Skip to main content
SpringerLink
Log in

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lui, H.: Science and Engineering of Droplets. Noyes, New York (2000)

    Google Scholar 

  2. Govekar, E., Jerič, A., Weigl, M., Schmidt, M.: Laser droplet generation: application to droplet joining. CIRP Ann. 58, 205–208 (2009)

    Article  Google Scholar 

  3. Kokalj, T., Klemenčič, J., Mužič, P., Grabec, I., Govekar, E.: Analysis of the laser droplet formation process. J. Manuf. Sci. Eng. 128, 307–314 (2006)

    Article  Google Scholar 

  4. Krese, B., Perc, M., Govekar, E.: The dynamics of laser droplet generation. Chaos 20, 013129-1-7 (2010)

    Article  Google Scholar 

  5. Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods. Wiley-Interscience, New York (1995)

    Book  MATH  Google Scholar 

  6. Abarbanel, H.D.I.: Analysis of Observed Chaotic Data. Springer, New York (1996)

    Book  MATH  Google Scholar 

  7. Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  8. Kodba, S., Perc, M., Marhl, M.: Detecting chaos from a time series. Eur. J. Phys. 26, 205–215 (2005)

    Article  Google Scholar 

  9. Schreiber, T.: Interdisciplinary application of nonlinear time series methods. Phys. Rep. 308, 1–64 (1999)

    Article  MathSciNet  Google Scholar 

  10. Benko, T.P., Perc, M.: Nonlinearities in mating sounds of American crocodiles. Biosystems 97, 154–159 (2009)

    Article  Google Scholar 

  11. Benko, T.P., Perc, M.: Singing of Neoconocephalus robustus as an example of deterministic chaos in insects. J. Biosci. 32, 797–804 (2007)

    Article  Google Scholar 

  12. Benko, T.P., Perc, M.: Deterministic chaos in sounds of Asian cicadas. J. Biol. Syst. 14, 555–566 (2006)

    Article  MATH  Google Scholar 

  13. Perc, M.: Nonlinear time series analysis of the human electrocardiogram. Eur. J. Phys. 26, 757–768 (2005)

    Article  MathSciNet  Google Scholar 

  14. Perc, M.: The dynamics of human gait. Eur. J. Phys. 26, 525–534 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gradišek, J., Govekar, E., Grabec, I.: Using coarse-grained entropy rate to detect chatter in cutting. J. Sound Vib. 214, 941–952 (1998)

    Article  Google Scholar 

  16. Litak, G., Sen, A.K., Syta, A.: Intermittent and chaotic vibrations in a regenerative cutting process. Chaos Solitons Fractals 41, 2115–2122 (2009)

    Article  Google Scholar 

  17. Gottwald, G.A., Melbourne, I.: A new test for chaos in deterministic systems. Proc. R. Soc. Lond. A 460, 603–611 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. Schreiber, T.: Detecting and analysing nonstationarity in a time series with nonlinear cross-predictions. Phys. Rev. Lett. 78, 843–846 (1997)

    Article  Google Scholar 

  19. Kaplan, D.T., Glass, L.: Direct test for determinism in a time series. Phys. Rev. Lett. 68, 427–430 (1992)

    Article  Google Scholar 

  20. Falconer, I., Gottwald, G.A., Melbourne, I., Wormnes, K.: Application of the 0–1 test for chaos to experimental data. SIAM J. Appl. Dyn. Syst. 6, 395–402 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gottwald, G.A., Melbourne, I.: On the implementation of the 0–1 test for chaos. SIAM J. Appl. Dyn. Syst. 8, 129–145 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Krese, B., Perc, M., Govekar, E.: Experimental observation of a chaos-to-chaos transition in laser droplet generation. Int. J. Bifurc. Chaos (in press). doi:10.1142/S0218127411029367

  23. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  24. Eckmann, J.-P., Kamphorst, S.O., Ruelle, D., Ciliberto, S.: Liapunov exponents from time series. Phys. Rev. A 34, 4971–4979 (1986)

    Article  MathSciNet  Google Scholar 

  25. Fraser, A.M., Swinney, H.L.: Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33, 1134–1140 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  26. Kennel, M.B., Brown, R., Abarbanel, H.D.I.: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403–3411 (1992)

    Article  Google Scholar 

  27. Gottwald, G.A., Melbourne, I.: Testing for chaos in deterministic systems with noise. Physica D 212, 100–110 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Gottwald, G.A., Melbourne, I.: On the validity of the 0–1 test for chaos. Nonlinearity 22, 1367–1382 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Litak, G., Syta, A., Wiercigroch, M.: Identification of chaos in a cutting process by the 0–1 test. Chaos Solitons Fractals 40, 2095–2101 (2009)

    Article  Google Scholar 

  30. Syta, A., Litak, G.: Stochastic description of the deterministic Ricker’s population model. Chaos Solitons Fractals 37, 262–268 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Synergetics, Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva cesta 6, 1000, Ljubljana, Slovenia

    Blaž Krese & Edvard Govekar

Authors
  1. Blaž Krese
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edvard Govekar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Blaž Krese.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krese, B., Govekar, E. Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos. Nonlinear Dyn 67, 2101–2109 (2012). https://doi.org/10.1007/s11071-011-0132-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-0132-1

Keywords

Search

Navigation