Sentence examples for equation for the evolution from inspiring English sources

Boltzmann provided an equation for the evolution of the distribution of the velocities of particles from a non-equilibrium initial state for dilute gases, the Boltzmann equation.

This method makes use of an equation for the evolution with time of the volume fraction crystallized.

The dynamics is analyzed through a Langevin equation for the evolution of the state of the system through its energy landscape.

The model consists of a modified form of the Landau-Lifshitz-Gilbert equation for the evolution of the magnetization vector in a rigid ferromagnet.

Such fluid flow systems have been modeled by coupling the Darcy Korteweg equation with the convection diffusion equation for the evolution of the solute concentration.

The model involves six equations obtained from conservation principles applied to each phase, completed by a seventh equation for the evolution of the volume fraction.

Equations for the evolution of the gradient values are solved.

Equation (6) may also be used to obtain the governing equations for the evolution of the slow plasma electron velocities.

We next demonstrate how fast-slow analysis can beused to derive reduced equations for the evolution of solutions during both the silentand active phases.

The method of multiple scales is used to derive two first-order ordinary-differential equations for the evolution of the amplitude and phase of the response.

The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks.