthrough curves at late time, and power law decline in the measured mobile mass. The MADE site mobile tritium mass decline is consistent with a fractional time derivative of order γ = 0.33, while Haggerty et al.'s [2002] stream tracer test is well modeled by a fractional time derivative of order γ = 0.3.</description><identifier>ISSN: 0043-1397</identifier><identifier>EISSN: 1944-7973</identifier><identifier>DOI: 10.1029/2003WR002141</identifier><language>eng</language><publisher>Blackwell Publishing Ltd</publisher><subject>CTRW ; fractal ; fractional derivative ; immobile phase</subject><ispartof>Water resources research, 2003-10, Vol.39 (10), p.n/a</ispartof><rights>Copyright 2003 by the American Geophysical Union.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a5153-39f031c1abfe42ae8a23c50e2692db128ed55ac17a65837a60598f9404bcfdf03</citedby><cites>FETCH-LOGICAL-a5153-39f031c1abfe42ae8a23c50e2692db128ed55ac17a65837a60598f9404bcfdf03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1029%2F2003WR002141$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1029%2F2003WR002141$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,11514,27924,27925,45574,45575,46468,46892</link.rule.ids></links><search><creatorcontrib>Schumer, Rina</creatorcontrib><creatorcontrib>Benson, David A.</creatorcontrib><creatorcontrib>Meerschaert, Mark M.</creatorcontrib><creatorcontrib>Baeumer, Boris</creatorcontrib><title>Fractal mobile/immobile solute transport</title><title>Water resources research</title><addtitle>Water Resour. 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The MADE site mobile tritium mass decline is consistent with a fractional time derivative of order γ = 0.33, while Haggerty et al.'s [2002] stream tracer test is well modeled by a fractional time derivative of order γ = 0.3.</description><subject>CTRW</subject><subject>fractal</subject><subject>fractional derivative</subject><subject>immobile phase</subject><issn>0043-1397</issn><issn>1944-7973</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><recordid>eNp9kE1Lw0AQhhdRsFZv_oCexIOxM_uRzR6l2CpWxaL2uGy2G4gmTdxNqf33rkTEk5eZgXmegXkJOUW4RKBqTAHYcgFAkeMeGaDiPJFKsn0yAOAsQabkITkK4Q0AuUjlgJxPvbGdqUZ1k5eVG5d1P4xCU206N-q8WYe28d0xOShMFdzJTx-Sl-n18-QmmT_ObidX88QIFCxhqgCGFk1eOE6NywxlVoCjqaKrHGnmVkIYi9KkImOxglBZoTjw3Bar6A7JWX-39c3HxoVO12WwrqrM2jWboFFR4DLFCF70oPVNCN4VuvVlbfxOI-jvOPTfOCJOe3wbv9v9y-rlYrJQqWRRSnqpDJ37_JWMf9dxLYVePsx0djd_Yuxe6Ff2BeKybvc</recordid><startdate>200310</startdate><enddate>200310</enddate><creator>Schumer, Rina</creator><creator>Benson, David A.</creator><creator>Meerschaert, Mark M.</creator><creator>Baeumer, Boris</creator><general>Blackwell Publishing Ltd</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QH</scope><scope>7UA</scope><scope>C1K</scope><scope>F1W</scope><scope>H96</scope><scope>L.G</scope></search><sort><creationdate>200310</creationdate><title>Fractal mobile/immobile solute transport</title><author>Schumer, Rina ; Benson, David A. ; Meerschaert, Mark M. ; Baeumer, Boris</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a5153-39f031c1abfe42ae8a23c50e2692db128ed55ac17a65837a60598f9404bcfdf03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><topic>CTRW</topic><topic>fractal</topic><topic>fractional derivative</topic><topic>immobile phase</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schumer, Rina</creatorcontrib><creatorcontrib>Benson, David A.</creatorcontrib><creatorcontrib>Meerschaert, Mark M.</creatorcontrib><creatorcontrib>Baeumer, Boris</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Aqualine</collection><collection>Water Resources Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><jtitle>Water resources research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schumer, Rina</au><au>Benson, David A.</au><au>Meerschaert, Mark M.</au><au>Baeumer, Boris</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fractal mobile/immobile solute transport</atitle><jtitle>Water resources research</jtitle><addtitle>Water Resour. 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The solutions capture the anomalous behavior of tracer plumes in heterogeneous aquifers, including power law breakthrough curves at late time, and power law decline in the measured mobile mass. The MADE site mobile tritium mass decline is consistent with a fractional time derivative of order γ = 0.33, while Haggerty et al.'s [2002] stream tracer test is well modeled by a fractional time derivative of order γ = 0.3.</abstract><pub>Blackwell Publishing Ltd</pub><doi>10.1029/2003WR002141</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record> |
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subjects | CTRW fractal fractional derivative immobile phase |
title | Fractal mobile/immobile solute transport |
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