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New Numerical Method for Analysis of Large Matrices

Research Project

Project/Area Number 13450038
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionHokkaido University

Principal Investigator

NAKAYA Tsuneyoshi  Hokkaido Univ., Grad. School. of Eng., Prof., 大学院・工学研究科, 教授 (80002236)

Co-Investigator(Kenkyū-buntansha) SHIMA Hiroyuki  Hokkaido Univ., Grad. School. of Eng., Inst., 大学院・工学研究科, 助手 (40312392)
YAKUBO Kousuke  Hokkaido Univ., Grad. School. of Eng., Asso. Prof., 大学院・工学研究科, 助教授 (40200480)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥9,200,000 (Direct Cost: ¥9,200,000)
Fiscal Year 2003: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2002: ¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2001: ¥3,900,000 (Direct Cost: ¥3,900,000)
KeywordsNumerical Algorithm / Forced oscillator method / Eigenvalue Analysis / Very large matrices / Correlation function
Research Abstract

The aim of this research project is to develop the efficient algorithm for the eigenvalue analysis of very large matrices of [10^6×10^6], and computing dynamic correlation functions of the systems described by those matrices. In addition, we try to extend this numerical to apply for method non-Hermitian large-scale matrices. In these term, we have succeeded to develop the algorithm to use any type of large-scale matrices. We have also applied this algorithm to actual physical systems and demonstrated its surprising efficiency.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (39 results)

All Other

All Publications (39 results)

  • [Publications] K.Yakubo: "AC current due to photon-assisted tunneling in driven mesoscopic systems"Physica. 18・1-3. 97-98 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yakubo: "Persistent currents in Mobius strips"Phys.Rev.B. 67・12. 125319-1-125319-5 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 中山恒義: "シリカガラスのボソン・ピークとその物理"日本物理学会誌. 58・7. 512-519 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Terao: "Crossover phenomena in flocculations of colloidal suspensions"Physica A. 320. 77-83 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Shima: "Dielectric anomaly in coupled rotor systems"Phys.Rev.B. 69・3. 035202-1-035202-5 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Shima: "Glass-like behaviors of crystalline Ge with O-impurities at low temperatures"Physica Status Solidi. (in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Nakayama: "Fractal Concepts in Condensed Matter Physics"Springer-Verlag. 210 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Terao, T.Nakayama: "Observation of antiferromagnetic fractons"Physical Review B. 66(13). 132400-1-132400-5 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Nakayama: "Boson peak and terahertz frequency dynamics of vitreous silica"Reports on Progress in Physics. 65(8). 1195-1242 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Nakayama: "Microscopic buckling as an origin of the boson peak in network glasses"Physica B-Condensed Matter. 316. 497-499 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Terao, T.Nakayama: "Adsorption of colloidal particles on a charged surface : Cluster Monte-Carlo simulations"Physical Review E. 65(2). 021405-1-021405-8 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Shima, K.Yakubo, T.Nakayama: "Acceleration of the forced oscillator method and its application to a model far glasses"Physica B. 316. 521-523 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Obuse, K.Yakubo: "Non-universal exponents at the Anderson transition"Physica E. 18(1-3). 276-277 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] J.Ohe, K.Yakubo: "Numerical study of the sideband quenching in driven mesoscopic systems"Physica E. 18(1-3). 333-334 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yakubo, Y.Avishai, D.Cohen: "Persistent currents in Mebius strips"Physical Review B. 67(12). 125319 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yakubo, H.Obuse: "Fluctuations of the correlation dimension of critical wavefunctions in two-dimensional symplectic systems"J.Phys.Soc.of Japan. 72 Supplment A. 143-144 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Terao, T.Ikeda, T.Nakayama: "Crossover phenomena in flocculations of colloidal suspensions"Physica A. 320. 77-83 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Yakubo, J.Ohe: "AC current due to photon-assisted tunneling in driven mesoscopic systems"Physica E. 18(1-3). 97-98 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Shima, T.Nakayama: "Dielectric anomaly in coupled rotor systems"Phys.Rev.B. 69(3). 035202-1-035202-5 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Shima, T.Nakayama: "Low-temperature anomalies of crystalline Ge with O-impurities"(Submitted).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Shima, T.Nakayama: "Alignment of Interacting Quantum Rotors by Ultrashort Laser Pulses"(submitted).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Shima: "Dielectric anomaly in coupled rotor systems"Phys.Rev.B. 69・3. 035202-1-035202-5 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Terao: "Crossover phenomena in flocculations of colloidal suspensions"Physica A. 320. 77-83 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 中山恒義: "シリカガラスのボソン・ピークとその物理"日本物理学会誌. 58・7. 512-519 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Shima: "Glass-like behaviors of crystalline Ge with O-impurities at low temperatures"Physica Status Solidi. (in press).

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Yakubo: "AC current due to photon-assisted tunneling in driven mesoscopic systems"Physica. 18・1-3. 97-98 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Yakubo: "Persistent currents in Mobius strips"Phys.Rev.B. 67・12. 125319 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Nakayama: "Fractal Concepts in Condensed Matter Physics"Springer-Verlag. 210 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Terao: "Adsorption of colloidal particles on a charged surface : Cluster Monte Carlo simulations"Phys. Rev. E. 65・2. 021405-1-021405-5 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Shima: "Acceleration of the forced oscillator method and its application to a model for glasses"Physica B. 316. 521-523 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Nakayama: "Microscopic buckling as an origin of the boson peak in network glasses"Physica B. 316. 497-499 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Nakayama: "Boson peak and terahertz frequency dynamics of vitreous silica"Rep. Prog. Phys.. 65・8. 1195-1242 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Nakayama: "The role of buckled molecules for THz dynamics of network glasses"J. Non-Cryst. Solids. 307. 73-79 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T. Nakayama: "The forced oscillator method : Eigenvalue analysis and computing linear response function"Physics Reports. 349. 239-299 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H. Shima: "Quantum-interference effects on ac transport in long-range random magnetid fields"J. Phys. Soc. Jpn.. 70. 2682-2688 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T. Terao: "Charge inversion of colloidal particles in an aqueous solution : Screeningby multivalent ions"Phys. Rev. E.. 63. 41401-1-41401-6 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] K. Yakubo: "Transfer-matrix formalism for 2D quantum transport in long-range inhomogeneous magnetic fields"J. Phys. Soc. Jpn.. 70. (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] J. Ohe: "Photon-assisted ac transport through quantum dots"J. J. Appl. Phys.. 40. (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H. Shima: "The forced oscillator method incorporating the first time-evolution method"Comp. Phys. Comm.. 142・1-3. 418-423 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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