In fact, the new version of the equations includes on the right-hand side of the Ampaere's law the term [rho]V which is not

solenoidal. Despite the presence of [rho]V, the equation of continuity (2.6) still holds and ensures that, apart from the boundaries, there are no forcing current terms inside the capacitor.

Define the auxiliary spaces which are projections for the

solenoidal vector functions,

To attenuate errors of projection onto

solenoidal field and resultant errors of volume conservation, the ECS (Error Compensating Source) of PPE was proposed for both MPS and ISPH methods (Khayyer and Gotoh, 2011).

Separating [u.sup.v] into its longitudinal (irrotational) component [u.sup.v.sub.[parallel]] and its transverse (

solenoidal) component [u.sup.sub.[perpendicular to]] Using the Helmholtz theorem in four dimensions [32] according to

Also, [J.sub.imp] is the impressed current source, which is usually

solenoidal because it is generated by coils in magnetic problems.

The

solenoidal condition div u = 0 indicates that the flows are incompressible.

If ([B.sub.x], [B.sub.y], [B.sub.z]) are the components of the magnetic field vector [bar.B], the

solenoidal relation [nabla] x [bar.B] = 0 gives [B.sub.z] = constant = [B.sub.0], everywhere in the fluid.

It is a well-known fact that the coaxial transmission line supports a transverse electromagnetic mode, with E-field lines perpendicular to the central conductor spanning to the surrounding ground plane, whereas the H-field lines are

solenoidal, closing around the central conductor strip.

Klessen, "Modelling H2 formation in the turbulent interstellar medium:

solenoidal versus compressive turbulent forcing," Monthly Notices of the Royal Astronomical Society, vol.

In the case of fluid flow, u gives the fluid velocity, p is the pressure, [epsilon] [much less than] 1 represents the fluid viscosity, b is a

solenoidal vector function, [nabla] * b = 0, representing the associated velocity field, and c is a reaction term.

The system was embedded in a 1.5 T

solenoidal magnetic field; the detection system was cylindrical in shape with cylinder axis (2 m in length and 1.8 m in diameter) parallel to the

solenoidal field.