1997 Fiscal Year Final Research Report Summary
STUDY OF DIFFERNTIAL EQUATIONS BY RENORMALIZATION GROUP METHODS
| Project/Area Number |
08640244
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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 |
解析学
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| Research Institution | SETSUNAN UNIVERSITY |
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Principal Investigator |
IKEBE Teruo SESTUNSN UNIVERSITY,MATHEMATICS DEPARTMENT,PROFESSOR, 工学部, 教授 (00025280)
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| Co-Investigator(Kenkyū-buntansha) |
WATARAI Seizo SESTUNSN UNIVERSITY ASSOCIATE PROFESSOR MATHEMATICS DEPARTMENT, 工学部, 助教授 (20131500)
TERAMOTO Yoshiaki SESTUNSN UNIVERSITY ASSOCIATE PROFESSOR MATHEMATICS DEPARTMENT, 工学部, 助教授 (40237011)
ITO Keiichi R SESTUNSN UNIVERSITY PROFESSOR MATHEMATICS DEPARTMENT, 工学部, 教授 (50268489)
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| Project Period (FY) |
1996 – 1997
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| Keywords | Renormalization Group / Random Walk / Critical Temperature / O(N) Spin Model / Navier-Stokes equaion / Viscosity / Kormogorov law / Dissipation |
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| Research Abstract |
1.ITO and TAMURA (Kanazawa Univ.) studied classical O(N) symmetric spin model by renormalization group (block spin transformation) method. They first showed that the correlation functions can be described by self-avoiding walks which enabled them to obtain almost optimal bounds for the critical temperatures. In the second stage, they argued the integrability of the functional determinent det^<N/2>(1+2iGpsi/ROO<N>) with respect to psi, where psi is the auxially field introcuced for Fourier Transformation. Using the technique called the polymer (cluster) expansion, they showed that the inverse critical temperature beta_C obeys the bound beta_C>N log N in two dimensions, which implies the existence of strong deviation. (beta_C-N for the dimension more than or equal to 3.) This method is expected to establish a complete proof of the conjecture beta_C=* and they are currently working in this direction.
2.Teramoto investigated flow of non-compressible viscous fluid around a cyclinder by using cylindrical coordinate. He established that the equation exhibits global solution in time if the initial condition is sufficiently close to the stational current.
3.Teramoto and Ito investigated properties of turbulence, among them, the Kolmogorov law about the dissipation of energy and deviation from it. They tried to derive the deviation from the Navier-Stokes equation but they could not obtain concrete results this year.
4.Ikebe and Shimada (Setuanan Univ.) showed that the Schroedinger Operator with the potential V(x)=muf(x)delta(x<@D12@>D1-a<@D12@>D1) distributed on the sphere conveges (in the sense of resolvent convergence) as mu*(]SY.+-。[)*. This is related the the alpha decay of atoms.
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Research Products
(13 results)
