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Development of new matching method for boundary-layer problem in fusion plasmas

Research Project

Project/Area Number 23760805
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Nuclear fusion studies
Research InstitutionTottori University (2012-2015)
The University of Tokyo (2011)

Principal Investigator

Furukawa Masaru  鳥取大学, 工学(系)研究科(研究院), 准教授 (80360428)

Project Period (FY) 2011-04-28 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsプラズマ・核融合 / 境界層 / 数理物理 / 特異摂動 / 波動
Outline of Final Research Achievements

We have developed and extended a new solution method for resistive MagnetoHydroDynamics (MHD) stability problems in magnetized plasmas. The new matching method is applicable to situations where the matched asymptotic expansion (boundary-layer theory), one of the conventional solution methods, cannot apply or is difficult to apply actually. We have extended our previous studies on the new method to (1) stability problem of axisymmetric toroidal plasmas and (2) weakly nonlinear evolution of cylindrical plasmas. We have not only formulated the theory but also developed the numerical codes. Furthermore, we have extended the method for applying a model including finite Larmor radius effects. We have also studied a solution method for stationary states of ideal MHD, which is used for outer solution of the new matching method, on the basis of the noncanonical Hamiltonian theory.

Report

(6 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (59 results)

All 2016 2015 2014 2013 2012 2011 Other

All Journal Article (9 results) (of which Peer Reviewed: 8 results,  Open Access: 1 results,  Acknowledgement Compliant: 4 results) Presentation (49 results) (of which Int'l Joint Research: 2 results,  Invited: 4 results) Remarks (1 results)

  • [Journal Article] High-Accuracy Numerical Integration of Charged Particle Motion – with Application to Ponderomotive Force2016

    • Author(s)
      M. Furukawa, A. Matsuyama and Y. Ohkawa
    • Journal Title

      Plasma and Fusion Research

      Volume: 11 Issue: 0 Pages: 1303003-1303003

    • DOI

      10.1585/pfr.11.1303003

    • NAID

      130005311641

    • ISSN
      1880-6821
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Adjustment of vorticity fields with specified values of Casimir invariants as initial condition for simulated annealing of an incompressible, ideal neutral fluid and its MHD in two dimensions2015

    • Author(s)
      Y. Chikasue and M. Furukawa
    • Journal Title

      Journal of Fluid Mechanics

      Volume: 774 Pages: 443-459

    • DOI

      10.1017/jfm.2015.263

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Simulated annealing applied to two-dimensional low-beta reduced magnetohydrodynamics2015

    • Author(s)
      Y. Chikasue and M. Furukawa
    • Journal Title

      Physics of Plasmas

      Volume: 22 Issue: 2

    • DOI

      10.1063/1.4913234

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Peeling-off of the external kink modes at tokamak plasma edge2014

    • Author(s)
      L. J. Zheng and M. Furukawa
    • Journal Title

      Physics of Plasmas

      Volume: 21 Issue: 8

    • DOI

      10.1063/1.4894105

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Effects of pressure anisotropy on magnetospheric magnetohydrodynamics equilibrium of an internal ring current system2014

    • Author(s)
      M. Furukawa
    • Journal Title

      Physics of Plasmas

      Volume: 21 Issue: 1

    • DOI

      10.1063/1.4862037

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nonlinear variational method for predicting fast collisionless magnetic reconnection2013

    • Author(s)
      M. Hirota, P. J. Morrison, Y. Ishii, M. Yagi and N. Aiba
    • Journal Title

      Nuclear Fusion

      Volume: 53 Issue: 7 Pages: 63024-63024

    • DOI

      10.1088/0029-5515/51/7/073012

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Inclusion of diamagnetic drift effect in the matching method using finite-width inner region for stability analysis of magnetohydrodynamic modes2012

    • Author(s)
      M. Furukawa and S. Tokuda
    • Journal Title

      Physics of Plasmas

      Volume: 19 Issue: 10

    • DOI

      10.1063/1.4764077

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] 不整磁場・摂動磁場の閉じ込めへの影響2012

    • Author(s)
      古川 勝
    • Journal Title

      プラズマ・核融合学会誌

      Volume: 88 Pages: 158-161

    • NAID

      110009426273

    • Related Report
      2011 Research-status Report
  • [Journal Article] A new matching method for linear stability analysis of MHD modes close to the ideal MHD marginal stability2011

