Diffusion of an Inhomogeneous Vortex Tangle

The spatial diffusion of an inhomogeneous vortex tangle is studied numerically with the vortex filament model. A localized initial tangle is prepared by applying a counterflow, and the tangle is allowed to diffuse freely after the counterflow is turned off. Comparison with the solution of a generalization of the Vinen equation that takes diffusion into account leads to a very small diffusion constant, as expected from simple theoretical considerations. The relevance of this result to recent experiments on the generation and decay of superfluid turbulence at very low temperatures is discussed.Comment: 2 pages, 2 figure

The Expectations of Adulting: Developing Soft Skills through Active Learning Classrooms

The technologically enhanced classroom assists students in developing their interpersonal, or soft skills, and helps them strengthen needed competencies as they move into their careers. This may be particularly helpful for millennial students, who have grown up interacting with others electronically, via text message, Instagram, and the like. Once on campus, students must adapt to increasing expectations of adulthood: along with becoming more responsible and independent critical thinkers, they must also be able to speak effectively with others face-to-face and to negotiate relationships in groups, skills that they often noticeably lack

An Interdisciplinary Consideration of Marginality

As the university increases its commitment to interdisciplinary studies, it is imperative that we find productive models of interdisciplinarity in scholarly and creative activities, teaching, and institutional structures. This coauthored essay, written in the spirit of sharing work across disciplines, seeks to participate in the conversation about interdisciplinary scholarship. Interdisciplinarity in scholarship can be discussed in two ways. First, interdisicplinarity can be enhanced by encouraging people to read across the disciplines. Second, it can be enhanced by encouraging scholarship that is interdisciplinary and multi-methodological. This essay speaks to both of these levels

Specific heat of the Kelvin modes in low temperature superfluid turbulence

It is pointed out that the specific heat of helical vortex line excitations, in low temperature superfluid turbulence experiments carried out in helium II, can be of the same order as the specific heat of the phononic quasiparticles. The ratio of Kelvin mode and phonon specific heats scales with L_0 T^{-5/2}, where L_0 represents the smoothed line length per volume within the vortex tangle, such that the contribution of the vortex mode specific heat should be observable for L_0 = 10^6-10^8 cm^{-2}, and at temperatures which are of order 1-10 mK.Comment: 3 pages, 1 figur

Trends in Iowa’s K-12 Public Education: An Analysis of School Spending & Student Achievement

Prior research has examined the effect of K-12 public education spending on student academic achievement; researchers disagree about whether increasing public education spending improves academic achievement. The purpose of this study is to determine if K-12 public education spending has an effect on student academic achievement in Iowa. This project will use a secondary analysis of data from the past twenty years to examine the relationship between K-12 public education spending in Iowa and student academic achievement in Iowa. The findings of this research can be used to inform policymakers and citizens about how K-12 public education spending is affecting Iowa student academic achievement

Kolmogorov Spectrum of Quantum Turbulence

There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introduce a dissipation term that works only at scales below the healing length. Second, to obtain steady turbulence through the balance between injection and decay, we add energy injection at large scales. The energy spectrum is quantitatively consistent with the Kolmogorov law in both decaying and steady turbulence. Consequently, this is the first study that confirms the inertial range of quantum turbulence.Comment: 14pages, 24 figures and 1 table. Appeared in Journal of the Physical Society of Japan, Vol.74, No.12, p.3248-325

The State of the Art in Hydrodynamic Turbulence: Past Successes and Future Challenges

We present a personal view of the state of the art in turbulence research. We summarize first the main achievements in the recent past, and then point ahead to the main challenges that remain for experimental and theoretical efforts.Comment: 19 pages, 6 figures, submitted to Physica

Dynamics of vortex tangle without mutual friction in superfluid 4^4He

A recent experiment has shown that a tangle of quantized vortices in superfluid $^4$He decayed even at mK temperatures where the normal fluid was negligible and no mutual friction worked. Motivated by this experiment, this work studies numerically the dynamics of the vortex tangle without the mutual friction, thus showing that a self-similar cascade process, whereby large vortex loops break up to smaller ones, proceeds in the vortex tangle and is closely related with its free decay. This cascade process which may be covered with the mutual friction at higher temperatures is just the one at zero temperature Feynman proposed long ago. The full Biot-Savart calculation is made for dilute vortices, while the localized induction approximation is used for a dense tangle. The former finds the elementary scenario: the reconnection of the vortices excites vortex waves along them and makes them kinked, which could be suppressed if the mutual friction worked. The kinked parts reconnect with the vortex they belong to, dividing into small loops. The latter simulation under the localized induction approximation shows that such cascade process actually proceeds self-similarly in a dense tangle and continues to make small vortices. Considering that the vortices of the interatomic size no longer keep the picture of vortex, the cascade process leads to the decay of the vortex line density. The presence of the cascade process is supported also by investigating the classification of the reconnection type and the size distribution of vortices. The decay of the vortex line density is consistent with the solution of the Vinen's equation which was originally derived on the basis of the idea of homogeneous turbulence with the cascade process. The obtained result is compared with the recent Vinen's theory.Comment: 16 pages, 16 figures, submitted to PR

Instability of vortex array and transitions to turbulent states in rotating helium II

We consider superfluid helium inside a container which rotates at constant angular velocity and investigate numerically the stability of the array of quantized vortices in the presence of an imposed axial counterflow. This problem was studied experimentally by Swanson {\it et al.}, who reported evidence of instabilities at increasing axial flow but were not able to explain their nature. We find that Kelvin waves on individual vortices become unstable and grow in amplitude, until the amplitude of the waves becomes large enough that vortex reconnections take place and the vortex array is destabilized. The eventual nonlinear saturation of the instability consists of a turbulent tangle of quantized vortices which is strongly polarized. The computed results compare well with the experiments. Finally we suggest a theoretical explanation for the second instability which was observed at higher values of the axial flow

Quantum hydrodynamics

Quantum hydrodynamics in superfluid helium and atomic Bose-Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function appears because of Bose-Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in 4He, which has no analogue with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), "Quantized vortices in superfluid helium and atomic Bose--Einstein condensates", and other review articles.Comment: 102 pages, 29 figures, 1 tabl