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Modeling with diffirential equations and numerical methods for solving inverse problems

使用微分方程和数值方法建模来解决反问题

基本信息

批准号：
16540106
负责人：
WATANABE Masaji
金额：
$ 2.41万
依托单位：
Okayama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

项目摘要

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 … More 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

我们的目标是数学问题的对象，如数学模型，反问题的分析，以及生物降解问题中常见的数值技术的发展，其中高分子化合物是通过微生物和水锤产生的水蒸气两相流的作用降解的。在供水钢管等管道中，液体流动时由于水锤作用而产生的压降而产生的压力波动。对于高分子化合物的生物降解，我们的目标是建立数学分析技术，如数学模型的提出，实验结果的分析，并通过数值模拟验证模型的合理性。微生物解聚过程分为外源性解聚过程和内源性解聚过程。外源性解聚过程是指降解仅限于分子末端，单体单元逐步分离；内源性解聚过程是指分子在任意位置分离。我们基于外源解聚过程和内源解聚过程的模型进行了更多的分析，其中降解率仅取决于分子量。另一方面，如果微生物数量和温度等临时因素影响生物降解，则有必要将这些临时因素引入降解率。在假设降解率是时间函数和分子量函数的乘积的情况下，我们证明了通过变量的变化将模型转换为降解与时间无关的模型，并且可以使用先前开发的分析技术获得依赖于分子量的因子。得到了有关时间因素的结果。我们将实验结果引入分析，用数值方法求解反问题，并模拟了质量分布相对于分子量t的转变，以验证该模型与一般模型一样适用。少