Sentence examples for equations for the surface from inspiring English sources

Such an evaluation requires the simultaneous solution of the system of equations for the surface water and energy balance, and subsurface heat transport and water flow.

Such effects pose various theoretical and computational challenges, since they are caused by non-convex surface energies, which lead to ill-posed evolution equations for the surfaces.

The thermodynamic extremum principle is applied to derive the evolution equations for the surfaces of both bodies as well as the contact conditions at the triple line.

A dimensionless equation for the surface potential was obtained.

An approximate analytical equation for the surface tension at the cmc was obtained.

An equation for the surface tortuosity for liquid and gas filled pores in terms of the is obtained.

Frequency equation for the surface wave propagation near the surface of the cylindrical bore is obtained, characterizing the dispersive nature of the wave.

To this end, we show that the equation for the surface stresses is an integral equation of the first kind whose ill-posedness is the source of spurious oscillations in the stresses.

These depth-integrated (or shallow water) equations are discretized by means of an augmented system, which holds an evolution equation for the surface tension in order to avoid numerical instabilities of classical upwind and centered schemes.

To account for these effects the Batchelor model of microflow and the Gouy Stern Grahame double-layer model together with the Nernst equation for the surface potential are used.

A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall.