Display equations (set on their own line) can be included.
Kinetic equations that describe the evolution of these microstructural features with time and strain, derived from exhaustive experimental measurements for two steels, are incorporated into a creep equation set based on the damage mechanics philosophy.
Thermodynamics and kinetics of phase transformation in intercalation battery electrodes are investigated by phenomenological models which include a mean-field lattice-gas thermodynamic model and a generalized Poisson Nernst Planck equation set based on linear irreversible thermodynamics.
It should also be noted that estimates of change over time are somewhat less sensitive to equation choice than stock estimates, so if change is the primary variable of interest, the user can select either equation set, based on personal preference.
Whereas the analysis showed in this article does not need introducing such an operator matrix, it is directly based on the coupled equation set (2.10 - 2.11) to study the existence, uniqueness, and convergence of the numerical solution.
The equation is set on a Polish topological space endowed with a measure and the linear operator is induced by a carré du champs (equivalently, the equation is set in a diffusion Markov triple).
You don't have to help clean up!
But the equation changes when parents have their hearts set on the handful of schools considered the Baby Ivies, or on this year's list of hot schools.
For the density current (viscous), the SE and DG models using set 3 (mass and total energy) give less dissipative results than the other equation sets; based on these results we recommend set 3 for the development of future multiscale research codes.
Instead of the traditional LVRPA, the Helmholtz equation, set with the Dirichlet conditions on the boundary, was used to model the light distribution inside the photoreactor.
