1990 年度実績報告書

間歇性カオスの大域的スペクトル構造と時空スケ-リング則の統計物理学的研究

研究課題

研究課題/領域番号	63540276
研究機関	九州大学
研究代表者	岡本寿夫九州大学, 理学部, 助教授 (50037222)
研究分担者	森肇九州共立大学, 工学部, 教授 (90037143)
キーワード	カオス / 間歇性カオス / パワ-スペクトル / 粗視化の統計測 / カオスの動的構造関数の統計熱力学形式 / カオスにおけるqー相転移 / 微分方程式系のカオス / エネルギ-散逸とその揺らぎ
研究概要	非平衡開放系の非線形ダイナミックスを力学系の立場から作る気運が1980年前後から急速に高まってきた。その契機は運動形態の転移(分岐現象)に対する力学系理論の発展と,閉水路系の流体乱流,非線形化学反応,非線形振動子等におけるカオス発生の物理的実験の登場とである。周期運動から非周期運動(カオス)が発生する普遍的シナリオとして,周期倍化のカスケ-ドによるもの,バ-ストが間歇的に現われることによるもの,準周期運動を表わすト-ラスが崩壊することによるもの,の3つが明らかになってきた。これら3つのシナリオによって発生したカオスを,それぞれ、周期性カオス,間歇性カオス,準周期性カオスと呼ぶ。カオスの際立った性質(挙動と応答)は,(A)時間及び空間のスケ-ルについて,諸種のスケ-リング則を示すことと,(B)著しい時間相関・コヒ-レンスを示すことである。とりわけ,間歇性カオスの時系列は層流的振動と乱流的バ-ストからなり,その層流的振動は,後者の典型的例を与える。本研究は,まず,カオスの発生と構造を力学的に特徴づける量と方法を見出し,ついで,非平衡開放系に特有な物理的プロセス(エネルギ-散逸,諸々の物質量の混合・拡散など)の挙動と応答をカオスの構造から統計物理的に解明することを目指して次の研究を行った。即ち,1.開歇性カオスの大域的スペクトル構造。2.カオスの構造を特徴づける軌道拡大率スペクトルΨ(Λ)とqー相転移。(1)1次元写像及び散逸2次元写像のカオスとqー相転移,(2)微分方程式系におけるカオスの構造とqー相転移,(3)アトラクタ-のフラクタル構造とqー相転移。3.臨界軌道の記憶現象とψ(Λ)の臨界スケ-リング則。4.ハミルトン力学系における混合と拡散。(1)ハミルトン力学系における広域的カオスのqー相転移,(2)流体のラグランジュ乱流。5.カオス的な力学系におけるエネルギ-散逸とその揺らぎ。

研究成果

(30件)

すべてその他

すべて文献書誌 (30件)

