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SST turbulence model is used with extra source terms introduced to account for the interaction between the bubbles and the liquid.
The exact solution for the problem is obtained using improved Fourier series method, in which each of three displacements of the shell is represented by a Fourier series supplemented by several terms introduced to ensure and accelerate the convergence of the series expansions.
And each of beam displacements, regardless of boundary conditions, is expanded as a modified Fourier series composed of a standard cosine Fourier series and certain supplementary terms introduced to remove the potential discontinuities at the ends, thus ensure and accelerate the convergence of the series representation.
A two-fluid enhanced k ɛ model has been used, with the extra source terms introduced to account for the interaction between the bubbles and the liquid and transient calculations have been performed to study the plume growth, the acceleration of the liquid due to viscous drag, and the approach to steady-state conditions.
The pace of change can also further obscure the clarity in understanding the existing terms introduced to teachers.
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(And motherhood: Sarah Palin notwithstanding, "soccer moms" — a term introduced to the political world in 1996, by a Republican consultant — are the proverbial key demographic).
The 2003 Si/O functional form was further augmented by a three-body conjugation term introduced to handle −NO2 group chemistry in nitramines, where a triple-bond stabilisation term was added to improve the description of terminal triple bonds.
Dimensionless terms were introduced to recognize the effect of design parameters on the tools performance.
Non-smooth regularization terms are introduced to tradeoff network performance with sparsity of the feedback-gain matrix.
In particular, spectral vanishing viscosity terms are introduced to stabilize short wavelengths inconsistent with the long wavelength approximation of the two-fluid model.
Coder decoder procedures are proposed for both continuous and discrete singular systems, in which compensation terms are introduced to meet the compatible requirement.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com