Mathematical modeling for a nonlinear phenomena appearing engineering field and its analysis

工程领域出现的非线性现象的数学建模及其分析

• 批准号: 20540205
• 负责人: AIKI Toyohiko
• 金额: $ 2.91万
• 依托单位: Gifu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540205/
• 关键词: 非線形現象; 形状記憶合金; コンクリートの中性化; 自由境界問題; 弱解の一意性

We consider the mathematical model for dynamics of a sensor made of shape memory alloys. We established the well-posedness of our model without the smallness condition for initial data even if the temperature filed is unknown.Also, we study a one-dimensional free boundary problem as a mathematical model describing the concrete carbonation process. In this research we could guarantee the experimental law that the carbonation depth is proportionally to the square root of the time from mathematical modeling point of view.

考虑了形状记忆合金传感器的动力学数学模型。在温度场未知的情况下，在不满足初始数据小的条件下，建立了模型的适定性。同时，我们研究了一维自由边界问题作为描述混凝土碳化过程的数学模型。本研究从数学建模的角度保证了碳化深度与时间平方根成正比的实验规律。

项目成果

Motion of essentially admissible V-shaped polygonal curves governed by generalized crystalline motion with a driving force

由具有驱动力的广义晶体运动控制的基本上允许的 V 形多边形曲线的运动

• 发表时间: 2011
• 期刊: Journal of Math-for-Industry
• 作者: T. Ishiwata

On the motion of polygons by crystalline curvature

通过晶体曲率论多边形的运动

• 发表时间: 2008
• 作者: C. Hirota;T. Ishiwata;S. Yazaki;石渡 哲哉
• 通讯作者: 石渡 哲哉

On the motion of polygonal curves with asymptotic lines by crys talline curvature flow with bulk effect

体效应晶体曲率流论渐近线折线运动

• 发表时间: 2011
• 期刊: Discrete and Continuous Dynamical Systems Series S
• 作者: R.Kajikiya;Yong-Hoon Lee;Inbo Sim;小栗栖修;小野太幹;T.Ishiwata
• 通讯作者: T.Ishiwata

A mathematical model for a valve made of a spring of a shape memory alloy, Nonlinear Phenomena with Energy Dissipation

由形状记忆合金弹簧制成的阀门的数学模型，能量耗散的非线性现象

• 发表时间: 2008
• 期刊: mathematical analysis, modeling and simulation, Gakuto International Series, Mathematical Sciences and Applications
• 作者: 長田まりゑ;N. Fukuda and T. Kinoshita;Y.Naito;石渡哲哉;梶木屋龍治;Marie Choda;T. Aiki
• 通讯作者: T. Aiki

クリスタライン曲率流による開曲線の運動

由于晶体曲率流动而产生开曲线运动

• 发表时间: 2012
• 作者: K.Anada;T.Ishiwata;T.Ishiwata;T.Ishiwata;T.Ishiwata;石渡哲哉;石渡哲哉
• 通讯作者: 石渡哲哉