Sentence examples for through these equations from inspiring English sources

Through these equations, they found that temperature differences between the fluid drop and the fluid bath create convection, or circulating currents in the intervening layer of air.

The basic objective of this method is to observe the evolution of the system through these equations, because it is through the interactions among the particles that the system is able to maintain both mechanical and thermal equilibrium, and if there is any external perturbation, the system tends to reach a new equilibrium [22].

Assuming constant and equal proportional growth rates μ for MCS and MCX [eqns (20)] and constant substrate C fraction, CS [eqn (11)], eqns (23) become (divide through by MCX) (24) These equations are solved for μ and CS.

Through comparison of results of these equations and experimental data, good agreement was achieved.

Then, through introducing a force function, these equations reduced to a set of coupled nonlinear partial differential equations and a compatibility equation.

The use of these equations is discussed through examples.

The solutions for these equations are coupled through the boundary conditions.

These equations are solved simultaneously through iterations.

These equations are solved simultaneously through iterative process.

As he worked through the equations, one step stood out.

Run through the equations above.