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| 1 | Hierarchical structures in climate and atmospheric turbulence显示文摘The climatic time series encompass many time scales, forming multi-scale climatic variations and hierarchies. The periods and magnitudes of cooling or warming, especially for extreme climatic events, vary with the time scales. On the other hand, high-frequency atmospheric turbulent motions, which are certainly related to the climatic changes, are also typical multi-scale phenomena. In this paper, certain properties of the fluctuations are examined that are invariant with the change of the time scales. Specifically, the existence of a statistical similarity law is demonstrated in climatic time series and in atmospheric turbulent motions. This is the hierarchical similarity law. Further analyses show that the hierarchical similarity law is a general property of multi-scale fluctuation systems. Therefore, the study on the hierarchical similarity law is important for understanding the inherent universal physical mechanism of complex systems in the atmospheric motions. | SHE Zhensu, FU Zuntao, CHEN Jiong, LIANG Shuang and LIU Shida(1. State Key Laboratory for Studies of Turbulence and Complex Systems, Department of Mechanics and Engineering Sciences, Peking University, Beijing 100871, China 2. School of Physics, Peking University, Beijing 100871, China 3. LAPC, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China) | 2002 | Progress in Natural Science:Materials International2002，12，10： | 3 |
| 2 | Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations 显示文摘 | LIU Shikuo FU Zuntao LIU Shida | 2001 | Physics Letters A2001，289，： | 1 |
| 3 | New transformations and new approah to find exact solutions to nonlinear equations显示文摘 | Fu Zuntao Liu Shikuo Liu Shida | 2002 | Phys Lett A2002，299，： | 1 |
| 4 | New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations显示文摘 | Fu Zuntao Liu Shikuo Liu Shida | 2001 | Phys Lett A2001，290，： | 1 |
| 5 | Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equation显示文摘 | Liu Shikuo Fu Zuntao Liu Shida | 2001 | Phys Lett A2001，289，： | 1 |
| 6 | Jacobi Elliptic Function Expansion Method and Periodic Wave Solutions of Nonlinear Wave Equations显示文摘 | LIU SHIKUO FU ZUNTAO LIU SHIDA | 2001 | Physics Letters A2001，289，： | 1 |
| 7 | The periodic solutions for a class of coupled nonlinear Klein–Gordon equations显示文摘 | Shikuo Liu Zuntao Fu Shida Liu Zhanggui Wang | 2004 | Physics Letters A2004，，5： | 1 |
| 8 | Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations显示文摘 | Shikuo Liu Zuntao Fu Shida Liu Qiang Zhao | 2001 | Physics Letters A2001，，1： | 1 |
| 9 | New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations显示文摘 | Zuntao Fu Shikuo Liu Shida Liu Qiang Zhao | 2001 | Physics Letters A2001，，1： | 1 |
| 10 | Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equation显示文摘 | Liu Shikuo Fu Zuntao Liu Shida | 2001 | Phys Lett A2001，289，： | 1 |
| 11 | New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations显示文摘 | Fu Zuntao Liu Shikuo Liu Shida | 2001 | Phys Lett A2001，290，2： | 1 |
| 12 | New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations显示文摘 | Fu Zuntao Liu Shikuo Liu Shida | 2001 | Phys Lett A2001，290，： | 1 |
| 13 | Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations显示文摘 | Liu Shikuo Fu Zuntao Liu Shida | 2001 | Phys Lett:A2001，，289： | 1 |
| 14 | New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations显示文摘 | Fu Zuntao Liu Shida Liu Shikuo | 2001 | Phys Lett:A2001，，290： | 1 |
| 15 | New Solutions to nlKdV Equation 显示文摘 | Fu Zuntao Liu Shida Liu Shikuo | 2004 | Physics Letters A2004，326，： | 1 |
| 16 | New Kinds of Solutions to Gardner Equation显示文摘 | Fu Zuntao Liu Shida Liu Shikuo | 2004 | Chaos Solitons and Fraetals2004，20，： | 1 |
| 17 | New solutions to mKdV equation显示文摘 | FU Zuntao HU Shida LIU Shikuo | 2004 | Physics Letters A2004，326，： | 1 |
| 18 | Different seal ing behaviors in daily temperature records over China 显示文摘 | YUAN Naiming FU Zuntao MAO Jiangyu | 2010 | Physica A2010，389，19： | 1 |
| 19 | Exact Solutions to Sine-Gordon-Type Equations显示文摘 | Zuntao Fu Shida Liu | 2006 | Physics Letters A2006，351，12： | 1 |
| 20 | The JEFE method and periodic solutions of two kinds of nonlinear wave equations显示文摘 | Fu Zuntao Liu Shikuo Liu Shida Zhao Qiang | 2003 | Communications in Nonlinear Science and Numerical Simulation2003，8，： | 1 |
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