教員紹介 複雑系知能学科

ヴラジミール・リアボフ   （教授）

Vladimir B. Riabov

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■所属学科：

複雑系知能学科

■専門分野：

電波物理学、非線形科学

■担当科目：

複雑系基礎セミナー、ファジー論理と制御、ウェブレット解析学、複雑系科 学応用、複雑系科学演習Ⅰ、複雑系科学演習Ⅱほか

プロフィール

Nonlinear dynamics, statistical methods, chaos and bifurcations, nonlinear oscillators, fractal dimension analysis, signal processing and applications of chaos theory in geophysics and astrophysics.

・最終学歴：ハリコフ州立大学
・学位　　：博士(物理学、数学)
・前歴　　：日本学術振興会　外国人特別研究員
・着任時期：2000年4月1日

仕事の紹介

1. Weakly nonlinear systems.
　Deterministic chaos is a common phenomenon in nonlinear systems. The motion described by three or more equations ( >1.5 degrees of freedom) may become very complex, if the degree of the nonlinearity is high enough. It is, however, not easy to predict "how much" nonlinearity is necessary for chaotic behavior, as well as what parameter values lead to other complicated nonlinear regimes like quasiperiodic motion or hysteresis. On the other hand, the problem of predicting the parameters bringing complex regimes (control) is of signi ficant importance for numerous real world application, even if nonlinearity is a small effect or chaos is an unexpected behavior. An illustrative example can be a simple pendulum, which is linear when oscillating at a small amplitude and becomes a nonlinear system when it reaches the vicinity of the upper equilibrium position. Other examples of nonlinear systems, like wave transformation on a sea surface, nonlinear coupling of optical or microwave modes in resonators, electromagnetic wave interaction with charged particles, also at the focus of many research works. Some of the questions I am trying to answer in my research are:

- what are the basic mechanisms and conditions for the appearance of chaos in nonlinear dynamical systems?
- what is the role of resonances in the complexity of motion?
- how to predict the chaos onset in nonlinear systems by using theoretical methods, like, for example,  averaging method or Melnikov theory?

2. Signal processing.
The discovery of the phenomenon of deterministic chaos resulted in the revision of the notions of "noise" and "order" in physics. It turned out that deterministic chaos, being partially ordered, occupies an intermediate position between regular and irregular states. The regularity of chaos consists in the presence of well defined self-similar (or fractal) structures in the areas of the phase space occupied by chaotic motions. Those structures can be detected experimentally by specially designed methods and algorithms based on the Takens embedding theorem, correlation dimension and wavelet analysis. The question of whether a given experimental time series is of deterministically chaotic or random origin is of fundamental importance for designing a mathematical model for the phenomenon under study. In this area of research I have been working on the development of new methods of signal processing and their application to the mathematical modeling in astrophysics and geophysics.

3. Secure communication and synchronization of chaos.
It has been recently found out that chaotic systems, being connected in arrays, or, in other words, coupled, can demonstrate collective or synchronized behavior. This means that, being considered separately, the parts of the whole system behave chaotically, but, at the same time, all the parts move synchronously, when the coupling between the elements is sufficient. This phenomenon can be used for designing secure communication circuits, when the information signal is mixed with a chaotic carrier in the transmitter, and can be successfully decoded in the receiver. I am interested in designing secure communication algorithms and systems based on the phenomenon of synchronization and so called "inverse system" approach.

4. Sporadic radio emissions from Jupiter (S-bursts) and exoplanets search
An interesting example of a real system with very complex behavior is planet Jupiter. It is a source of powerful radio bursts, originating from its strong magnetic field and charged particles provided by its satellite Io. In fact, Jupiter-Io system is a big electric machine producing huge electric currents in the space, and it is an excellent demonstration of the law of electromagnetic induction by Faraday. As there is no wires between Io and Jupiter, the electrical currents flow along the Jovian magnetic field lines producing a strong radio emission. These radio waves can be detected at Earth via radio telescopes and analyzed by various methods to give valuable information about the physics of planetary magnetospheres, plasma processes, radio waves interaction with the medium, etc. I am particularly interested in ultra fast processes in Jovian magnetosphere (typical time scales 1-100 milliseconds), that are called S-bursts, and in the development of signal processing methods for the search of planets around distant stars (see below).
Are we alone in the Universe? Is our Solar system unique? How the life appeared on the Earth? To find answers to these questions, it is necessary first to find out are there planets around other stars. The understanding of the basic properties of Jovian radio emission and its generation mechanisms can be used for this purpose of detecting planetary systems. Although the assumption that many stars have planets rotating around them seems quite natural, it is still very difficult to prove it experimentally. The main difficulty in the problem of direct detection is that the planets do not emit light and can not be easily observed from the Earth, being undistinguishable on the background of the mother star. However, if some distant star possesses a planet similar to Jupiter, it can be detected from the ground by its radio emission, which can be even stronger than the emission from the star. Such an exoplanet search program will start in 2000 in the framework of the international collaborative European project "Radio Search for Magnetized Extrasolar Planets".

5. Seismology
I am interested in applying the theory of nonlinear oscillations and chaos to modeling earthquakes. It seems that in some cases the earthquakes can originate from stick-slip motions of tectonic plates at their interface. Those motions have much in common with the phenomena demonstrated by any two surfaces experiencing friction from each other. Squeaking door or playing fiddle are well-known examples of stick-slip processes, when the system demonstrates alternating states of "stick" and "slip". Although the typical time scales in the case of earthquakes are quite different from the examples mentioned above (50-100 years for big earthquakes vs. 0.1-10 milliseconds for squeaking sounds), the mathematical forma lism used for the description of all these phenomena may be similar.

