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Dynamical properties of large-scale fractal networks

Research Project

Project/Area Number 02452044
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 物性一般(含極低温・固体物性に対する理論)
Research InstitutionHokkaido University

Principal Investigator

NAKAYAMA Tsuneyoshi  Fac., of Engineering, Hokkaido Univ, . Professor, 工学部, 教授 (80002236)

Co-Investigator(Kenkyū-buntansha) YAKUBO Kousuke  Fac., of Engineering, Hokkaido Univ, . Instructor, 工学部, 助手 (40200480)
Project Period (FY) 1990 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥5,300,000 (Direct Cost: ¥5,300,000)
Fiscal Year 1991: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1990: ¥4,600,000 (Direct Cost: ¥4,600,000)
Keywordsfractal / percolation / fracton / random / localization / dynamics / 局在励起 / ス-パ-・コンピュ-タ / 計算機シミュレ-ション
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.

Report

(3 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • Research Products

    (36 results)

All Other

All Publications (36 results)

  • [Publications] T.Nakayama: "Density of states of fractons on percolating networks" Proc.Indian Acad.Sci(Chemical Science). 102. 575-579 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K.Yakubo: "Superlocalization of fracton wavefunctions excited on percolating networks" proc.Indian Acad.Sci.(Chemical Science),. 102. 581-584 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K.Yakubo: "Crossover behavior from vector to scalar fractons in the density of states of percolating networks" J.Phys.Soc.Jpn.59. 1909-1912 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K.yakubo: "Missing modes in the density of states of fractal networks" Phys.Rev.B. 42. 1078-1081 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K.yakubo: "Analysis of a new method for finding eigenmodes of very large lattice systems" J.Phys.Soc.Jpn.60. 3249-3259 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Nakayama: "Raman correlation function of percolating networks" proc.Inter.Symp.on slow Dynamics in Condensed Matter,edited by M.Tokuyama(AIP press,NY),.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T,Nakayama: "Numerical method for the analysis of optical waveguides" Opt.Lett.,in press. 17. (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 矢久保 考介: "浸透網とフラクトン力学" 固体物理. 25. 141-154 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中山 恒義: "フラクタルネットの世界とス-パ-コンピュ-タ" パリティ. 5. 2-10 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 中山 恒義: "パ-コレ-ション・ネットの動的構造因子" 統計数理. 38. 73-88 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Nakayama and K. Yakubo: "Density of states of fractons on percolating networks" Proc. Indian Acad. Sci. (Chemical Science). 102, No. 5. 575-579 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K. Yakubo and T. Nakayama: "Superlocalization of fracton wavefunctions excited on percolating networks" Proc. Indian Acad. Sci. (Chemical Science). 102, No. 5. 581-584 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K. Yakubo, K. Takasugi and T. Nakayama: "Crossover behavior from vector to scalar fractons in the density of states of percolating networks" J. Phys. Soc. Jpn.59, No. 6. 1909-1912 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K. Yakubo, E. Courtens and T. Nakayama: "Missing modes in the density of states of fractal networks" Phys. Rev. B. 42, No. 1. 1078-1081 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] K. Yakubo, T. Nakayama and H. J. Maris: "Analysis of a new method for finding eigenmodes of very large lattice systems" J. Phys. Soc. Jpn.60, No. 10. 3249-3259 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Nakayama and K. Yakubo: "Raman correlation function of percolating networks" Proc. Inter. Symp. on Slow Dynamics in Condensed Matter. AIP press.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Nakayama and K. Yakubo: "Dynamical correlation function of fractal networks : computer simulations" Proc. Inter. Meeting on Computational Physics for Condened Matter Phenomena-Methodology and Application. edited by H. Takayama.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T. Nakayama, M. Takano, K. Yakubo, and T. Yamanaka: "Numerical method for the analysis of optical waveguides" Opt. Lett.17, No. 5. (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] T.Nakayama: "Density of states of fractons on percolating networks" Proc.Indian Acad,Sci.(Chemical Science). 102. 575-579 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] K.Yakubo: "Superlocalization of fracton wavefunctions excited on percolating networks" Proc.Indian Acad.Sci.(Chemical Science),. 102. 581-584 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] K.Yakubo: "Crossover behavior from vector to scalar fractons in the density of states of percolating networks" J.Phys.Soc.Jpn.59. 1909-1912 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] K.Yakubo: "Missing modes in the density of states of fractal networks" Phys.Rev.B. 42. 1078-1081 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] K.Yakubo: "Analysis of a new method for finding elgenmodes of very large lattice systems" J.Phys.Soc.Jpn.60. 3249-3259 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Nakayama: "Raman correlation function of percolating networks" Proc.Inter.Symp.on Slow Dynamics in Condensed Matter,edited by M.Tokuyama(AIP Press,NY).

    • Related Report
      1991 Annual Research Report
  • [Publications] T.Nakayama: "Numerical method for the analysis of optical waveguides" Opt.Lett.,in Press. 17. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 矢久保 考介: "浸透網とフラクトン力学" 固体物理. 25. 141-154 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] 中山 恒義: "フラクタルネットの世界とス-パ-コンピュ-タ" パリティ. 5. 2-10 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] 中山 恒義: "パ-コレ-ション・ネットの動的構造因子" 統計数理. 38. 73-88 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] K.Yakubo K.Takasugi T.Nakayama: "Crossover behavior from vector to scalar fractons in the density of state of percolating networks" Journal of Physical Society of Japan. 59. 1909-1912 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] K.Yakubo E.Courtens T.Nakayama: "Missing modes in the density of states of fractal networks" Physical Review B1. 42. 1078-1082 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.Nakayama K.Yakubo: "Density of states of fractons on percolating networks" Proceedings of the Indian Academy of SciencesーChemical Sciences. 102. 575-578 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] K.Yakubo T.Nakayama: "Superlocalization of fracton wavefunctions excited on percolating networks" Proceedings of the Indian Academy of SciencesーChemical Sciences. 102. 581-586 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] A.Ohi T.Nakayama: "Diffusion of ^3He quasiparticles in dilute ^3He- ^4He solution confined in porous media" Physical Review B1. 41. 7322-7326 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] A.Ohi T.NaKayama: "Spinーpolarization enhancement of dilute ^3He- ^4He solutions through porous media" Physical Review B1. 41. 7281-7285 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 矢久保 考介 中山 恒義: "固体物理" アグネ社, 15 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 中山 恒義: "超音波スペクトロスコピ-" 培風館, 20 (1990)

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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