[文献書誌] 森田照光(Terumitsu MORITA): "Spatial and Temporal Scaling Properties of Strange Attractors and their Representation by Unstable Periodic Orbits." Progress of Theoretical Physics. 79. 296-312 (1988)
[文献書誌] 岡本寿夫(Hisao OKAMOTO): "Global Spectral Structures of Type III Intermittent Chaos." Progress of Theoretical Physics. 79. 581-599 (1988)
[文献書誌] 森信之(Nobuyuki MORI): "Power Spectra of Intermittent Chaos Due to the Collapse of Periodー3 Windows." Progress of Theoretical Physics. 79. 1260-1264 (1988)
[文献書誌] 堀田武彦(Takehiko HORITA): "Local Structures of Chaotic Attractors and qーPhase Transitions at AttractorーMerging Crises in the SineーCircle Maps." Progress of Theoretical Physics. 80. 793-808 (1988)
[文献書誌] 秦浩起(Hiroki HATA): "Characterization of Local Structures of Chaotic Attractors in Terms of CoarseーGrained Local Expansion Rates." Progress of Theoretical Physics. 80. 809-826 (1988)
[文献書誌] 堀田武彦(Takehiko HORITA): "Singular Local Structures of Chaotic Attractors Due to Collisions with Unstable Periodic Orbits in TwoーDimensional Maps." Progress of Theoretical Physics. 80. 923-928 (1988)
[文献書誌] 冨田浩治(Kouju TOMITA): "Scaling Structures of Chaotic Attractors and qーPhase Transitions at Crises in the He^^´non and the Annulus Maps." Progress of Theoretical Physics. 80. 953-972 (1988)
[文献書誌] 冨田浩治(Kouji TOMITA): "Classification of Collisions of Chaotic Attractors with Unstable Periodic Orbits in Terms of the qーPhase Transitions." Progress of Theoretical Physics. 81. 1-6 (1989)
[文献書誌] 秦浩起(Hiroki HATA): "Singular Local structures of Chaotic Attractors and qーPhase Transitions of Spatial Scaling Structures." Progress of Theoretical Physics. 81. 11-16 (1989)
[文献書誌] 森信之(Nobuyuki MORI): "Scaling Structures and Statistical Mechanics of Type I Intermittent Chaos." Progress of Theoretical Physics. 81. 60-77 (1989)
[文献書誌] 堀田武彦(Takehiko HORITA): "Dynamics on Critical Tori at the Onset of Chaos and Critical KAM Tori." Progress of Theoretical Physics. 81. 1073-1078 (1989)
[文献書誌] 冨田浩治(Kouji TOMITA): "qーPhase Transitions in Chaotic Attractors of Differential Equations at Bifurcation Points." Progress of Theoretical Physics. 81. 1124-1134 (1989)
[文献書誌] 小林達治(Tatsuharu KOBAYASHI): "Critical Scaling Laws of Dynamic Structure Functions for Type I Intermittent Chaos." Progress of Theoretical Physics. 82. 1-6 (1989)
[文献書誌] 宮崎修次(Shuuji MIYAZAKI): "The qーPhase Transtions and Critical Phenomena Just After BandーCrises." Progress of Theoretical Physics. 82. 863-868 (1989)
[文献書誌] 吉田健(Takeshi YOSHIDA): "The qーPhase Transitions and Critical Scaling Laws Near the BandーCrisis Point of Chaotic Attractors." Progress of Theoretical Physics. 82. 879-896 (1989)
[文献書誌] 秦浩起(Hiroki HATA): "Dynamic Description of the Critical 2^∞ Attractor and 2^mーBand Chaos." Progress of Theoretical Physics. 82. 897-910 (1989)
[文献書誌] 森肇(Hazime MORI): "Statistical Mechanics of Dynamical Systems." Progress of Theoretical Physics Supplement. 99. 1-63 (1989)
[文献書誌] 村山徹(Touru MURAYAMA): "qーPhase Transitions and Dynamic Scaling Laws at AttractorーMerging Crises in the Driven Damped Pendulum." Progress of Theoretical Physics. 83. 649-654 (1990)
[文献書誌] 柴田博史(Hiroshi SHIBATA): "Dynamic Scaling Laws for the Intermittent Switching between Two Bands." Progress of Theoretical Physics. 83. 829-834 (1990)
[文献書誌] 堀田武彦(Takehiko HORITA): "LongーTime Correlations and ExpansionーRate Spectra of Chaos in Hamiltonian Systems." Progress of Theoretical Physics. 83. 1065-1070 (1990)
[文献書誌] 富永広貴(Hiroki TOMINAGA): "Linearities of the f(α) Spectrum at Bifurcations of Chaos in Dissipative differential Systems." Progress of Theoretical Physics. 84. 18-22 (1990)
[文献書誌] 石崎龍二(Ryuuji ISHIZAKI): "LongーTime Correlations and Anomalous Diffusion due to Accelerator Modes in the Standard Maps." Progress of Theoretical Physics. 84. 179-184 (1990)
[文献書誌] 富永広貴(Hiroki TOMINAGA): "Dynamic Scaling Laws for Bifurcations of Chaos is Disspative Differential Systems." Progress of Theoretical Physics. 84. 553-557 (1990)
[文献書誌] 堀田武彦(Takehiko HORITA): "Cascade of AttractorーMerging Crises to the Critical Golden Torus and Universal ExpansionーRate Spectra." Progress of Theoretical Physics. 84. 558-562 (1990)
[文献書誌] 大内克哉(Katsuya OUCHI): "Advective Diffusion of Particles in RayleighーBe^^´nard Convection." Progress of Theoretical Physics. (1991)
[文献書誌] 柴田博史(Hiroshi SHIBATA): "Scaling Structures for Dynamics of Intermittent Switching Just After ThreeーBand Crisis." Physica D. (1991)
[文献書誌] 森肇(Hazime MORI): "Geometrical Structures of Chaos and qーPhase Transition." “Phase Transition",ed.by K.Kawasaki and T.Fukami (Gordon & Breach Science Publishers Inc.,U.K.,1990). (1991)
[文献書誌] 石崎龍二(Ryuuji ISHIZAKI): "Anomalous Diffusion due to Accelerator Modes in the Standard Map." Progress of Theoretical Physics. (1991)
[文献書誌] 堀田武彦(Takehiko HORITA): "LongーTime Correlations and Anomalous Scaling Laws for Widespread Chaos in the Standard Map." Progress of Theoretical Physics. (1991)
[文献書誌] 森肇(Hazime MORI): "Energy Dissipation and Its Fluctuations in Chaotic Dynamical Systems." Progress of Theoretical Physics. (1991)

