This operator applied twice to a field F is equal to grad div F minus div grad
Computational models of MHD that must include a term for the fourth power of this operator applied to the magnetic field generally reduce that term to a biharmonic operator that requires 220 degrees of freedom per element. Following a starquake, the region around a neutron star is separated into regions called "cavity" and "j-bundle" depending on the value of this operator. Generally, this operation may be expressed using the exterior derivative with respect to a field F as the sharp of the Hodge dual of d F flat. Any smooth, rapidly-decaying vector field in three dimensions can be expressed as the sum of a solenoidal field and a field for which this operator is zero by Helmholtz's theorem. This operator applied twice to a field F is equal to grad div F minus div grad F. This operator of the gradient of a scalar field is zero, and applied to a velocity field, this operator gives the vorticity. It can be defined relative to a normal vector as the limit of the loop integral over the area of the loop as the loop becomes infinitesimal. For 10 points, name this operator symbolized del cross, which represents a vector field's rotation.
Computational models of MHD that must include a term for the fourth power of this operator applied to the magnetic field generally reduce that term to a biharmonic operator that requires 220 degrees of freedom per element.
{curl}