Study on random fields with long range correlations related to phase separating interfaces
| Project/Area Number |
26400147
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Keio University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 界面モデル / 相転移 / Gauss場 / Gibbs測度 / 自由エネルギー |
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| Outline of Final Research Achievements |
In this research, we studied several random fields with long range correlations for mathematical analysis of phase separating interfaces and membranes. In particular, we considered the Δφ interface model and obtained the following results:
(1) We give an estimate on the probability that the field stays positive in low dimensions and its behaviors differ greatly from those of the higher dimensional case or other random interface models.(2) We show that in the case of two or more dimensions, once we impose weak pinning potentials the field is always localized in the sense that the corresponding free energy is always positive.
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Report
(4 results)
Research Products
(3 results)
