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Experimental evidence for microscopic chaos

Author

Listed:
  • P. Gaspard

    (Université Libre de Bruxelles)

  • M. E. Briggs

    (University of Utah)

  • M. K. Francis

    (University of Maryland)

  • J. V. Sengers

    (University of Maryland)

  • R. W. Gammon

    (University of Maryland)

  • J. R. Dorfman

    (University of Maryland)

  • R. V. Calabrese

    (University of Maryland)

Abstract

Many macroscopic dynamical phenomena, for example in hydrodynamics and oscillatory chemical reactions, have been observed to display erratic or random time evolution, in spite of the deterministic character of their dynamics—a phenomenon known as macroscopic chaos1,2,3,4,5. On the other hand, it has been long supposed that the existence of chaotic behaviour in the microscopic motions of atoms and molecules in fluids or solids is responsible for their equilibrium and non-equilibrium properties. But this hypothesis of microscopic chaos has never been verified experimentally. Chaotic behaviour of a system is characterized by the existence of positive Lyapunov exponents, which determine the rate of exponential separation of very close trajectories in the phase space of the system6. Positive Lyapunov exponents indicate that the microscopic dynamics of the system are very sensitive to its initial state, which, in turn, indicates that the dynamics are chaotic; a small change in initial conditions will lead to a large change in the microscopic motion. Here we report direct experimental evidence for microscopic chaos in fluid systems, obtained by the observation of brownian motion of a colloidal particle suspended in water. We find a positive lower bound on the sum of positive Lyapunov exponents of the system composed of the brownian particle and the surrounding fluid.

Suggested Citation

  • P. Gaspard & M. E. Briggs & M. K. Francis & J. V. Sengers & R. W. Gammon & J. R. Dorfman & R. V. Calabrese, 1998. "Experimental evidence for microscopic chaos," Nature, Nature, vol. 394(6696), pages 865-868, August.
    • Handle: RePEc:nat:nature:v:394:y:1998:i:6696:d:10.1038_29721
    DOI: 10.1038/29721
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    Cited by:

    1. Litak, G. & Syta, A. & Budhraja, M. & Saha, L.M., 2009. "Detection of the chaotic behaviour of a bouncing ball by the 0–1 test," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1511-1517.
    2. Syta, Arkadiusz & Litak, Grzegorz, 2008. "Stochastic description of the deterministic Ricker’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 262-268.
    3. Bildirici, Melike E. & Sonustun, Bahri, 2021. "Chaotic behavior in gold, silver, copper and bitcoin prices," Resources Policy, Elsevier, vol. 74(C).
    4. Francisco Javier Martín-Pasquín & Alexander N. Pisarchik, 2021. "Brownian Behavior in Coupled Chaotic Oscillators," Mathematics, MDPI, vol. 9(19), pages 1-14, October.
    5. Liao, Shijun, 2013. "On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 1-12.
    6. Ning Cui & Junhong Li, 2018. "Dynamic Analysis of a Particle Motion System," Mathematics, MDPI, vol. 7(1), pages 1-14, December.
    7. C. A. Tapia Cortez & J. Coulton & C. Sammut & S. Saydam, 2018. "Determining the chaotic behaviour of copper prices in the long-term using annual price data," Palgrave Communications, Palgrave Macmillan, vol. 4(1), pages 1-13, December.
    8. Litak, Grzegorz & Syta, Arkadiusz & Wiercigroch, Marian, 2009. "Identification of chaos in a cutting process by the 0–1 test," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2095-2101.
    9. Saša Nježić & Jasna Radulović & Fatima Živić & Ana Mirić & Živana Jovanović Pešić & Mina Vasković Jovanović & Nenad Grujović, 2022. "Chaotic Model of Brownian Motion in Relation to Drug Delivery Systems Using Ferromagnetic Particles," Mathematics, MDPI, vol. 10(24), pages 1-19, December.

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