Sentence examples for modified equations of from inspiring English sources

The method can efficiently obtain the exact solution of the modified structure, without solving the complete set of modified equations of the new structure.

The cavitation in the models is based on the modified equations of Needleman and Rice.

The limitations implied by using conventional quadratic mixing rules for Redlich Kwong's modified equations of state are studied.

Based on a comparison with the given formulas, the modified equations of Chang and Degen are proposed to predict the minimum wall thickness to prevent scabbing and perforation in the case in which the UHPFRC structure is used.

Experimental curves of desorption isotherms were fitted to modified equations of Henderson, Halsey, Oswin and Chung-Pfost as well as the GAB model and then evaluated visually by using residual plots and also by some statistical error parameters.

Using F = q, p, q ˙, p ˙ ≜ ∑ k = 1 N p k q ˙ k − H Open image in new window, we find correspondingly the modified equations of motion: q ˙ k = ∂ H ∂ p k Open image in new window p ˙ k = − ∂ H ∂ q k − 1 ξ dξ dt + ξ − ∂ H ∂ q k q ˙ k + q ¨ k p k p k Open image in new window.

The predictions of the modified equations are compared with Equations of Shine et al., Kwak et al. and Khuntia et al. Both of the modified equations in this paper gave satisfied predictions for the shear strength of the tested RPC beams with COV of 7.9% and 10%.

The method of modified equations is used to explain failings of Euler-based methods.

The work of Warming and Hyett represents a key step in the development of the method of modified equations.

All the programs are open-source and allow for different learning approaches, from application exercises with these equations, to correlation of equation parameters or implementation of modified equations and calculation algorithms for more advanced courses.

Vector field plot of modified equations is qualitatively similar to Figure 2C.