2007 Fiscal Year Final Research Report Summary
Modeling with diffirential equations and numerical methods for solving inverse problems
| Project/Area Number |
16540106
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Okayama University |
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Principal Investigator |
WATANABE Masaji Okayama University, Graduate School of Environmental Science, Professor (30243546)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAI Fusako Okayama University, Research Institute for Bioresources, Professor (60118007)
HIMI Yasuhisa Okayama University, Faculty of Education, Associate Professor (70156636)
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| Project Period (FY) |
2004 – 2007
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| Keywords | Mathematical model / Numerical simulation / Biodegradation / Inverse problem / Polymer / Depolymerization / Differential equation / Numerical analysis |
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| Research Abstract |
We aimed at objects of mathematical problems such as mathematical models, analysis of inverse problems, and development of numerical techniques common to problems concerning biodegradation in which high molecular compounds are degraded by actions of microorganisms and water-vapor two-phase flow generated by waterhammer. pressure surge generated in liquid flow in pipelines such as steel pipes of water supply, and by pressure drop in reaction to waterhammer. For biodegradation of high molecular compounds, we aimed at establishment of mathematical techniques of analysis such as proposals of mathematical models, analysis with introduction of experimental results, and verification of propriety of model by numerical simulation. Microbial depolymerization processes are classified into exogenous type in which degradation is restricted to terminals of molecules and monomer units are separated stepwise, and endogenous type in which molecules are, separated at arbitrary positions. We conducted an
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alyses based on models for exogenous depolymerization processes and endogenous depolymerization processes, in which degradation rates depend only on molecular weight. On the other hand, in case temporary factors such as microbial population and temperature affect biodegradation, it becomes necessary to introduce those temporal factors into a degradation rate. Under the assumption that a degradation rate is a product of a function of time and a function of molecular weight, we showed that a model was transformed by a change of variable to one in which the degradation is independent of time, and that the factor dependent of molecular weight can be obtained with previously developed techniques of analysis. Results concerning temporal factor were also obtained. We introduced experimental results into analysis, solved inverse problems numerically, and simulated transitions of weight distribution with respect to molecular weigh t in order to verify that such models are appropriate as general models. Less
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Research Products
(59 results)
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[Journal Article] Analytical and computational techniques for exogenous depolymerization of xenobiotic polymers2004
Author(s)
Masaji, Watanabe, Fusako, Kawai, Masaru, Shibata, Shigeo, Yokoyama, Yasuhiro, Sudate, Shizue, Hayashi
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Journal Title
Mathematical Biosciences 192
Pages: 19-37
Description
「研究成果報告書概要(欧文)」より
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[Presentation] Depolymerization via bioprocesses2008
Author(s)
Masaji, Watanabe, Fusako, Kawai
Organizer
12th Okayama Research Park Research-Exhibition Presentation Meeting,(Techno Support)
Place of Presentation
Okayama
Year and Date
2008-02-01
Description
「研究成果報告書概要(欧文)」より
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[Presentation] Study on microbial action in PEG biodegradation2005
Author(s)
Masaji Watanabe, Fusako Kawai
Organizer
平成17年度統計数理研究所共同研究集会「環境データ解析の方法と実際」(Environmental Statistics:Theory and Practice)
Place of Presentation
情報・システム研究機構統計数理研究所 講堂(The institute of Statistical Mathematics, Tokyo)
Year and Date
2005-11-22
Description
「研究成果報告書概要(和文)」より
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