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Dynamics Behaviors and Scaling in Intermittent Turbulence of a Shell Model

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Communications in Theoretical Physics 2009年第1期51卷 149-152页

作者： SUN Peng CHEN Shi-Gang wang guang-rui physics Department Anshan Normal College Anshan 114005 China Graduate School of China Academy of Engineering Physics P.O. Box 2101 Beijing 100088 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

In this paper, the dynamics behaviors on fo-δ parameter surface is investigated for Gledzer-Ohkitani- Yamada model We indicate the type of intermittency chaos transitions is saddle node bifurcation. We plot phase diagram on fo-δ parameter surface, which is divided into periodic, quasi-periodic, and intermittent chaos areas. By means of varying Taylor-microscale Reynolds number, we calculate the extended self-similarity of velocity structure function.

关键词： saddle node bifurcation critical scaling Taylor-microscale Reynolds number extended self-similarity (ESS)

Probability Distribution Function of Passive Scalars in Shell Models

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Communications in Theoretical Physics 2008年第4期49卷 1033-1038页

作者： ZHANG Xiao-Qiang wang guang-rui CHEN Shi-Gang Department of Physics Hebei Normal University Shijiazhuang 050016 China Graduate School of the China Academy of Engineering Physics P.O. Box 8009（28） Beijing 100088 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 （1988） 983; K. Ohkitani and M. Yakhot, Prog. Theor. Phys. 81 （1988） 329]. As in the original problem, the prescribed random velocity field is Gaussian and 5 correlated in time. Deterministic differential equations are regarded as nonlinear Langevin equation. Then, the Fokker-Planck equations of PDF for passive scalars are obtained and solved numerically. In energy input range （n 〈 5, n is the shell number.）, the probability distribution function （PDF） of passive scalars is near the Gaussian distribution. In inertial range （5≤ n ≤ 16） and dissipation range （n ≥ 17）, the probability distribution function （PDF） of passive scalars has obvious intermittence. And the scaling power of passive scalar is anomalous. The results of numerical simulations are compared with experimental measurements.

关键词： shell model passive scalar distribution function

Influence of Velocity Shell Correlations on Anomalous Scaling Exponents of Passive Scalars in Shell Models

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Communications in Theoretical Physics 2008年第7期50卷 211-214页

作者： ZHANG Xiao-Qiang wang guang-rui CHEN Shi-Gang Graduate School of China Academy of Engineer Physics P.O. Box 8009（28） Beijing 100088 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics P.O. Box 8009（28） Beijing 100088 China

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random velocity field is multi-dimensional normal and delta-correlated in time. Here, our random velocity field is spatially correlative. For comparison, we also give the result obtained by the Gaussian random velocity field without spatial correlation. The anomalous scaling exponents H（p） of passive scalar advected by two kinds of random velocity above are determined for structure function up to p= 15 by numerical simulations of the random shell model with Runge-Kutta methods to solve the stochastic differential equations. We observed that the H（p）＇s obtained by the multi-dimeasional normal distribution random velocity are more anomalous than those obtained by the independent Gaussian random velocity.

关键词： shell models passive scalar distribution function

Stability of GOY Model Under Modulation of Periodic External Force

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Communications in Theoretical Physics 2008年第2期49卷 521-524页

作者： ZHAO Ying-Kui CHEN Shi-Gang wang guang-rui Institute of Applied Physics and Computational Mathematics P.O. Box 8009（14） Beijing 100088 China

There is a phase transition between quasi-periodic state and intermittent chaos in GOY model with a critical value δ0. When we add a modulated periodic externa/force to the system, the phase transition can also be found with a critical value δe. Due to coupling between the force and the intrinsic fluctuation of the velocity on shells in GOY model, the stability of the system has been changed, which results in the variation of the critical value. For proper intensity and period of the force, δe is unequal to δ0. The critical value is a nonlinear function of amplitude of the force, and the fluctuation of the velocity can resonate with the external force for certain period Te.

关键词： chaos GOY model phase transition

Control of Spiral Waves and Spatiotemporal Chaos by Exciting Travel Wave Trains

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Communications in Theoretical Physics 2005年第5X期44卷 858-862页

作者： YUAN Guo-Yong wang guang-rui CHEN Shi-Gang Department of Physics Hebei Normal University Shijiazhuang 050016 China Graduate School of the Chinese Academy of Engineering Physics P.O. Box 2101 Beijing 100088 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.

关键词： spatiotemporal chaos spiral waves control

A Generalized Frenkel-Kontorova Model with Morse Potentials

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Chinese Physics Letters 1997年第11期14卷 820-822页

作者： XU Ai-guo wang guang-rui CHEN Shi-gang Graduate Schoo1 China Academy of Engineering PhysicsBeijing 100088 Center for Nonlinear Studies Institute of Applied Physics and Computational MathematicsBeijing 100088

A generalized Frenkel-Kontorova model with the Morse potentials is *** phase diagram reflects the nonlinear nature of the Morse *** correspondences of the ground states and the orbits of the area-preserving map are st... 详细信息

关键词： potential. Morse preserving

Frenkel-Kontorova Model of the Dimerized Overlayer System with Vacancies

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Chinese Physics Letters 2000年第9期17卷 689-690页

作者： XU Hai-Bo wang guang-rui CHEN Shi-Gang Graduate School China Academy of Engineering PhysicsP.O.Box 2101Beijing 100088 Center for Nonlinear Studies Institute of Applied Physics and Computational mathematicsBeijing 100088

The reconstruction of the dimerized overlayer system with vacancies is studied via a diatomic chain Frenkel Kontorova *** present the details of the exactly solvable model and the analytical solution of the atomic dis... 详细信息

关键词： state. details exactly

Controlling Strong Chaos by Adaptive Coupling Method in the Perturbed Cat Map

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Chinese Physics Letters 2001年第7期18卷 878-881页

The method for controlling Hamiltonian chaos by adaptive integrable mode coupling is extended to controlling strong chaos by adaptive integrable and near-integrable mode *** illustrate this method with a highly chaotic system,the perturbed cat *** orbits can be effectively controlled to the periodic or quasiperiodic *** method is robust against the presence of weak external noise.

关键词： integrable chaos controlling

Segmented Spiral Waves and Anti-phase Synchronization in a Model System with Two Identical Time-Delayed Coupled Layers

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Communications in Theoretical Physics 2008年第1期49卷 174-180页

作者： YUAN Guo-Yong YANG Shi-Ping wang guang-rui CHEN Shi-Gang Department of Physics Hebei Normal University Shijiazhuang 0500167 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spiral waves, which are constituted by many thin trips, are found in each layer of two identical time-delayed coupled layers, and are different from the segmented spiral waves in a water-in-oil aerosol sodium bis（2-ethylhexyl） sulfosuccinate （AOT） microemulsion （ME）（BZ-AOT system）, which consists of many small segments. ＂Anti-phase spiral wave synchronization＂ can be realized between the first layer and the second one. For different excitable parameters, we also give the minimum values of the coupling strength to generate segmented spiral waves and the tip orbits of spiral waves in the whole bilayer.

关键词： spiral wave synchronization anti-phase synchronization