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Hydrodynamics of superfluids confined in blocked rings and wedges
- Source :
- Phys. Rev,. E 79, 016303 (2009)
- Publication Year :
- 2008
-
Abstract
- Motivated by many recent experimental studies of non-classical rotational inertia (NCRI) in superfluid and supersolid samples, we present a study of the hydrodynamics of a superfluid confined in the two-dimensional region (equivalent to a long cylinder) between two concentric arcs of radii $b$ and $a$ ($b<a$) subtending an angle $\beta$, with $0 \le \beta \le 2\pi$. The case $\beta= 2 \pi$ corresponds to a blocked ring. We discuss the methodology to compute the NCRI effects, and calculate these effects both for small angular velocities, when no vortices are present, and in the presence of a vortex. We find that, for a blocked ring, the NCRI effect is small, and that therefore there will be a large discontinuity in the moment of inertia associated with blocking or unblocking circular paths. For blocked wedges ($b=0$) with $\beta > \pi$, we find an unexpected divergence of the velocity at the origin, which implies the presence of either a region of normal fluid or a vortex for {\it any} nonzero value of the angular velocity. Implications of our results for experiments on "supersolid" behavior in solid $^4{\rm He}$ are discussed. A number of mathematical issues are pointed out and resolved.<br />Comment: 15 pages, including figures. To appear in Phys. Rev. E
Details
- Database :
- arXiv
- Journal :
- Phys. Rev,. E 79, 016303 (2009)
- Publication Type :
- Report
- Accession number :
- edsarx.0812.3112
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevE.79.016303