1999 Fiscal Year Final Research Report Summary
Research on Equilibrium Vector Potentials
| Project/Area Number |
09640181
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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 | Shiga University |
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Principal Investigator |
OOKUBO Katsumi Shiga Univ., Faculty of Education, Prof., 教育学部, 教授 (80024933)
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| Co-Investigator(Kenkyū-buntansha) |
MURAKAMI Ichirou Shiga Univ., Faculty of Education, Prof., 教育学部, 教授 (70210002)
YAMAZOE Shirou Shiga Univ., Faculty of Education, Prof., 教育学部, 教授 (10075137)
NIWA Masahiko Shiga Univ., Faculty of Education, Prof., 教育学部, 教授 (00024969)
YAMAGUCHI Hiroshi Nara Women Univ., Faculty of Science, Prof., 理学部, 教授 (20025406)
SUGIE Touru Shiga Univ., Faculty of Education, Ass. Prof., 教育学部, 助教授 (90135509)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Electro-magnetic fields / Solenoid / Equilibrium vector potential / Surface current density / Bochnar-Martinelli |
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| Research Abstract |
The mathematical research of the electric condenser at the beginning of 20 century introduced the notion "equilibrium scalar potential". In the previous work we introduced the new notion "equilibrium vector potential" from the study of the electric solenoid. Namely, for the given closed surface Σ in the Eulidean space RィイD13ィエD1, we can construct the surface current density T on Σsuch that T induces the magnetic fields B only inside the domain D bounded by Σ, that is, B is identically zero outside D. We call such T and B the equilibrium surface current density and equilibrium vector field for Σ. We also call its generating vector field A such that rot A = B the equilibrium vector potential for Σ. In this research we construct the algorithm (the alternating method with significant meaning from the electromagnetisms) along which we can obtain such current density T on Σ from the arbitrarily given surface current density TィイD20ィエD2 on Σ with trivial conditions. This algorithm suggests the possibility of obtaining the equilibrium surface current density T for Σ by the computational method.
In another research we try to extend the above phenomena in the case RィイD13ィエD1 to the case of the complex Euclidean space CィイD1nィエD1, and showed that, in the special case, this corresponds to the famous Bochnar-Martinelli theorem. This suggest the existence of the equilibrium vector potentials in the case of CィイD1nィエD1.
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