1991 Fiscal Year Final Research Report Summary
Dynamical properties of large-scale fractal networks
| Project/Area Number |
02452044
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Hokkaido University |
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Principal Investigator |
NAKAYAMA Tsuneyoshi Fac., of Engineering, Hokkaido Univ, . Professor, 工学部, 教授 (80002236)
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| Co-Investigator(Kenkyū-buntansha) |
YAKUBO Kousuke Fac., of Engineering, Hokkaido Univ, . Instructor, 工学部, 助手 (40200480)
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| Project Period (FY) |
1990 – 1991
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| Keywords | fractal / percolation / fracton / random / localization / dynamics |
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| Research Abstract |
Computer simulations are essential to develop the insight into dynamics of percolating nets. We have succeeded in treating very large percolation clusters of more than 10^5 particles, revealing a wealth of detailed quantitative information. These have become possible with the advent of array-processing supercomputers, and with the use of a numerical method that does not require diagonalization. The vibrational densities of states for these large percolating networks obtained. It was confirmed for both 2d- and 3d-networks, that the vibrational denisity of states is proportional to w^df with d_f close to 4/3 in the regime above the characteristic frequency w_c. We also found that fracton modes possess a quite unique character, i. e., the core of fracton excitations falls off sharply at their edges. This is in contrast with the case of homogeneously extended modes (phonons), in which the change in their amplitudes is correlated smoothly over a long distance.
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