Sentence examples for use the analytical solution from inspiring English sources

We use the analytical solution of the diffusive mass flux of volatiles for the bubble growth process, assuming that the diffusion of volatiles in the melt is fast.

We use the analytical solution for thermal rectification in such a binary system that considers the local temperature dependence of the thermal conductivity to identify combinations that produce reasonable rectification.

In this study, we use the analytical solution for an elastic half-space derived by Okada (1992) for U i. To estimate the slip deficit rate distribution on the plate interface from the synthetic surface displacement data, we used the inversion technique developed by Yabuki and Matsu'ura (1992).

However, we used the analytical solution for a rectangular fault (Okada 1985, 1992) which required us to modify the fault elements.

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

A theoretical analysis is carried out to calculate the uplift of the tunnel using the analytical solution presented above.

It is also shown that by using the analytical solution 'affected thermal well bore radius' can be estimated.

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.

The MT responses from the theoretical models (Fig. 15b) were then calculated using the analytical solution (see Chave and Jones 2012).