    • Author(s)
      M. Furukawa and S. Tokuda
    • Journal Title

      Phys. Plasmas

      Volume: 18 Issue: 6

    • DOI

      10.1063/1.3592666

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] 抵抗性MHDの初期値問題に対する有限幅内部領域を用いた 数値接続解法: 弱く非線形な場合への拡張2016

    • Author(s)
      古川勝
    • Organizer
      日本物理学会第71回年次大会
    • Place of Presentation
      東北学院大学 泉キャンパス
    • Year and Date
      2016-03-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] High-accuracy numerical integrator for general dynamical systems using vector-field decomposition and reccurence formula2016

    • Author(s)
      M. Furukawa
    • Organizer
      The 21st NEXT workshop
    • Place of Presentation
      京都テルサ
    • Year and Date
      2016-03-10
    • Related Report
      2015 Annual Research Report
  • [Presentation] Numerical integration of chaotic magnetic field line trajectory2016

    • Author(s)
      Y. Ohkawa and M. Furukawa
    • Organizer
      The 21st NEXT workshop
    • Place of Presentation
      京都テルサ
    • Year and Date
      2016-03-10
    • Related Report
      2015 Annual Research Report
  • [Presentation] Simulated annealing for calculating steady state of ideal MHD2016

    • Author(s)
      M. Furukawa
    • Organizer
      US-J MHD WS on “Fundamental understanding of 3-D magnetic field effect for further optimization of operation scenarios for fusion devices"
    • Place of Presentation
      核融合科学研究所
    • Year and Date
      2016-03-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 軸対称トロイダルプラズマの有限幅内部層を用いた 抵抗性MHD安定性解析2015

    • Author(s)
      古川勝
    • Organizer
      MHD研究会(NIFS共同研究研究会「電磁モデルによるプラズマ中の不安定性・乱流に関する理論・シミュレーション」)
    • Place of Presentation
      核融合科学研究所
    • Year and Date
      2015-12-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] 核融合プラズマの磁気流体力学研究2015

    • Author(s)
      古川勝
    • Organizer
      2015 年度 第 2 回 日本流体力学会 中四国・九州支部講演会
    • Place of Presentation
      鳥取大学 湖山キャンパス
    • Year and Date
      2015-11-28
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] トロイダル磁場配位における抵抗性MHD 安定性解析2015

    • Author(s)
      古川勝
    • Organizer
      第32回プラズマ・核融合学会年会
    • Place of Presentation
      名古屋大学 東山キャンパス 豊田講堂
    • Year and Date
      2015-11-24
    • Related Report
      2015 Annual Research Report
  • [Presentation] 2次元低ベータ簡約化MHDのアニーリングシミュレーションにおけるCasimir不変量の調整2015

    • Author(s)
      古川勝,近末吉人
    • Organizer
      日本物理学会2015年秋季大会
    • Place of Presentation
      関西大学 千里山キャンパス
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] Simulated annealing for stationary states of low-beta reduced MHD in two dimensions2015

    • Author(s)
      M. Furukawa
    • Organizer
      US-Japan JIFT Workshop on "Recent studies of extended MHD and MHD simulations"
    • Place of Presentation
      The Golden Hotel, Golden, CO, USA
    • Year and Date
      2015-08-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 負三角度トカマクにおける輸送改善機構2015

    • Author(s)
      菊池満,S. Medvedev,滝塚知典,古川勝,長崎百伸
    • Organizer
      日本物理学会第70回年次大会
    • Place of Presentation
      早稲田大学 早稲田キャンパス
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Accuracy analysis of numerical integration of charged particle motion based on recurrence formula with symmetric operator decomposition2015

    • Author(s)
      M. Furukawa
    • Organizer
      The 20th NEXT workshop
    • Place of Presentation
      京都テルサ
    • Year and Date
      2015-01-13 – 2015-01-14
    • Related Report
      2014 Research-status Report
  • [Presentation] 2次元低ベータ簡約化MHDのアニーリングシミュレーションにおける対称カー ネルの効果2014

    • Author(s)
      近末吉人,古川勝
    • Organizer
      MHD研究会(平成26年度NIFS共同研究 研究会「MHDと流体力学における共鳴・分岐・構造形成の理論・シミュレーション研究」 )
    • Place of Presentation
      核融合科学研究所
    • Year and Date
      2014-12-25 – 2014-12-26
    • Related Report
      2014 Research-status Report
  • [Presentation] High-accuracy numerical integration of charged particle dynamics based on recurrence formula with symmetric decomposition2014

