| Project/Area Number |
60460033
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
固体物性
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| Research Institution | Okayama University |
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Principal Investigator |
YAMAZAKI Hitoshi Okayama University, Faculty of Science; Assistant Professor, 理学部, 助教授 (40013495)
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| Co-Investigator(Kenkyū-buntansha) |
TANAKA Motoyuki Okayama University, Faculty of Science; Assistant Professor, 理学部, 助教授 (80032803)
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| Project Period (FY) |
1985 – 1986
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| Project Status |
Completed (Fiscal Year 1986)
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| Budget Amount *help |
¥7,000,000 (Direct Cost: ¥7,000,000)
Fiscal Year 1986: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1985: ¥6,400,000 (Direct Cost: ¥6,400,000)
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| Keywords | Chaos / Strange Attractor / Spin Waves / Magnon / Parallel Pumping / ストレンジアトラクタ |
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| Research Abstract |
Parallel pumping experiments in ferromagnetic <(CH_3NH_3)_2> <CuCl_4> (MACC) and yttrium-iron-garnet(YIG) are studied at the pumping frequencies of 9 GHz band and the Helium temperatures. Above the spin-wave instability threshold, auto-oscillations of magnon amplitude with a frequency of 1-100 kHz are detected. Amplitude modulated microwave reflected from magnetic crystals is detected by a tunnel diode which offers fast frequency response and recorded in computer files through a digital memory and a signal analyzer. As the pumping power is increased, period-doubling, chaos and periodic windows are observed.
Phase portraits in three-dimensional phase space are constructed from experimental time series data of chaotic oscillations by means of time delay method. Definite one-dimensional return maps are obtained. The Poincare sections of the phase space trajectories are two-dimensional sheet-like and exhibit the stretching and holding effect which are characteristics of a strange attractor. By using empirical return maps Lyapunov exponents are obtained as 0.43 for MACC and 0.34 for YIG. A positive Lyapunov exponent indicates the average rate of exponential divergence of nearby trajectories within the attractor and it causes sensitive dependence on initial conditions and therefore chaotic behavior. Infinitely repeated stretching and folding with the evolution of trajectories causes a fractal structure to the strange attractor. Fractal dimension of strange attractors are calculated by the method of correlation integral as 2.3 for MACC and 2.0 for YIG. Other chaotic characteristics such as power spectra, Kolmogorov entropy and invariant measure are also studied.
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