Sentence examples for analytical transformations from inspiring English sources
Analytical transformations are developed and applied to the outer subdomain coordinate system in order to match the inner and outer grids along the domain interface and to properly address the outflow boundary conditions using a regularly spaced grid.
It is showed that with the help of the small parameter method it is possible to obtain the expression for the transverse normal strain in a form, which is convenient for analytical transformations.
On the basis of an analytical transformation model, the transformed fraction has been evaluated for isothermal and isochronal solid-state transformations.
The corresponding compensator can be directly calculated and thus efficiently implemented from the model by analytical transformation laws.
This is due to the inability to get the relationship β(p), i.e., make analytical transformation which is an inverse with respect to β(p).
This approach of analytical transformation has fully restored the BEM's distinctive notion that only the boundary needs to be discretized.
The goal of TPA is to "create decision advantage in support of natural decision making through a process of analytical transformation that integrates psychosocial and physical models by leveraging insights from both the social and natural sciences" [6].
An evaluation of the maximum in the transformation rate of a solid-state transformation is given for isothermal and isochronal transformations, on the basis of a general, flexible, analytical transformation model incorporating different combinations of nucleation, growth and impingement modes.
In the present work, the "additivity rule" was proved to be compatible with an analytical transformation model assuming mixed nucleation (with site saturation and continuous nucleation as two extremes), for some specified conditions.
This observation led researchers to postulate the extension of this methodology to bridge sections, based on the analytical transformation of aeroelastic derivatives into time-dependent functions, to be used in step-by-step finite-element or equivalent simulations.
In this paper, the exact, analytical transformation of the volume integral associated with thermal effects to surface ones is achieved for a transversely isotropic material using a similar approach which the authors have previously employed for the same task in BEM for 2D general anisotropy.
