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Recovering deterministic behavior from experimental time series in mixing reactor
Author(s) -
Letellier C.,
Sceller L. Le,
Gouesbet G.,
Lusseyran F.,
Kemoun A.,
Izrar B.
Publication year - 1997
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690430906
Subject(s) - mixing (physics) , phase space , vector field , impeller , nonlinear system , series (stratigraphy) , mathematics , ordinary differential equation , statistical physics , dynamical systems theory , field (mathematics) , mathematical analysis , dynamical system (definition) , correlation dimension , dimension (graph theory) , motion (physics) , velocity vector , rotation (mathematics) , classical mechanics , differential equation , physics , mechanics , thermodynamics , geometry , pure mathematics , paleontology , fractal dimension , quantum mechanics , biology , fractal
The velocity field in a standard mixing reactor with a Rushton impeller is analyzed by using techniques from the theory of nonlinear dynamical systems. It is shown that the dynamical behavior contains a quasi‐periodic motion with three frequencies, f p , the frequency associated with the rotation of blades, f p /6, and a third frequency f'. Relying on an evaluation of the correlation dimension equal to 3.9, the phase space is likely to be at least four‐dimensional. Moreover, a set of four ordinary differential equations is indeed automatically obtained by using a global vector field reconstruction technique, confirming the existence of a 4–D‐deterministic behavior contributing to the dynamics of the system.