封闭环和楔中超流体的流体动力学
Hydrodynamics of superfluids confined in blocked rings and wedges
摘要：
受超流体和超固体样品中非经典转动惯量（NCRI）的实验研究的启发，本文研究了二维区域（相当于一个长圆柱体）中超流体的流体动力学，该区域位于两个半径为$b$和$a$（$b<a$）的同心圆弧之间，半径为$β$，半径为$0 \le β\le 2π$ .情况$β= 2 π$对应于阻塞环。我们讨论的方法来计算NCRI的影响，并计算这些影响都为小的角速度，当没有涡流存在，并在涡流的存在下。我们发现，对于一个阻塞环，NCRI效应是小的，因此将有一个大的不连续性的转动惯量与阻塞或非阻塞的圆形路径。对于具有$β> π$的阻塞楔形体（$b=0$），我们发现在原点处速度的意外发散，这意味着对于{ \it any}非零角速度值，存在正常流体区域或涡旋。我们的研究结果的“超固体”的行为在固体$^4{\rm He}$的实验的影响进行了讨论。指出并解决了一些数学问题。
英文摘要：
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 $β$, with $0 \le β\le 2π$. The case $β= 2 π$ 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 $β> π$, 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
