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Register a new userQuantized vortices and superflow in arbitrary dimensions: Structure, energetics and dynamics
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The structure and energetics of superflow around quantized vortices, and the motion inherited by these vortices from this superflow, are explored in the general setting of the superfluidity of helium-four in arbitrary dimensions. The vortices may be idealized as objects of co-dimension two, such as one-dimensional loops and two-dimensional closed surfaces, respectively, in the cases of three- and four-dimensional superfluidity. By using the analogy between vorticial superflow and Ampere-Maxwell magnetostatics, the equilibrium superflow containing any specified collection of vortices is constructed. The energy of the superflow is found to take on a simple form for vortices that are smooth and asymptotically large, compared with the vortex core size. The motion of vortices is analyzed in general, as well as for the special cases of hyper-spherical and weakly distorted hyper-planar vortices. In all dimensions, vortex motion reflects vortex geometry. In dimension four and higher, this includes not only extrinsic but also intrinsic aspects of the vortex shape, which enter via the first and second fundamental forms of classical geometry. For hyper-spherical vortices, which generalize the vortex rings of three dimensional superfluidity, the energy-momentum relation is determined. Simple scaling arguments recover the essential features of these results, up to numerical and logarithmic factors.
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Motivated by the general problem of moving topological defects in an otherwise ordered state and specifically, by the anomalous dynamics observed in vortex-antivortex annihilation and coarsening experiments in freely-suspended smectic-C films by Clark, et al., I study the deformation, energetics and dynamics of moving vortices in an overdamped xy-model and show that their properties are significantly and qualitatively modified by the motion.
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We review recent important topics in quantized vortices and quantum turbulence in atomic Bose--Einstein condensates (BECs). They have previously been studied for a long time in superfluid helium. Quantum turbulence is currently one of the most important topics in low-temperature physics. Atomic BECs have two distinct advantages over liquid helium for investigating such topics: quantized vortices can be directly visualized and the interaction parameters can be controlled by the Feshbach resonance. A general introduction is followed by a description of the dynamics of quantized vortices, hydrodynamic instability, and quantum turbulence in atomic BECs.
Many fluctuating systems consist of macroscopic structures in addition to noisy signals. Thus, for this class of fluctuating systems, the scaling behaviors are very complicated. Such phenomena are quite commonly observed in Nature, ranging from physics, chemistry, geophysics, even to molecular biology and physiology. In this paper, we take an extensive analytical study on the ``generalized detrended fluctuation analysis method. For continuous fluctuating systems in arbitrary dimensions, we not only derive the explicit and exact expression of macroscopic structures, but also obtain the exact relations between the detrended variance functions and the correlation function. Besides, we undertake a general scaling analysis, applicable for this class of fluctuating systems in any dimensions. Finally, as an application, we discuss some important examples in interfacial superroughening phenomena.
A propagation torsion model for quantized vortices is proposed.The model is applied to superfluids and liquid Helium II.
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