1990 年度 実績報告書

間歇性カオスの大域的スペクトル構造と時空スケ-リング則の統計物理学的研究

研究代表者

岡本 寿夫 九州大学, 理学部, 助教授 (50037222)

研究成果

[文献書誌] 森田 照光(Terumitsu MORITA): "Spatial and Temporal Scaling Properties of Strange Attractors and their Representation by Unstable Periodic Orbits." Progress of Theoretical Physics. 79. 296-312 (1988)

[文献書誌] 岡本 寿夫(Hisao OKAMOTO): "Global Spectral Structures of Type III Intermittent Chaos." Progress of Theoretical Physics. 79. 581-599 (1988)

[文献書誌] 森 信之(Nobuyuki MORI): "Power Spectra of Intermittent Chaos Due to the Collapse of Periodー3 Windows." Progress of Theoretical Physics. 79. 1260-1264 (1988)

[文献書誌] 堀田 武彦(Takehiko HORITA): "Local Structures of Chaotic Attractors and qーPhase Transitions at AttractorーMerging Crises in the SineーCircle Maps." Progress of Theoretical Physics. 80. 793-808 (1988)

[文献書誌] 秦 浩起(Hiroki HATA): "Characterization of Local Structures of Chaotic Attractors in Terms of CoarseーGrained Local Expansion Rates." Progress of Theoretical Physics. 80. 809-826 (1988)

[文献書誌] 堀田 武彦(Takehiko HORITA): "Singular Local Structures of Chaotic Attractors Due to Collisions with Unstable Periodic Orbits in TwoーDimensional Maps." Progress of Theoretical Physics. 80. 923-928 (1988)

[文献書誌] 冨田 浩治(Kouju TOMITA): "Scaling Structures of Chaotic Attractors and qーPhase Transitions at Crises in the He^^´non and the Annulus Maps." Progress of Theoretical Physics. 80. 953-972 (1988)

[文献書誌] 冨田 浩治(Kouji TOMITA): "Classification of Collisions of Chaotic Attractors with Unstable Periodic Orbits in Terms of the qーPhase Transitions." Progress of Theoretical Physics. 81. 1-6 (1989)