    • Author(s)
      M. Furukawa
    • Organizer
      Plasma Conference 2014(日本物理学会(領域2)2014年秋季大会,応用物理学会プラズマエレクトロニクス分科会 第32回プラズマプロセシング研究会,プラズマ・核融合学会第31回年会)
    • Place of Presentation
      朱鷺メッセ(新潟市)
    • Year and Date
      2014-11-18 – 2014-11-21
    • Related Report
      2014 Research-status Report
  • [Presentation] Peeling-off modes at tokamak plasma edge2014

    • Author(s)
      Linjin Zheng, M. Furukawa
    • Organizer
      56th Annual Meeting of Division of Plasma Physics, American Physical Society
    • Place of Presentation
      New Orleans, Louisiana, USA
    • Year and Date
      2014-10-27 – 2014-10-31
    • Related Report
      2014 Research-status Report
  • [Presentation] Pressure Driven MHD Instabilities in Intrinsic and Externally Enhanced Magnetic Stochastic Region of LHD2014

    • Author(s)
      S. Ohdachi, Y. Suzuki, H. Tsuchiya, K. Y. Watanabe, S. Sakakibara, Y. Narushima, X. D. Du, T. F. Ming, M. Furukawa, K. Toi, H. Yamada and LHD Experiment Group
    • Organizer
      25th IAEA Fusion Energy Conference
    • Place of Presentation
      Saint Petersburg, Russia
    • Year and Date
      2014-10-13 – 2014-10-18
    • Related Report
      2014 Research-status Report
  • [Presentation] Experimental observation of response to resonant magnetic perturbation and its hysteresis in LHD2014

    • Author(s)
      Y. Narushima, S. Sakakibara, S. Ohdachi, Y. Suzuki, K.Y. Watanabe, S. Nishimura, M. Furukawa, Y. Takemura, K. Ida, M. Yoshinuma, I. Yamada, LHD experiment Group
    • Organizer
      25th IAEA Fusion Energy Conference
    • Place of Presentation
      Saint Petersburg, Russia
    • Year and Date
      2014-10-13 – 2014-10-18
    • Related Report
      2014 Research-status Report
  • [Presentation] Numerical computation of stationary state of 2D reduced MHD on Casimir leaf2014

    • Author(s)
      M. Furukawa
    • Organizer
      Physics / BK21+ Seminar
    • Place of Presentation
      POSTECH, Pohang, Korea
    • Year and Date
      2014-08-12
    • Related Report
      2014 Research-status Report
  • [Presentation] Simulated Annealing for stationary states of 2D low-beta reduced MHD2014

    • Author(s)
      Y. Chikasue and M. Furukawa
    • Organizer
      11th Asia Pacific Plasma Theory Conference and Japan-Korea Workshop on “Modeling and Simulation of Magnetic Fusion Plasmas”
    • Place of Presentation
      Jeju Island, Korea
    • Year and Date
      2014-07-01 – 2014-07-04
    • Related Report
      2014 Research-status Report
  • [Presentation] Numerical computation of stationary state of 2D reducedMHD on Casimir leaf2014

    • Author(s)
      M. Furukawa and Y. Chikasue
    • Organizer
      International Conference on Geometrical Algorithms and Methods for Plasma Physics
    • Place of Presentation
      Hefei, China
    • Year and Date
      2014-05-13 – 2014-05-15
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 2次元低β簡約化MHDの定常状態のアニーリングシミュレーション2014

    • Author(s)
      近末吉人,古川勝
    • Organizer
      日本物理学会第69回年次大会
    • Place of Presentation
      東海大学 湘南キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] シア流に関連するスペクトル汚染のモデル解析2014

    • Author(s)
      佐々木悠大,古川勝
    • Organizer
      日本物理学会第69回年次大会
    • Place of Presentation
      東海大学 湘南キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 負三角度トカマク核融合プラズマの可能性(1: 配位の特長)2014

    • Author(s)
      菊池満,滝塚知典,古川勝
    • Organizer
      日本物理学会第69回年次大会
    • Place of Presentation
      東海大学 湘南キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 外部印加摂動磁場に対する磁気島の履歴応答2013

