The approximations are validated by comparing with other analytical solutions for the linear case and full numerics for the nonlinear case.
All the approximations are validated through Monte Carlo simulation within a wide parameter space.
This approximation was validated via a finite element simulation.
The simulation is validated by the 3D printed structures.
The product is validated by customers and meets other criteria.
This approximation was validated using electron microscopy and appears to provide good values.
Finally, the analytical approximations are validated with direct numerical simulations.
Our result based on the generalized gradient approximation has been validated by the state-of-the-art B3LYP level of theory for Pt adsorption on the graphene surface.
The system behavior was modeled by a simple line-of-charge approximation, which was validated by a more detailed Lagrangian model and by experiments on an individual electrospray.
In the numerical results and simulations conducted throughout this paper, the validity of the Gaussian approximation for has been validated by testing for normality with the Lilliefors test for the selected values of and.
When the normality approximation fails due to extremely low MAF, the p-values were validated by the Fisher's exact test.