[文献書誌] 秦 浩起(Hiroki HATA): "Singular Local structures of Chaotic Attractors and qーPhase Transitions of Spatial Scaling Structures." Progress of Theoretical Physics. 81. 11-16 (1989)

[文献書誌] 森 信之(Nobuyuki MORI): "Scaling Structures and Statistical Mechanics of Type I Intermittent Chaos." Progress of Theoretical Physics. 81. 60-77 (1989)

[文献書誌] 堀田 武彦(Takehiko HORITA): "Dynamics on Critical Tori at the Onset of Chaos and Critical KAM Tori." Progress of Theoretical Physics. 81. 1073-1078 (1989)

[文献書誌] 冨田 浩治(Kouji TOMITA): "qーPhase Transitions in Chaotic Attractors of Differential Equations at Bifurcation Points." Progress of Theoretical Physics. 81. 1124-1134 (1989)

[文献書誌] 小林 達治(Tatsuharu KOBAYASHI): "Critical Scaling Laws of Dynamic Structure Functions for Type I Intermittent Chaos." Progress of Theoretical Physics. 82. 1-6 (1989)

[文献書誌] 宮崎 修次(Shuuji MIYAZAKI): "The qーPhase Transtions and Critical Phenomena Just After BandーCrises." Progress of Theoretical Physics. 82. 863-868 (1989)

[文献書誌] 吉田 健(Takeshi YOSHIDA): "The qーPhase Transitions and Critical Scaling Laws Near the BandーCrisis Point of Chaotic Attractors." Progress of Theoretical Physics. 82. 879-896 (1989)

[文献書誌] 秦 浩起(Hiroki HATA): "Dynamic Description of the Critical 2^∞ Attractor and 2^mーBand Chaos." Progress of Theoretical Physics. 82. 897-910 (1989)

[文献書誌] 森 肇(Hazime MORI): "Statistical Mechanics of Dynamical Systems." Progress of Theoretical Physics Supplement. 99. 1-63 (1989)

[文献書誌] 村山 徹(Touru MURAYAMA): "qーPhase Transitions and Dynamic Scaling Laws at AttractorーMerging Crises in the Driven Damped Pendulum." Progress of Theoretical Physics. 83. 649-654 (1990)

[文献書誌] 柴田 博史(Hiroshi SHIBATA): "Dynamic Scaling Laws for the Intermittent Switching between Two Bands." Progress of Theoretical Physics. 83. 829-834 (1990)

[文献書誌] 堀田 武彦(Takehiko HORITA): "LongーTime Correlations and ExpansionーRate Spectra of Chaos in Hamiltonian Systems." Progress of Theoretical Physics. 83. 1065-1070 (1990)

[文献書誌] 富永 広貴(Hiroki TOMINAGA): "Linearities of the f(α) Spectrum at Bifurcations of Chaos in Dissipative differential Systems." Progress of Theoretical Physics. 84. 18-22 (1990)

[文献書誌] 石崎 龍二(Ryuuji ISHIZAKI): "LongーTime Correlations and Anomalous Diffusion due to Accelerator Modes in the Standard Maps." Progress of Theoretical Physics. 84. 179-184 (1990)

[文献書誌] 富永 広貴(Hiroki TOMINAGA): "Dynamic Scaling Laws for Bifurcations of Chaos is Disspative Differential Systems." Progress of Theoretical Physics. 84. 553-557 (1990)

[文献書誌] 堀田 武彦(Takehiko HORITA): "Cascade of AttractorーMerging Crises to the Critical Golden Torus and Universal ExpansionーRate Spectra." Progress of Theoretical Physics. 84. 558-562 (1990)

[文献書誌] 大内 克哉(Katsuya OUCHI): "Advective Diffusion of Particles in RayleighーBe^^´nard Convection." Progress of Theoretical Physics. (1991)

