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By Behzad Razavi

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DONNELLY [Ch. 1, $2 force necessary to balance t h e tension tending to shrink a ring. Feynman reasoned that when the ring is small enough quantum effects balance the tension and the ring will be at rest, or nearly so, near the roton minimum of the dispersion curve (see fig. 1). Donnelly (1974) has written a history of the idea of the “ghost of a vanished vortex ring” for a conference honoring Onsager‘s 70th birthday. Donnelly and Roberts (197 1) noted that the data then available seemed to lead the large vortex ring sequence into the dispersion spectrum to t h e right of the roton minimum (see fig.

5, but the interpretation of them in terms of a core parameter is model dependent. 3. GINZBURG-PITAEVSKII THEORY In the preceding sections, the vortex core is described as being “hollow” or “rotating”. These descriptions are clearly inadequate for dealing with the structure of an object whose size is of the order of the interparticle spacing. Indeed it is one of the mysteries of superfluid physics that simple phenomenological concepts work as well as they do on a microscopic scale. A first principles quantum mechanical description of the vortex core has thus far eluded theorists.

This section of our review should not be closed without a few remarks on the stability of classical vortex rings. Vortex rings in nature have generally been considered to be both stable and persistent flows. J. Thomson (1883) and others was directed towards establishing the stability of vortex rings and calculating their frequencies of oscillation in order to investigate atomic structure. In practice, however, vortex lines (such as aircraft trailing vortices) and vortex rings are often unstable.

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Design of Analog CMOS Integrated Circuits solutions by Behzad Razavi


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