| Abstract: | Continuous, three-dimensional control of the vorticity vector is possible
     by progressively transitioning the field symmetry by applying or removing
     a dc bias along one of the principal axes of mutually orthogonal
     alternating fields. By exploiting this transition, the vorticity vector
     can be oriented in a wide range of directions that comprise all three
     spatial dimensions. Detuning one or more field components to create phase
     modulation causes the vorticity vector to trace out complex orbits of a
     wide variety, creating very robust multiaxial stirring. This multiaxial,
     non-contact stirring is particularly attractive for applications where
     the fluid volume has complex boundaries, or is congested. |