Фазовые портреты пространственных моментов коллимированного волнового пучка в управляемом и свободном режимах
Аннотация
Представлены результаты экспериментального исследования структуры фазовых траекторий энергетического центра коллимированного волнового пучка. Установлено существенное различие фазовых портретов и значений размерности пространства вложения для вертикальных и горизонтальных компонент первого пространственного момента. Рассмотрено качественное отличие фазовых портретов, реализуемых при ламинарных течениях, когерентной турбулентности. Выполнена предварительная оценка спектров времен возврата Пуанкаре. Реконструкция и анализ фазовых портретов для стационарных режимов и фазовых траекторий для нестационарных могут быть положены в основу метода визуального контроля динамических режимов пространственно-временных аберраций пучка и классификации состояний нестационарной и неравновесной атмосферы.
- коллимированный пучок
- турбулентная атмосфера
- фазовый портрет
- карты хаоса
- время возврата Пуанкаре
- коррекция наклона
- collimated beam
- turbulent atmosphere
- phase portrait
- chaos maps
- Poincare return time
- Tilt correction
Abstract (in English)
Phase portraits of spatial moments of a collimated wave beam in controlled and free modes
The results of an experimental study of the structure of phase trajectories of the energy center of a collimated wave beam are presented. A significant difference was found between phase portraits and values of the dimension of the embedded space for the vertical and horizontal components of the first spatial moment. A qualitative difference between phase portraits realized in laminar flows and coherent turbulence is considered. A preliminary estimation of the spectra of the Poincaré return times is performed. The reconstruction and analysis of phase portraits for stationary modes and phase trajectories for non-stationary can be the basis for the method of visual control of the dynamic modes of spatio-temporal beam aberrations and the classification of states of non-stationary and nonequilibrium atmospheres.
Для цитирования
Бланк А.В., Сухарева Н.А. Фазовые портреты пространственных моментов коллимированного волнового пучка в управляемом и свободном режимах // Журнал радиоэлектроники. – 2019. – № 11. https://doi.org/10.30898/1684-1719.2019.11.9
Литература
- Sauer T., Yorke J. A., Casdagli M. Embedology. Statistical Physics. 1991. Vol.65. P. 79�616.
- Ruelle D., Takens F. On the nature of turbulence. Communications in Mathematical Physics. 1971. Vol.20. P.167�192.
- Hasegawa A., Maclennan C., Kodama Y. Nonlinear behavior and turbulence spectra of drift waves and Rossby waves. The Physics of Fluids. 1979. Vol.22. P.2122�2129.
- Takens F. Detecting strange attractors in turbulence. Berlin: Springer, 1981. 381 p.
- Wolf A., Swift J., Swinney H. Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena. 1985. Vol.16. P.285� 317.
- Ruelle D. Strange attractors. The Mathematical Intelligencer. 1980. Vol.2. P.126�137.
- Casdagli M. Nonlinear prediction of chaotic time series. Physica D: Nonlinear Phenomena. 1989. Vol.35. P.335�356.
- Temam R. Navier-Stokes equations and nonlinear functional analysis. Philadelphia: Siam. 1987. 160 p.
- Sagaut P., Cambon C. Homogeneous turbulence dynamics. Berlin: Springer. 2008. 481 p.
- Fraedrich K. Estimating the dimensions of weather and climate attractors. Journal of the Atmospheric Sciences. 1986. Vol.43. P.419�432.
- Hoover W. Canonical dynamics: equilibrium phase-space distributions. Physical Review A. 1985. Vol.31. P.1�3.
- Trahan C., Wyatt R. Evolution of classical and quantum phase-space distributions: A new trajectory approach for phase space hydrodynamics. The Journal of Chemical Physics. 2003. Vol. 19. P. 0177029.
- van der Veen R., Huisman S., Dung O. Exploring the phase space of multiple states in highly turbulent Taylor-Couette flow. Physical Review Fluids. 2016. Vol.1. P.114.
- Berera A., Ho R. Chaotic properties of a turbulent isotropic fluid. Physical Review Letters. 2018. Vol.120. Pp.1-5.
- Lacorata G., Vulpiani A. Chaotic Lagrangian models for turbulent relative dispersion. Physical Review E. 2017. Vol. 95. P.19.
- Hilborn R. Chaos and nonlinear dynamics: an introduction for scientists and engineers. Oxford University Press on Demand, 2000. 654 p.
- Thompson J., Stewart H. Nonlinear dynamics and chaos. NY: John Wiley & Sons, 2002. 458 p.
- Gutman Y., Qiao Y., Szabo G. The embedding problem in topological dynamics and Takens- theorem. Nonlinearity. 2018. Vol. 1. P.1-25.
- Harnack D., Laminski E., Schunemann M. Topological Causality in Dynamical Systems. Physical Review Letters. 2017. Vol. 119. P.1-5.
- Jiang H., He H. State space reconstruction from noisy nonlinear time series: An autoencoder-based approach. Neural Networks (IJCNN). 2017. P.3191-3198.
- Kapranov V.V., Matsak I.S., Blank A.V., et al. Atmospheric turbulence effects on the performance of the laser wireless power transfer system. Free-Space Laser Communication and Atmospheric Propagation XXIX. 2017. Vol.10096. P.1-13.
- Arsenyan T.I., Grebennikov D. Yu., Sukhareva N.A., et al. Reconstruction of phase trajectories of a laser beam propagated through a turbulent medium. Atmospheric and Oceanic Optics. 2014. Vol.27. P.205-210.
- Babanin E.A., Kapranov V.V., Suhareva N.A., et al. Space-temporal stochastic characteristics of complex amplitude for the sounding vector optical beam. 2017 Progress In Electromagnetics Research Symposium-Spring (PIERS). 2017. P.902-908.
- Deyle E. R., Sugihara G. Generalized theorems for nonlinear state space reconstruction. PLoS One. 2011. Vol.6. P.1-8.
- Babanin E. A., Blank A.V., Nasonov A. A., et al. Profile management of astigmatic energy-carrying collimated beam. Proceedings of SPIE - The International Society for Optical Engineering. 2019. P.1-13.
- Noakes L. The Takens embedding theorem. International Journal of Bifurcation and Chaos. 1991. Vol.1. P.867-872.
- Pikulev S., Semenkov V., Chernykh A. Tests of an adaptive optical system on a model atmospheric turbulent path. Optoelectronics, Instrumentation and Data Processing. 2012. Vol.48. P.166-173.
- Tomashevsky A. I., Kapranov M. V. Fractal properties of chaotic dynamical systems in reverse time and its applications. International Conference Physics and Control. 2005. P.443-446.
- Blank A.V., Kapranov V.V., Mikhailov R.V., et al. Non-linear dynamics of positional parameters of the collimated coherent beam at the end of the long atmospheric path. Progress In Electromagnetics Research Symposium - Spring PIERS. 2017. St. Petersburg. P.708-714.
- Matsak I.S., Kapranov V.V., Tugaenko V. Yu. Super narrow beam shaping system for remote power supply at long atmospheric paths. Laser Resonators, Microresonators, and Beam Control XIX. 2017. Vol.10090. P.1-12.
- Klyatskin V. I. Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Coherent Phenomena in Stochastic Dynamic Systems. Berlin: Springer. 2016. 491 p.