| Project/Area Number |
19540133
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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 | Yamaguchi University |
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Principal Investigator |
NISHIYAMA Takahiro Yamaguchi University, 大学院・理工学研究科, 准教授 (60333241)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | クーロン波動関数 / 合流型超幾何関数 / オイラー方程式 / 円管ポアズイユ流 / 特殊関数 / 流体力学 |
|---|
| Research Abstract |
Coulomb wave functions belong to a family of confluent hypergeometric functions and are mainly used in scattering theories in quantum physics. The aim of the research is to apply them to fluid mechanics. First, the convergence of an orthogonal series whose bases are Stokes stream functions of axisymmetric stationary Euler flows and represented with a Coulomb wave function is studied. As a result, a convergence theorem analogous to that of the Fourier or the Fourier-Bessel series is proved. Next, the distribution of complex phase velocities for small disturbances to pipe Poiseuille flow is analytically explained by using asymptotic forms of a Coulomb wave function with a complex variable and a complex parameter.
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