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RISS 인기검색어
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- 저자 : Yoji Aizawa (검색결과 4 건)
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New Aspects of the Correlation Functions in Non-Hyperbolic Chaotic Systems
Takuma Akimoto,Yoji Aizawa 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.1I
The initial ensemble dependence of statistical laws in non-hyperbolic dynamical systems with in.nite ergodicity are studied by use of the modi.ed Bernoulli maps. We show that statistical laws crucially depend on the initial ensemble and that the time average for the Lyapunov exponent converges in distribution for the non-stationary regime. This is completely consistent with the Darling-Kac-Aaronson (DKA) limit theorem from the fact that the Lyapunov exponent is an L1 ¹- class function. Next, we study the correlation function, which is not an L1 ¹-class function. The most remarkable result is that the transformed correlation function also reveals uniform convergence in distribution in the same sense of the DKA limit theorem.
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The Lempel-Ziv Complexity in Infinite Ergodic Systems
Soya Shinkai,Yoji Aizawa 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.1I
The L1-function property of the Lempel-Ziv complexity of 2- and 3-symbol sequences is numerically studied in the framework of the in.nite ergodic theory. Our results show that the L1-function property is consistent in the case of plural indierent .xed points with same order singularities near each point.
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Heteroclinic Turbulence in the Lotka-Volterra Reaction Diffusion Equation
Kenji Orihashi,Yoji Aizawa 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.1I
Heteroclinic turbulence in the Lotka-Volterra reaction diusion equation is studied numerically and theoretically, and the statistical feature is analyzed precisely in reference to the onset mechanism of the turbulence. First, the bifurcation diagram is demonstrated in detail, and a variety of attractors are discussed. It is emphasized that the diversity of the attractor enhances when the system size increases. Next, the transition from a regular attractor to a turbulent one is characterized by a correlation function, as well as by the Lyapunov exponent, where one can observe the scaling laws clearly for the correlation length and the maximum Lyapunov exponent.m
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Takahito Mitsui,Yoji Aizawa 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.1I
In a previous study, the refractory-activation oscillator system (RAO system) was proposed to explain the crossbridge formation process in the actomyosin system. In this paper, the RAO system is analyzed to make clear how the geometrical structure of the actomyosin system affects its sliding dynamics and cooperative phenomena in the muscle contraction process. The geometrical structure is characterized by the spatial period ratio between myosin and actin filaments. First, the sliding velocity of the RAO model is shown to depend very sensitively on the period ratio, which we call velocity resonance. Next, the origin and the detailed aspects of the resonance are discussed based on the notion of maximum spacing between the relative equilibrium positions of myosin molecules. An important result is that the condition for the resonance depends not only on the period ratio but also on the number of myosin molecules (the system size N) because the width of each resonance zone changes by a law of O(N.1). This means that an appropriate value of the period ratio must be realized in order to accomplish a coherent sliding motion in the actomyosin system under the condition of a finite N.
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