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Using the explicit extrapolation formula, the transient response of interfacial cracks in piezoelectric bi-materials under electro-mechanical impacts is studied by time-domain BEM together with a sub-domain technique.
A variational formulation of the Navier Stokes equations is adopted using a fractional-step time discretization with the classical second-order backward difference scheme combined with explicit extrapolation of the nonlinear term.
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However, the guide provides no explicit criteria for extrapolation.
While there is no explicit standard for extrapolation beyond the observation [ 18], this model showed an extreme goodness of fit, validated by observational data [ 17].
Moreover, uncertainties related to very small magnitudes of effect and/or very small incidences in the population can be made explicit and transparent (see Supplemental Material, "Extrapolation to magnitudes of effect below a critical effect size" and "Extrapolation to very low incidences").
In this paper, a universal matrix-form displacement extrapolation formula and the explicit form are derived to determine the dynamic intensity factors of an interface crack in general anisotropic piezoelectric bi-materials.
The method is based on extrapolation of the two-step explicit midpoint rule and incorporates adaptive time step and order selection.
Using whole brain and region of interest (ROI) analyses, we compared the brain activity evoked by these VSE tasks to similar control judgements or eye movements made to explicit (dot) targets that did not require extrapolation.
Models for baseline estimations range from relatively simple extrapolations of past trends in land use to more complex extrapolations of past trends using spatially explicit models of land-use change driven by biophysical and socioeconomic factors [20].
Models for baseline estimations range from relatively simple extrapolations of past trends in land use to more complex extrapolations of past trends using spatially explicit models of land-use change driven by biophysical and socioeconomic factors [ 20].
An explicit variation, wherein future quantities are obtained by extrapolation, can provide attenuation but not large-timestep stability.
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