[文献書誌] 柴田 博史(Hiroshi SHIBATA): "Scaling Structures for Dynamics of Intermittent Switching Just After ThreeーBand Crisis." Physica D. (1991)

[文献書誌] 森 肇(Hazime MORI): "Geometrical Structures of Chaos and qーPhase Transition." “Phase Transition",ed.by K.Kawasaki and T.Fukami (Gordon & Breach Science Publishers Inc.,U.K.,1990). (1991)

[文献書誌] 石崎 龍二(Ryuuji ISHIZAKI): "Anomalous Diffusion due to Accelerator Modes in the Standard Map." Progress of Theoretical Physics. (1991)

[文献書誌] 堀田 武彦(Takehiko HORITA): "LongーTime Correlations and Anomalous Scaling Laws for Widespread Chaos in the Standard Map." Progress of Theoretical Physics. (1991)

[文献書誌] 森 肇(Hazime MORI): "Energy Dissipation and Its Fluctuations in Chaotic Dynamical Systems." Progress of Theoretical Physics. (1991)

1990 年度実績報告書

岡本寿夫九州大学, 理学部, 助教授 (50037222)

[文献書誌] 森田照光(Terumitsu MORITA): "Spatial and Temporal Scaling Properties of Strange Attractors and their Representation by Unstable Periodic Orbits." Progress of Theoretical Physics. 79. 296-312 (1988)

[文献書誌] 岡本寿夫(Hisao OKAMOTO): "Global Spectral Structures of Type III Intermittent Chaos." Progress of Theoretical Physics. 79. 581-599 (1988)

[文献書誌] 森信之(Nobuyuki MORI): "Power Spectra of Intermittent Chaos Due to the Collapse of Periodー3 Windows." Progress of Theoretical Physics. 79. 1260-1264 (1988)

[文献書誌] 堀田武彦(Takehiko HORITA): "Local Structures of Chaotic Attractors and qーPhase Transitions at AttractorーMerging Crises in the SineーCircle Maps." Progress of Theoretical Physics. 80. 793-808 (1988)

[文献書誌] 秦浩起(Hiroki HATA): "Characterization of Local Structures of Chaotic Attractors in Terms of CoarseーGrained Local Expansion Rates." Progress of Theoretical Physics. 80. 809-826 (1988)

[文献書誌] 堀田武彦(Takehiko HORITA): "Singular Local Structures of Chaotic Attractors Due to Collisions with Unstable Periodic Orbits in TwoーDimensional Maps." Progress of Theoretical Physics. 80. 923-928 (1988)

[文献書誌] 冨田浩治(Kouju TOMITA): "Scaling Structures of Chaotic Attractors and qーPhase Transitions at Crises in the He^^´non and the Annulus Maps." Progress of Theoretical Physics. 80. 953-972 (1988)

[文献書誌] 冨田浩治(Kouji TOMITA): "Classification of Collisions of Chaotic Attractors with Unstable Periodic Orbits in Terms of the qーPhase Transitions." Progress of Theoretical Physics. 81. 1-6 (1989)

[文献書誌] 秦浩起(Hiroki HATA): "Singular Local structures of Chaotic Attractors and qーPhase Transitions of Spatial Scaling Structures." Progress of Theoretical Physics. 81. 11-16 (1989)

[文献書誌] 森信之(Nobuyuki MORI): "Scaling Structures and Statistical Mechanics of Type I Intermittent Chaos." Progress of Theoretical Physics. 81. 60-77 (1989)

[文献書誌] 堀田武彦(Takehiko HORITA): "Dynamics on Critical Tori at the Onset of Chaos and Critical KAM Tori." Progress of Theoretical Physics. 81. 1073-1078 (1989)

[文献書誌] 冨田浩治(Kouji TOMITA): "qーPhase Transitions in Chaotic Attractors of Differential Equations at Bifurcation Points." Progress of Theoretical Physics. 81. 1124-1134 (1989)

