Traveling waves, relaxation, and oscillations in a model for biodegradation

Persistent Link:
http://hdl.handle.net/10150/283975
Title:
Traveling waves, relaxation, and oscillations in a model for biodegradation
Author:
Murray, Regan E.
Issue Date:
1999
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In-situ bioremediation is a promising biotechnology for removing aqueous phase contaminants from groundwater. Utilizing indigenous bacteria to degrade organic contaminants into non-toxic components, bioremediation is relatively inexpensive, fast, and complete. Making predictions about its applicability and success is difficult because of the complexity and variability intrinsic to the subsurface environment. Analytical studies of models, independent of this detailed subsurface data, are essential to finding accurate quantitative results, yet few have been obtained. This dissertation is a collection of three mathematical reports on a one-dimensional model for bioremediation. Using degree theory, the elliptic maximum principle, and comparison theorems, existence of traveling wave solutions to the biodegradation model is proved, a formula for the speed of the traveling concentration front is derived, and bounds on the biomass concentration are obtained. In the second section, the model is shown to reduce to a single equation in the relaxation limit by using properties of systems of hyperbolic conservation laws. In the third section, a formula is found for the parameters at which an unstable traveling wave solution bifurcates to a stable limit cycle (oscillatory solution). These results provide practical information about the structure of concentration fronts for the contaminant, nutrient, and biomass. The fronts travel at speeds that are either constant or time-periodic, depending on the kinetic parameters of the bacteria and the sorption properties of the contaminant. When there is little growth in biomass, many critical properties of the concentrations are derived. For aquifers with low permeability, the model is reduced to a much simpler system, also allowing the derivation of many analytical properties. Though comparisons with experimental data have not yet been done, numerical simulations support these results.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.; Agriculture, Soil Science.; Engineering, Environmental.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Xin, Jack X.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleTraveling waves, relaxation, and oscillations in a model for biodegradationen_US
dc.creatorMurray, Regan E.en_US
dc.contributor.authorMurray, Regan E.en_US
dc.date.issued1999en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn-situ bioremediation is a promising biotechnology for removing aqueous phase contaminants from groundwater. Utilizing indigenous bacteria to degrade organic contaminants into non-toxic components, bioremediation is relatively inexpensive, fast, and complete. Making predictions about its applicability and success is difficult because of the complexity and variability intrinsic to the subsurface environment. Analytical studies of models, independent of this detailed subsurface data, are essential to finding accurate quantitative results, yet few have been obtained. This dissertation is a collection of three mathematical reports on a one-dimensional model for bioremediation. Using degree theory, the elliptic maximum principle, and comparison theorems, existence of traveling wave solutions to the biodegradation model is proved, a formula for the speed of the traveling concentration front is derived, and bounds on the biomass concentration are obtained. In the second section, the model is shown to reduce to a single equation in the relaxation limit by using properties of systems of hyperbolic conservation laws. In the third section, a formula is found for the parameters at which an unstable traveling wave solution bifurcates to a stable limit cycle (oscillatory solution). These results provide practical information about the structure of concentration fronts for the contaminant, nutrient, and biomass. The fronts travel at speeds that are either constant or time-periodic, depending on the kinetic parameters of the bacteria and the sorption properties of the contaminant. When there is little growth in biomass, many critical properties of the concentrations are derived. For aquifers with low permeability, the model is reduced to a much simpler system, also allowing the derivation of many analytical properties. Though comparisons with experimental data have not yet been done, numerical simulations support these results.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
dc.subjectAgriculture, Soil Science.en_US
dc.subjectEngineering, Environmental.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorXin, Jack X.en_US
dc.identifier.proquest9946853en_US
dc.identifier.bibrecord.b39918142en_US
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