In existing publications [3, 4, 6, 9], the decay rate of [mathematical expression not reproducible] is controlled by the first eigenvalue of the operator A = -P[DELTA], where P is the projection operator on a solenoidal
subspace of [L.sup.2]([OMEGA]).
Hence, a new corrective velocity field, [u.sup.**], is computed to project [u.sup.*] onto a solenoidal
, or divergence-free, field so that the final velocity field, [u.sup.k+1], would be solenoidal
Most analytical solutions which are solenoidal
possess nonzero essential boundary conditions, and most analytical solutions which possess homogeneous boundary conditions are not solenoidal
The positron momentum is measured by a magnetic spectrometer, composed by an almost solenoidal
magnet (COBRA) with an axial gradient field and by a system of sixteen ultrathin drift chambers (from now on DC).
At low frequencies, the electric field generated by the solenoidal
part of the electric current is largely overwhelmed by that generated by the nonsolenoidal part of the current.
The functional [F.sub.div][V] enforces the velocity field to be solenoidal
, and the last functional [F.sub.pen][V] is the regularization functional which tries to minimize the kinetic energy.
THE CLEBSCH REPRESENTATIONS OF ARBITRARY SOLENOIDAL
where n denotes the unit outward normal vector on [partial derivative][OMEGA] and u, T, C, p are unknown functions and represent the solenoidal
velocity of the fluid, the temperature of the fluid, the concentration of a solute, the pressure of the fluid respectively.
We conclude with the remark that the analysis of the TE- and the TM-modes of a vane-loaded circular cylindrical waveguide presented in this paper parallels the analysis of the solenoidal
and the irrotational modes of a cylindrical magnetron cavity presented in .
Since the magnetic induction field [??] is generally a nonnull function, this field must be solenoidal
, that is, [nabla] x [??]([??], t) = 0.
micro coils manufactured with a wire bonder, in Proc.