[文献書誌] 小林達治(Tatsuharu KOBAYASHI): "Critical Scaling Laws of Dynamic Structure Functions for Type I Intermittent Chaos." Progress of Theoretical Physics. 82. 1-6 (1989)

[文献書誌] 宮崎修次(Shuuji MIYAZAKI): "The qーPhase Transtions and Critical Phenomena Just After BandーCrises." Progress of Theoretical Physics. 82. 863-868 (1989)

[文献書誌] 吉田健(Takeshi YOSHIDA): "The qーPhase Transitions and Critical Scaling Laws Near the BandーCrisis Point of Chaotic Attractors." Progress of Theoretical Physics. 82. 879-896 (1989)

[文献書誌] 秦浩起(Hiroki HATA): "Dynamic Description of the Critical 2^∞ Attractor and 2^mーBand Chaos." Progress of Theoretical Physics. 82. 897-910 (1989)

[文献書誌] 森肇(Hazime MORI): "Statistical Mechanics of Dynamical Systems." Progress of Theoretical Physics Supplement. 99. 1-63 (1989)

[文献書誌] 村山徹(Touru MURAYAMA): "qーPhase Transitions and Dynamic Scaling Laws at AttractorーMerging Crises in the Driven Damped Pendulum." Progress of Theoretical Physics. 83. 649-654 (1990)

[文献書誌] 柴田博史(Hiroshi SHIBATA): "Dynamic Scaling Laws for the Intermittent Switching between Two Bands." Progress of Theoretical Physics. 83. 829-834 (1990)

[文献書誌] 堀田武彦(Takehiko HORITA): "LongーTime Correlations and ExpansionーRate Spectra of Chaos in Hamiltonian Systems." Progress of Theoretical Physics. 83. 1065-1070 (1990)

[文献書誌] 富永広貴(Hiroki TOMINAGA): "Linearities of the f(α) Spectrum at Bifurcations of Chaos in Dissipative differential Systems." Progress of Theoretical Physics. 84. 18-22 (1990)

[文献書誌] 石崎龍二(Ryuuji ISHIZAKI): "LongーTime Correlations and Anomalous Diffusion due to Accelerator Modes in the Standard Maps." Progress of Theoretical Physics. 84. 179-184 (1990)

[文献書誌] 富永広貴(Hiroki TOMINAGA): "Dynamic Scaling Laws for Bifurcations of Chaos is Disspative Differential Systems." Progress of Theoretical Physics. 84. 553-557 (1990)

[文献書誌] 堀田武彦(Takehiko HORITA): "Cascade of AttractorーMerging Crises to the Critical Golden Torus and Universal ExpansionーRate Spectra." Progress of Theoretical Physics. 84. 558-562 (1990)

[文献書誌] 大内克哉(Katsuya OUCHI): "Advective Diffusion of Particles in RayleighーBe^^´nard Convection." Progress of Theoretical Physics. (1991)

[文献書誌] 柴田博史(Hiroshi SHIBATA): "Scaling Structures for Dynamics of Intermittent Switching Just After ThreeーBand Crisis." Physica D. (1991)

[文献書誌] 森肇(Hazime MORI): "Geometrical Structures of Chaos and qーPhase Transition." “Phase Transition",ed.by K.Kawasaki and T.Fukami (Gordon & Breach Science Publishers Inc.,U.K.,1990). (1991)

[文献書誌] 石崎龍二(Ryuuji ISHIZAKI): "Anomalous Diffusion due to Accelerator Modes in the Standard Map." Progress of Theoretical Physics. (1991)

[文献書誌] 堀田武彦(Takehiko HORITA): "LongーTime Correlations and Anomalous Scaling Laws for Widespread Chaos in the Standard Map." Progress of Theoretical Physics. (1991)

[文献書誌] 森肇(Hazime MORI): "Energy Dissipation and Its Fluctuations in Chaotic Dynamical Systems." Progress of Theoretical Physics. (1991)