Project/Area Number  10640221 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Global analysis

Research Institution  SETSUNAN UNIVERSITY 
Principal Investigator 
IKEBE Teruo SETSUNAN UNIVERSITY, MATHEMATICS DEPARTMENT, PROFESSOR, 工学部, 教授 (00025280)

CoInvestigator(Kenkyūbuntansha) 
WATARAI Seizou Setsunan University, Mathematics Department, Associate Professor, 工学部, 助教授 (20131500)
NAKAWAKI Yuuji Setsunan University, Mathematics Department, Professor, 工学部, 教授 (60207959)
ITO Keiichi r. Setsunan University, Mathematics Department, Professor, 工学部, 教授 (50268489)
NAKABAYASHI Kouzaburo Setsunan University, Mathematics Department, Associate Professor (30207857)
TERAMOTO Yoshiaki Setsunan University, Mathematics Department, Associate Professor, 工学部, 助教授 (40237011)
SHIMADA Shinichi Setsunan University, Mathematics Department, Associate Professor, 工学部, 助教授 (40196481)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  classical spin model / block spin transformation / random walks / Navier  Stokes eqs. / turbulence / scattering theory / Aharonov  Bohm effect / 古典スピン系 / block spin変換 / NavierStokes方程式 / 乱流 / 散乱理論 / AharonovBohm効果 / Kolmogorov 則 / block spin 変換 / AharonovBohm 効果 / NavierSrokes方程式 
Research Abstract 
(1) In the joint study with Prof. Tamura in Kanazawa University, Ito obtained several new results on the problems of phase transition of low dimensional O(N) spin models. Though it has been conjectured that he phase transition never occurs in such models, no one proves this rigourously. They could get a better estimate for the inverse critical temperature, by use of several steps of renormalization. (2) Teramoto studied the stability of stationary solution to the problem of The NavierStokes flow down an inclined plane and showed that under certain conditions there occurs Hopf bifurcation. To apply the bifurcation theory he must show that the linear operator arising in this problem generates an analytic semigroup. Ito and Teramoto are now preparing a new method to study the interactions between the roll waves obtained above and try to give new insights to the mechanism of transition to turbulence. (3) It is conjectured that the difficulty of diversity of the "antiderivatives" in the study of Nakawaki has something to do with renormalization group. (4) Shimada studied the mathematical scattering theory on the Aharonov  Bohm effect in the quantum mechanics. He obtained the engenfunctions of the operator associated with this problem and constructed the wave operator, the scattering matrix and the representation of scattering amplitude. This work gives the mathematical foundation on the study of the Aharonov  Bohm effect.
