The depth term is expressed as follows.
The spurious currents source term is expressed from the vorticity equation and used to discuss and compare the methods.
The acoustic source term is expressed simply by the integral of the product between the mean heat release rate and the acoustic energy.
For a 3D ellipsoidal crack model, this first-order term is expressed as a simple integral thanks to the Cauchy residue theorem.
It can be seen from Eqs. (25) and (26) that each term is expressed as an inverse Fourier transform of a particular matrix in the wavenumber domain.
The P-to-S single-scattering term is expressed as: (A.5) Here, the assumption of Eq. (17) is necessary to take exp -ηt) out of thexp -ηtral.
This term is expressed as the product of an instability enhanced burning rate factor, Pbi, and the mean volumetric heat release rate in an unstretched laminar flamelet of the mixture.
The P-to-P single-scattering term is expressed as: (18) This single-scattering term is equal to the scalar wave case with -wave velocity (e.g. Sato, 1993).
for x ∈ [1, W], y ∈ [2, H], where the vertical disparity penalty term is expressed as, {C}_{mathrm{smooth}}^{d_v}left left( x, yright), dright)=left|{d}_{max }- arg underset{d}{ min }{C}_{mathrm{smooth}}^vleft left( x, y-1right), dright)right|.
The coefficient C n ∈ R associated with the (2n+1 th order term is expressed as [19] C n = 1 ( n + 1 ) P in ∫ 0 ∞ p ( r ) G ( r ) r P in L n ( 1 ) r 2 P in dr 2, (12).
For example, the relative improvement over a nuGTR model conferred by the CG ⇔ TG term is expressed as LR CG ⇔ TG /LR diGTR), where the ratio is between models belonging to the same model form.
