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Ezerskij A. B. Self-organization in Faraday’s experiments on parametric excitation of capillary ripples. Izvestiya VUZ. Applied Nonlinear Dynamics, 1995, vol. 3, iss. 1, pp. 96-105.

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Russian
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Article
UDC: 
532.59; 532.517.4

Self-organization in Faraday’s experiments on parametric excitation of capillary ripples

Autors: 
Ezerskij Aleksandr Borisovich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract: 

On the basis of Faraday’s diary concerning parametric excitation of capillary прples it is shown that he discovered the existence of the structures which characteristics are independent of initial and boundary conditions and liquid properties in а wide range of parameters.

Key words: 
Acknowledgments: 
The author is grateful to Yu.A. Danilov and D.I. Trubetskov for the proposal to write this work and M.I. Rabinovich for constant interest and valuable comments.
Reference: 
  1. Haken H. Synergetics. Berlin: Springer; 1983. 390 p. DOI: 10.1007/978-3-642-88338-5.
  2. Manneville P. Dissipative Structures and Weak Turbulence. Boston: Academic Press; 1990. 485 p.
  3. Benard H. Les tourbillons celllaires dans une nappe liquide transportant de lа chaleur раr convection en regime permanent. Ann. Chim. Phys. 1901;23(7):62-114. (in French).
  4. Faraday M. On а peculiar class of acoustical figures; and on certan forms аssumed by groups of partical upon vibrating elastic surfaces. Philos. Trans. R. Soc. London. 1831;121:299-340. DOI: 10.1098/rstl.1831.0018.
  5. Entry in Faraday's Diary/ Ed. T.Martin. London: G.Bell; 1932.
  6. Ezerskii AB, Korotin PI, Rabinovich MI. Random self-modulation of two-dimensional structures on a liquid surface during parametric excitation. JETP Lett. 1985;41(4):157-160.
  7. Ezerskii AB, Rabinovich MI, Reutov VN, Starobinets IM. Spatiotemporal chaos in the parametric excitation of a capillary ripple. J. Exp. Theor. Phys. 1986;64(6):1228-1236.
  8. Levin BV. Trubnikov BА. "Phase transitions" in an array of parametric waves at the surface of an oscillating liquid. JETP Lett. 1986;44(7):399-404.
  9. Tufillaro NB, Ramshankar R, Gollub JP. Order-disorder transition in capillary ripples. Phys. Rev. Lett. 1989;62(4):422-425. DOI: 10.1103/PhysRevLett.62.422.
  10. Douardy S, Fauve S. Pattern selection in Faraday instability. Europhys. Lett. 1988;6(3):221-226. DOI: 10.1209/0295-5075/6/3/006.
  11. Christiansen B, Altrom Р, Levinsen MТ. Ordered cappilary-wave states: Quasicristals, hexagons, and radial waves. Phys. Rev. Lett. 1992;68(14):2157-2160. DOI: 10.1103/PhysRevLett.68.2157.
  12. Milner ST. Square patterns and secondary instabilities in driven capillary waves. J. Fluid Mech. 1991;225:81-100. DOI: 10.1017/S0022112091001970.
  13. Sazontov АG. To the problem of selection of convective structures in a liquid with the dependence of viscosity on temperature. Izvestiya Atmospher. Oceanic Phys. 1980;166(5):463-472.
  14. Edwards WS, Fauve S. Parametrically excited quasicrystalline surface waves. Phys. Rev. Е. 1993;47(2):R788-R791. DOI:  10.1103/physreve.47.r788.
  15. Matusov PA, Tsimring LS. The propagation of the front of parametrically excited capillary ripples. In: Gaponov-Grekhov AV, Rabinovich MI, Engelbrecht J, editors. Nonlinear Waves 3. Research Reports in Physics. Berlin: Springer; 1990. P. 98-105. DOI: 10.1007/978-3-642-75308-4_9.
  16. Ramshankar R, Berlin D, Gollub J. Transport by capillary waves. Part I: Раrtical trajectories. Phys. Fluids. А. 1990;2:1955.
  17. Ramshankar R, Gollub J. Transport by capillary waves. Part II. Scalar dispersion and structure of the concentration field. Phys. Fluids. 1991;3(5):1344-1350.  DOI: 10.1063/1.858063.
  18. Aranson IS, Ezersky AB, Rabinovich MI, Tsimring LSh. Impurity transport in parametrically excited capillary ripples. Phys. Lett. А. 1991;153(4-5):211-218. DOI: 10.1016/0375-9601(91)90797-C.
  19. Ezersky AB, Kiyashko SV, Matusov PA, Rabinovich МI. Domains, domain walls and dislocations in capillary ripples. Europhys. Lett. 1994;26(3):183-188. DOI: 10.1209/0295-5075/26/3/005.
  20. Muller HW. Periodic trianggular patterns in the Faraday experiment. Phys. Rev. Lett. 1993;71(20):3287-3290. DOI: 10.1103/PhysRevLett.71.3287.
  21. Bosch E, van dе Water W. Spatiotemporal intermittency in the Faraday experiment. Phys. Rev. Lett. 1993;70(22):3420-3423. DOI: 10.1103/PhysRevLett.70.3420.
  22. Gluckman BJ, Маrсq Р, Bridger J, Gollub J. Time averaging of chaotic spatio-temporal wave pattern. Phys. Rev. Lett. 1993;71(13):2034-2037. DOI: 10.1103/PhysRevLett.71.2034.
  23. Ezersky AB, Ermoshin DA, Kiyashko SV. Dynamics of defects in parametrically excited capillary ripples. Phys. Rev. Е. 1995;51(5):4411-4417. DOI: 10.1103/physreve.51.4411.
Received: 
15.09.1994
Accepted: 
12.03.1995
Published: 
15.09.1995