    • Author(s)
      成嶋吉朗,榊原悟,大舘暁,渡邊清政,西村征也,鈴木康浩,古川勝,武村勇輝,居田克巳,吉沼幹朗,山田一博,LHD実験グループ
    • Organizer
      プラズマ・核融合学会 第30回年会
    • Place of Presentation
      東京工業大学 大岡山キャンパス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Anisotropic pressure effects on magnetospheric MHD equilibrium2013

    • Author(s)
      M. Furukawa
    • Organizer
      55th Annual Meeting of Division of Plasma Physics, American Physical Society
    • Place of Presentation
      Sheraton Denver Downtown Hotel, Denver, Colorado, USA
    • Related Report
      2013 Research-status Report
  • [Presentation] 2次元中性流体の定常状態のアニーリングシミュレーション2013

    • Author(s)
      近末吉人,古川勝
    • Organizer
      日本物理学会2013年秋季大会
    • Place of Presentation
      徳島大学 常三島キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 2次元中性流体の定常状態のアニーリングシミュレーション2013

    • Author(s)
      近末吉人,古川勝
    • Organizer
      日本流体力学会 年会2013
    • Place of Presentation
      東京農工大学 小金井キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] Properties of MHD equilibrium with pressure anisotropy in axisymmetric magnetospheric configuration2013

    • Author(s)
      M. Furukawa
    • Organizer
      The 12th Asia Pacific Physics Conference
    • Place of Presentation
      Makuhari Messe, Chiba, Japan
    • Related Report
      2013 Research-status Report
  • [Presentation] Negative D shape plasma as possible operational scenario of tokamak2013

    • Author(s)
      M. Kikuchi, T. Takizuka, M. Furukawa
    • Organizer
      The 12th Asia Pacific Physics Conference
    • Place of Presentation
      Makuhari Messe, Chiba, Japan
    • Related Report
      2013 Research-status Report
  • [Presentation] トカマクプラズマのシア回転による モード間結合とバルーニングモード安定化2013

    • Author(s)
      古川勝
    • Organizer
      MHD研究会(平成25年度NIFS共同研究 研究会「MHDおよび流体力学における流れの安定性に関する理論・シミュレーション研究」 )
    • Place of Presentation
      核融合科学研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] シア流にまつわるスペクトル汚染のモデル解析と解法に関する考察2013

    • Author(s)
      佐々木悠大,古川勝
    • Organizer
      MHD研究会(平成25年度NIFS共同研究 研究会「MHDおよび流体力学における流れの安定性に関する理論・シミュレーション研究」 )
    • Place of Presentation
      核融合科学研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] 2次元低ベータ簡約化MHDのカシミール不変量の束縛とアニーリングシミュレーション2013

    • Author(s)
      近末吉人,古川勝
    • Organizer
      MHD研究会(平成25年度NIFS共同研究 研究会「MHDおよび流体力学における流れの安定性に関する理論・シミュレーション研究」 )
    • Place of Presentation
      核融合科学研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] Properties of magnetospheric MHD equilibrium with anisotropic pressure2013

    • Author(s)
      M. Furukawa
    • Organizer
      US-Japan JIFT Workshop on “Recent studies of extended MHD and MHD simulations”
    • Place of Presentation
      Sheraton Denver Downtown Hotel, Denver, Colorado, USA
    • Related Report
      2013 Research-status Report
  • [Presentation] 3次元MHD平衡の新しい計算法2013

    • Author(s)
      古川勝
    • Organizer
      核融合エネルギーフォーラム プラズマ物理クラスター MHD安定性・高エネルギー粒子サブクラスター会合
    • Place of Presentation
      核融合科学研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] Beta limit of MHD equilibrium with pressure anisotropy in magnetospheric configuration2013

    • Author(s)
      M. Furukawa
    • Organizer
      The 19th NEXT workshop
    • Place of Presentation
      京都大学 桂キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 磁気圏型プラズマのMHD平衡における圧力非等方性による磁場変化2013

    • Author(s)
      古川勝
    • Organizer
      日本物理学会 第68回年次大会
    • Place of Presentation
      広島大学 東広島キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] 背景磁場に垂直に伝播する電磁波に対する高温電子の温度非等方性効果2013

