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The adopted smoothing techniques working in time, frequency and time-frequency domain are the Savitzky-Golay filter modeled by third-order polynomial, the Fourier Transform and two types of Wavelet Transform (Mexican hat and Morlet).
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The relaxation characteristics of these thermodynamic fluxes, which are a symbol of nonequilibrium characteristics, are modeled by first-order relaxation equations.
In particular, a 1D mathematical model is presented for tubular reactors considering a cylindrical symmetry, which is modeled by first- or second-order differential equations depending on the importance played by the axial diffusion.
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