Showed that the work of on vortex filaments is closely related to the nonlinear Schr�dinger equation.
2.
Subsequently used this correspondence to show that breather solutions can also arise for a vortex filament.
3.
According to the the shedding of a vortex filament down the flow, behind the wing.
4.
Water striders generate thrust by shedding vortices in the water : a series of " U "-shaped vortex filaments is created during the power stroke.
5.
This immediately made the problem part of " modern science " since it was then realized that vortex filaments can support solitary twist waves of large amplitude.
6.
Turbulence in classical fluid is often modelled simply using virtual vortex filaments, around which there is a certain circulation of the fluid, to get a grasp on what is happening in the fluid.
7.
In 1972 H . Hasimoto used Da Rios'" intrinsic equations " ( later re-discovered independently by R . Betchov ) to show how the motion of a vortex filament under LIA could be related to the non-linear Schr�dinger equation.
8.
Structural complexity methods are based on applications of differential geometry and topology ( and in particular knot theory ) to interpret physical properties of dynamical systems ( Abraham & Shaw 1992; Ricca 2009 ), such as relations between kinetic energy and tangles of vortex filaments in a turbulent flow or magnetic energy and braiding of magnetic fields in the solar corona, including aspects of topological fluid dynamics.
9.
Another example of this kind is the so-called " localized induction approximation " ( LIA ) for three-dimensional vortex filament motion, which gained favor in the mid-1960s through the work of Arms, Hama, Betchov and others, but turns out to date from the early years of the 20th century in the work of Da Rios, a gifted student of the noted Italian mathematician T . Levi-Civita.
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