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The concept of fractal experiments: New possibilities in quantitative description of quasi-reproducible measurements

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  • Nigmatullin, R.R.
  • Evdokimov, Yu.K.

Abstract

In this paper the authors suggest a new conception of the so-called fractal (self-similar) experiment. Under the fractal experiment (FE) one can imply a cycle of measurements that are subjected by the scaling transformations F(z)→F(zξm) in contrast with conventional scheme F(z)→F(z+mT) (m=0,1,…, M–1), where z defines the controllable (input) variable and can be associated with time, complex frequency, wavelength and etc., T – mean period of time between successive measurements and m defines a number of successive measurements. One can connect a fractal experiment with specific memory effect that arises between successive measurements. The general theory of experiment for quasi-periodic measurements proposed in [1] after some transformations can be applied for the set of the FE, as well. But attentive analysis shown in this paper allows generalizing the previous results for the case when the influence of uncontrollable factors becomes significant. The theory developed for this case allows to consider more real cases when the influence of dynamic (unstable) processes taking place during the cycle of measurements corresponding to some FE is becoming essential. These experiments we define as quasi-reproducible (QR) fractal experiments.

Suggested Citation

  • Nigmatullin, R.R. & Evdokimov, Yu.K., 2016. "The concept of fractal experiments: New possibilities in quantitative description of quasi-reproducible measurements," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 319-328.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:319-328
    DOI: 10.1016/j.chaos.2016.06.014
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    References listed on IDEAS

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    1. Hilfer, R., 1995. "An extension of the dynamical foundation for the statistical equilibrium concept," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 89-96.
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    Cited by:

    1. Nigmatullin, Raoul & Sarkar, Samyadip & Biswas, Karabi, 2021. "New class of fractal elements with log-periodic corrections: Confirmation on experimental data," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Nigmatullin, R.R. & Budnikov, H.C. & Sidelnikov, A.V., 2018. "Mesoscopic theory of percolation currents associated with quantitative description of VAGs: Confirmation on real data," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 171-183.

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