    • Author(s)
      後藤義哉,古川勝
    • Organizer
      日本物理学会 第68回年次大会
    • Place of Presentation
      広島大学 東広島キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] 磁化プラズマにおける特異摂動問題の新しい数値解法2013

    • Author(s)
      古川勝
    • Organizer
      クロスボーダーセミナー
    • Place of Presentation
      北海道大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 有限Larmor半径効果を含めたMHDモード安定性の接続解法の収束特性2012

    • Author(s)
      古川勝
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学常盤台キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] 磁場に垂直に伝播する電磁波への 高エネルギー電子の影響2012

    • Author(s)
      後藤義哉,古川勝
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学常盤台キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] 境界層問題の接続解法の収束特性に関する考察2012

    • Author(s)
      古川勝
    • Organizer
      MHD研究会
    • Place of Presentation
      核融合科学研究所
    • Related Report
      2012 Research-status Report
  • [Presentation] A new matching method for stability analysis of boundary-layer-type MHD modes in magnetized plasmas2012

    • Author(s)
      M. Furukawa
    • Organizer
      Nonlinearity Workshop
    • Place of Presentation
      Tottori Univeristy
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 有限Larmor半径効果を含む簡約化MHDモデルに対する新しい接続解法の開発2012

    • Author(s)
      古川勝
    • Organizer
      日本物理学会第67回年次大会
    • Place of Presentation
      関西学院大学 西宮上ケ原キャンパス
    • Related Report
      2011 Research-status Report
  • [Presentation] 磁気圏型プラズマの短波長MHD安定性に対するプラズマ回転効果の分析2012

    • Author(s)
      古川勝
    • Organizer
      日本天文学会 2012年春季年会
    • Place of Presentation
      龍谷大学深草キャンパス
    • Related Report
      2011 Research-status Report
  • [Presentation] A new matching method for resistive MHD stability analysis2012

    • Author(s)
      M. Furukawa, S. Tokuda
    • Organizer
      Joint 18th International Stellarator/Heliotron Workshop and 10th Asia Pacific Plasma Theory Conference
    • Place of Presentation
      Australian Natioal University, Canberra and Murramarang Beachfront Nature Reserve, Australia
    • Related Report
      2011 Research-status Report
  • [Presentation] A new solution method for singular perturbation problems in magnetized plasmas2011

    • Author(s)
      M. Furukawa
    • Organizer
      Joint Res. WS IMI, Kyushu Univ. & MEXT Collaborative WS Math. and Math. Sci. with Various Sci. and Industrial Technologies 2011(招待講演)
    • Place of Presentation
      Ito Campus, Kyushu University, Japan
    • Related Report
      2011 Research-status Report
  • [Presentation] 抵抗性MHD安定性解析の未解決問題に対する新しい近似解法2011

    • Author(s)
      古川勝,徳田伸二
    • Organizer
      Plasma Conference 2011(プラズマ・核融合学会第28回年会/応用物理学会第29回プラズマプロセシング研究会/日本物理学会(領域2)2011年秋季大会)(招待講演)
    • Place of Presentation
      石川県立音楽堂
    • Related Report
      2011 Research-status Report
  • [Presentation] 磁気圏型プラズマ閉じ込めのバルーニング安定性に対する流れの効果の分析2011

    • Author(s)
      古川勝
    • Organizer
      Plasma Conference 2011(プラズマ・核融合学会第28回年会/応用物理学会第29回プラズマプロセシング研究会/日本物理学会(領域2)2011年秋季大会)
    • Place of Presentation
      石川県立音楽堂
    • Related Report
      2011 Research-status Report
  • [Presentation] 磁気圏型プラズマ平衡における反磁性電流に対する非等方圧力効果2011

    • Author(s)
      飯塚将太,古川勝
    • Organizer
      Plasma Conference 2011(プラズマ・核融合学会第28回年会/応用物理学会第29回プラズマプロセシング研究会/日本物理学会(領域2)2011年秋季大会)
    • Place of Presentation
      石川県立音楽堂
    • Related Report
      2011 Research-status Report
  • [Presentation] 磁化プラズマにおける境界層問題に対する新しい接続解法の開発2011

    • Author(s)
      古川勝,徳田伸二
    • Organizer
      日本応用数理学会2011年度年会
    • Place of Presentation
      同志社大学今出川キャンパス
    • Related Report
      2011 Research-status Report
  • [Remarks] なし

    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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