2009 Fiscal Year Final Research Report
Inverse Problems for elasticity system and conductivity equation
| Project/Area Number |
19540113
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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 | Gunma University |
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Principal Investigator |
TANUMA Kazumi Gunma University, 大学院・工学研究科, 准教授 (60217156)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Gen 北海道大学, 大学院・理学研究院, 教授 (50118535)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 非等方弾性体 / 弾性表面波 / Rayleigh波 / Stroh formalism / 逆問題 / 導電体 / インピーダンストモグラフィー / 残留応力 |
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| Research Abstract |
The Stroh formalism is a powerful and elegant mathematical method developed for the systematic analysis of the equations of anisotropic elasticity. The representative wrote an exposition which introduces this formalism and its applications to both static and dynamic elasticity. On the basis of this formalism he investigated the behavior of elastic surface waves called Rayleigh waves propagating near the traction-free surface. This work provides an approach to the inverse problem of determining anisotropy of the materials by making measurements of Rayleigh waves. Electrical impedance tomography, where one detects the conductivity distribution inside an unknown body from electrical measurements at the boundary, is described as inverse boundary value problems for the conductivity equation. The representative gave reconstruction formulas for the conductivity at the boundary in a general setting, using the metric tensor pertaining to the boundary surface.
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