Sentence examples for using the analytical solutions from inspiring English sources

The required training and test data sets have been generated by using the analytical solutions of commonly-used reservoir models.

A set of field-scale scenarios are considered using the analytical solutions.

The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models.

Predictions for the highest 10 values of SCFs using the analytical solutions are within 10% of that by FEA.

The novel ACCPFDD-CUFFT implementation is verified using the analytical solutions for the stress field around an infinite edge dislocation and subsequently applied to simulate the interaction and motion of dislocations through a bi-phase copper-nickel (Cu Ni) interface.

The solution for piles embedded in layered soils is achieved according to the direct stiffness approach by using the analytical solutions derived for generic pile sections embedded in homogeneous soils.

The simulated neural network model is trained and validated using the analytical solution of Richards' equation.

Then their characteristics are determined by using the analytical solution together with the experimental data.

The focal length, which is the necessary distance to effectively concentrate particles in a microchannel, is calculated using the analytical solution of the particle equation of motion.

Sensitivity studies using the analytical solution were also conducted to investigate the vibration performance of the PCT floor system.

A premixedness parameter is identified using the analytical solution to the mixing field downstream of a splitter plate.