6. Radars and remote sensing
Oil spills on the sea surface create a serious environmental problem. Now it is clear that the most effective way of the detection of oil films is through special type of microwave radars and radiometers. Their application allows a fast scan of large areas from aircraft. Basically, the detection of the spills consists in the analysis of reflectivity charts. An oil film reduces the reflectivity coefficient of the water surface that is readily detected by the analysis of the energy characteristics of the backscattered radio emission. In the analysis of reflected signals spectral methods are usually used. However, these techniques do not always give an effective solution to the detection problem, mainly because of the following reasons. First, it is necessary to analyze and compare spectral components at widely separated frequencies. Second, nonlinear effects play a crucial role in the arising of wind excited waves on the sea surface. We suggest to use the new techniques of signal processing based on the fractal description of all scales on the surface and to exploit wavelet transformation of the reflected Doppler signals to discriminate effectively between different water wave scales. A new airborne mm-waveband radar system for oil-spill detection on a seasurface has been recently created and tested in Kharkov, Ukraine. The implemented design combines up-to-date developments in the fields of microwave components, compact oscillators (magnetrons), antenna systems (dielectric waveguide - diffraction grating), mm-band receivers, real-time digital signal processing (DSP) computer boards, with recent advances in the basic studies of electromagnetic waves propagation and diffraction on a sea surface, and novel methods of signal analysis utilizing the concepts of fractals and wavelets.

最近の著作

1. S. Hess, P. Zarka, F. Mottez, V.B. Ryabov (2009), Electric potential jumps in the Io-Jupiter flux tube. Planetary and Space Science, Vol.57, 23-33.
2. D. Nerukh, V.B. Ryabov, and R.C. Glen (2008), Complex temporal patterns in molecular dynamics: a direct measure of the phase space exploration by the trajectory at macroscopic time scales, Phys. Rev. E 77, 036225 (1-11).
3. Ryabov, V. B., B. P. Ryabov, D. M. Vavriv, P. Zarka, R. Kozhin, V. V. Vinogradov, and V. A. Shevchenko (2007), Jupiter S-bursts: Narrow-band origin of microsecond subpulses, J. Geophys. Res., 112, A09206, doi:10.1029/2007JA012607 (1-20).
4. T. Moriyama, V. Ryabov, and M. Migita (2005), The ability to express multiple-choice behavior in pill bugs. Cognitive Studies, Vol. 12(3), 188-206.
5. V.B. Ryabov, P. Zarka, and B.P. Ryabov (2004), Search of exoplanetary radio signals in the presence of strong interference: Enhancing sensitivity by data accumulation. Planetary and Space Science, Vol.52, 1479-1491.
6. V.B. Riabov (2004), Stability of Microwave and Electronic Devices: an Approach from Dynamical Systems Theory. Automatika, V. 45, No.1-2, p. 19-22.
7. V.B. Ryabov, A.M. Correig, M. Urquizu, and A. A. Zaikin (2003), Microseism oscillations: From deterministic to noise driven models. Chaos, Solitons and Fractals V.16, No.2, p.195-210.
8. V. B. Ryabov (2002), Using Lyapunov Exponents to Predict the Onset of Chaos in Nonlinear Oscillators, Phys. Rev. E, V. 66, 016214 (1–17).
9. V. B. Ryabov, K. Ito (2001), Intermittent Phase Transitions in a Slider-Block Model as a Mechanism for Earthquakes, Pure and Applied Geophysics, V. 158, No.5-6, p.919-930.
10. P. Zarka, R. A. Treumann, B. P. Ryabov, V.B.Ryabov (2001), Magnetically-Driven Planetary Radio Emissions and Application to Extrasolar Planets, Astrophysics and Space Science, V. 277, No. 1-2. p. 293-300.
11. V. B. Ryabov, P.V. Usik, and D.M. Vavriv. Chaotic masking without synchronization, International Journal of Bifurcations and Chaos, Vol. 9, No. 6, pp.1181-1187 (1999).
12. V.B. Ryabov, A.V. Stepanov, P.V. Usik, D.M. Vavriv, V.V. Vinogradov, Yu. A. Yurovsky, From chaotic to 1/f processes in solar mcw-bursts, Astronomy & Astrophysics, 324, P.750-762 (1997). 
13. D.M. Vavriv, V.B. Ryabov, S.A. Sharapov, and H.M. Ito, Chaotic states of weakly and strongly nonlinear oscillators with quasiperiodic excitation, Phys. Rev. E, 53, No.1, P.103-114 (1996). 
14. V.B.Ryabov, and H.M.Ito, Multistability and chaos in a spring-block model, Phys. Rev. E, 52, No.6, P.6101-6112 (1995). 
15.  P. Zarka, J. Queinnec, B.P. Ryabov, V.B. Ryabov, V.A. Shevchenko, A.V. Arkhipov, H.O. Rucker, L. Denis, A. Gerbault, P. Dierich, C. Rosolen, Ground-based high sensitivity radio astronomy at decameter wavelengths, in "Planetary Radio Emissions IV", edited by H.O. Rucker et al., Austrian Acad. Sci. Press, Vienna (1997).