| Project/Area Number |
17K05590
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kochi National College of Technology |
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Principal Investigator |
TANIZAWA Toshihiro 高知工業高等専門学校, ソーシャルデザイン工学科, 教授 (60311106)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 複雑ネットワーク理論 / 臨界現象 / 相転移 / 数値シミュレーション / 複雑ネットワーク / 統計物理 / 数理物理 / パーコレーション転移 / 強相関系 |
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| Outline of Final Research Achievements |
In 2007, Noh pointed out that percolation transition on ER networks with assortative correlation in node connection does not belong to mean-field type. However, it is not yet clear that whether it is generally applicable to networks with assortative correlation in node connection.
In this study, I performed extensive numerical simulations for networks with power-law degree distributions and assortative correlation in node connection and confirmed that the peak disappearance in finite-size cluster distribution at percolation transition does not observed. The apparent inconsistency between this result and Noh's might come from the difference in their network structure. To clarify this, analytical arguments based on rigorous equations is necessary.
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| Academic Significance and Societal Importance of the Research Achievements |
複雑ネットワークは規則的配列を取る正方格子よりも一般的な構造を持ち，統計物理学における相転移現象の研究対象としても興味深い。本研究課題は，ノード結合に正の次数相関があるネットワーク上でのパーコレーションが平均場型か否かという未解決問題を解明しようというもので，構成要素間の相関を取り入れた相転移現象の考察という点においても意義深い。本研究の成果から正相関ネットワークにおいては転移のタイプがネットワーク構造に依存する可能性が示唆され，その依存性をさらに理論的に厳密に考察する必要があることが明らかになった。
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