| 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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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Mathematical model / Numerical simulation / Biodegradation / Inverse problem / Polymer / Depolymerization / Differential equation / Numerical analysis / 数値計算 / Endogenous解重合 / Exogenous新重合 / Biodegradation / Xenobiotic polymers / Exogenous depolymerization / Endogenous depolymerization / Mathematical model / Differential equation / Inverse problem / Numerical simulation |
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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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