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

R.R. Nigmatullin and Yu.K. Evdokimov

Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 319-328

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.

Keywords: Fractal experiments; Intermediate model; The generalized prony spectrum; Quasi-reproducible measurements (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:91:y:2016:i:c:p:319-328

DOI: 10.1016/j.chaos.2016.06.014

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