| Project/Area Number |
16K05466
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical physics/Fundamental condensed matter physics
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
小布施 秀明 北海道大学, 工学研究院, 助教 (50415121)
|
|---|
| Project Period (FY) |
2016-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Keywords | フラクタル / 臨界現象 / 複雑ネットワーク / スモールワールド / 自己組織化 / 数理物理 |
|---|
| Outline of Final Research Achievements |
Studying the origin of fractality found in many real-world complex networks, we have obtained the following results. (1) We proposed a model of fractal complex networks based on an SOC dynamics driven by the antagonistic relationship between the growth of a functional network and its cascading overload failure, (2) we have shown a fractal and small-world structures, and their structural crossover in the process of time development of the SOC model, (3) to clarify the role of a long-range repulsive correlation between hub nodes to the fractal property, long-range degree correlations in a complex network have been formulated in a quite general manner, and (4) we have elucidated that fractality cannot be realized only by nearest-neighbor degree correlations but a long-range hub repulsion is closely related to the origin of fractality.
|
| Academic Significance and Societal Importance of the Research Achievements |
現実の複雑ネットワークはスモールワールド性を有する構造とフラクタル性をもつ構造に大別される。この内フラクタル構造の起源は未だ明らかにされていなかったが、本研究でSOCがフラクタル構造の一つの起源であることが解明されらことにより、大域的構造相関の発現がユークリッド距離の有無と無関係に統一的に理解できることが明らかとなった。また、複雑ネットワークにおける長距離次数相関という大域的構造相関が一般的に定式化されたことで、ネットワークの様々な構造的性質やネットワーク上のダイナミクスが長距離次数相関とどのように関係しているかを定量的に研究するための礎が築かれた。
|
