We also leave out the error term stemming from the approximation N u)/ n u)≈1.
To this end, we solved the advection-diffusion Eq. (8) and supplemented (24) with the term stemming from the Boussinesq approximation.
In order to exclude any error stemming from the linear approximation, we tested the control abilities of the pathway designs and observed the chemotactic behaviors by our program based on the original differential equations (Fig. 5).
The difference stems from the approximations made during the derivation of Pfa.
Stemming from a one-dimensional approach and thanks to a compact notation for the a priori kinematic field approximation over the beam cross-section, the model derivation is made general regardless the approximation order.
We refrain from plotting the recovered output ŷ (t, θ est ) as it is visually indiscriminable from the output in the left of Figure 4. Interestingly, the optimization target value J(θ est ) = 3329.56 implies J(θ est ) < J(θ ref ), which may stem from a slight approximation error in the reduced model or from the effects of the measurement noise.
There is a small difference, and the reason stems from all the approximations previously made: carriers are not orthogonal (Section 2.3), the embedding distortion is not exact (21), and projections in the secret subspace are modeled (24).
The approximations stem from application of standard central difference formulas to split forms of the convective terms in the compressible Euler equations, which guarantee strong numerical stability and (near) energy preservation in the inviscid limit.
The DFT-1/2 method stems from Slater's proposal of an approximation for the excitation energy, a transition state method24,25, to reduce the band gap inaccuracy by introducing a half-electron/half-hole occupation.
This figure also reveals that the difference between the original and the synthesized speech spectra mainly stems from the inaccuracy of the dual-band approximation of the LPC excitation, as compared to the effect of the LSF quantization.
The micromechanical approach stems from Eshelby's equivalent inclusion method and Mori Tanaka's mean-field approximation, and the macromechanical approach is based on the classical laminated plate theory.
