Sentence examples for macroscopic equation for from inspiring English sources

A homogenization technique is used to obtain a macroscopic equation for the case of plane wave propagation in effectively elastic media weakened by cracks.

On the other hand, we have a classic "macroscopic" equation for the medium-modified energy of interaction of the same two dipoles.

The approach is based on circumventing the explicit derivation of macroscopic equations for the system statistics (e.g., average coverage).

The model consists of a closed set of macroscopic equations for mass and momentum transport applicable for the dispersed and continuous phases.

The key problem here is that it is very difficult to provide a priori known and reliable input kinetic coefficients for macroscopic equations for each carrier group at non-equilibrium conditions.

In the second part, we use the first model [20] in order to determine an unknown function in the energy exchange of the macroscopic equations for gas mixtures described by Dellacherie [11].

Two-dimensional finite difference lattice Boltzmann models for single-component fluids are discussed and the corresponding macroscopic equations for mass and momentum conservation are derived by performing a Chapman Enskog expansion.

Furthermore, under the local mechanical equilibrium assumption, only one macroscopic equation arises for momentum transport, which resembles an extension of Darcy׳s law; whereas for mass transport, the equilibrium model reduces to the continuity equation.

Recently the kinetic theory has proposed an alternative approach for deriving macroscopic equations from the dynamics delivered at the mesoscopic scale: the asymptotic method.

Furthermore, particular care has to be taken in systems possessing multiple fixed points of the macroscopic equation, and we refer to [5] for a discussion of this aspect in the neural field setting.

Later, (u_{i}^{(0)}) will be defined as a solution of the homogenized macroscopic equation.