Energy spectra of vortex distributions in two-dimensional quantum turbulence

We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length $\xi$. We show that for the divergence-free portion of the superfluid velocity field, the kinetic energy spectrum over wavenumber $k$ may be decomposed into an ultraviolet regime ($k\gg \xi^{-1}$) having a universal $k^{-3}$ scaling arising from the vortex core structure, and an infrared regime ($k\ll\xi^{-1}$) with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent -1/3 for vortices of the same sign of circulation leads to an infrared kinetic energy spectrum with a Kolmogorov $k^{-5/3}$ power law, consistent with the existence of an inertial range. The presence of these $k^{-3}$ and $k^{-5/3}$ power laws, together with the constraint of continuity at the smallest configurational scale $k\approx\xi^{-1}$, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous compressible two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic energy distribution, once we introduce the concept of a {\em clustered fraction} consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical two-dimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.Comment: 19 pages, 8 figure

Vortices and turbulence in trapped atomic condensates

After over a decade of experiments generating and studying the physics of quantized vortices in atomic gas Bose-Einstein condensates, research is beginning to focus on the roles of vortices in quantum turbulence, as well as other measures of quantum turbulence in atomic condensates. Such research directions have the potential to uncover new insights into quantum turbulence, vortices and superfluidity, and also explore the similarities and differences between quantum and classical turbulence in entirely new settings. Here we present a critical assessment of theoretical and experimental studies in this emerging field of quantum turbulence in atomic condensates

Massively parallel support for a case-based planning system

Case-based planning (CBP), a kind of case-based reasoning, is a technique in which previously generated plans (cases) are stored in memory and can be reused to solve similar planning problems in the future. CBP can save considerable time over generative planning, in which a new plan is produced from scratch. CBP thus offers a potential (heuristic) mechanism for handling intractable problems. One drawback of CBP systems has been the need for a highly structured memory to reduce retrieval times. This approach requires significant domain engineering and complex memory indexing schemes to make these planners efficient. In contrast, our CBP system, CaPER, uses a massively parallel frame-based AI language (PARKA) and can do extremely fast retrieval of complex cases from a large, unindexed memory. The ability to do fast, frequent retrievals has many advantages: indexing is unnecessary; very large case bases can be used; memory can be probed in numerous alternate ways; and queries can be made at several levels, allowing more specific retrieval of stored plans that better fit the target problem with less adaptation. In this paper we describe CaPER's case retrieval techniques and some experimental results showing its good performance, even on large case bases

Snell's Law for a vortex dipole in a Bose-Einstein condensate

A quantum vortex dipole, comprised of a closely bound pair of vortices of equal strength with opposite circulation, is a spatially localized travelling excitation of a planar superfluid that carries linear momentum, suggesting a possible analogy with ray optics. We investigate numerically and analytically the motion of a quantum vortex dipole incident upon a step-change in the background superfluid density of an otherwise uniform two-dimensional Bose-Einstein condensate. Due to the conservation of fluid momentum and energy, the incident and refracted angles of the dipole satisfy a relation analogous to Snell's law, when crossing the interface between regions of different density. The predictions of the analogue Snell's law relation are confirmed for a wide range of incident angles by systematic numerical simulations of the Gross-Piteavskii equation. Near the critical angle for total internal reflection, we identify a regime of anomalous Snell's law behaviour where the finite size of the dipole causes transient capture by the interface. Remarkably, despite the extra complexity of the surface interaction, the incoming and outgoing dipole paths obey Snell's law.Comment: 16 pages, 7 figures, Scipost forma

Economic Impact of Deer Breeding Operations in Texas

The deer breeding industry is a growing industry in the Texas economy, particularly the rural economy. Industry participants were surveyed to provide estimates of economic activity, which was then input into the IMPLAN model. The industry generates an estimated $652 million in economic activity, while supporting 7,335 jobs.Industrial Organization,

In situ imaging of vortices in Bose-Einstein condensates

Laboratory observations of vortex dynamics in Bose-Einstein condensates (BECs) are essential for determination of many aspects of superfluid dynamics in these systems. We present a novel application of dark-field imaging that enables \texttt{\it in situ} detection of two-dimensional vortex distributions in single-component BECs, a step towards real-time measurements of complex two-dimensional vortex dynamics within a single BEC. By rotating a $^{87}$Rb BEC in a magnetic trap, we generate a triangular lattice of vortex cores in the BEC, with core diameters on the order of 400 nm and cores separated by approximately 9 $\mu$m. We have experimentally confirmed that the positions of the vortex cores can be determined without the need for ballistic expansion of the BEC.Comment: 5 pages, 4 figure

Financial Impacts of Regional Differences in Dairies

The sensitivity of net cash farm income to changes in selected production variables, output prices, and input costs varies significantly across representative U.S. dairies. Different regions of the country were impacted differently by changes to production and prices.Agricultural Finance, Q12, Q14,

Regional and Structural Impacts of Alternative Dairy Policy Options

Milk and dairy product prices have fallen to their lowest levels in 3 years following the record highs of 2004 and 2005. The large government stockpiles of non-fat dry milk are gone, but threaten to build again as non-fat dry milk and cheese prices decline nearer the support price level. A new farm bill is scheduled to be written in 2007. The Milk Income Loss Contract (MILC) program included in the last farm bill was only authorized through September 2005. Subsequent legislation reinstated the MILC program through August 2007. WTO negotiations are on-going and could influence U.S. farm programs 1/. Dairy’s role in the U.S. amber box limit of $19.1 billion may necessitate some possible trade-offs with other commodities. Dairy counts about$4.2 billion toward the annual amber box limit, but actual spending only averages about $1 billion (Outlaw, et al). The pressure of low prices, WTO negotiations, MILC continuation, and a new farm bill has created the potential for a number of options and alternatives for dairy policy. This paper examines the regional and structural impacts of 3 dairy policy options: MILC continuation, a target price/deficiency payment program, and an increase in the support price. All three options are designed to spend$400 million in amber box payments per year. The analysis uses representative dairy farms in major milk producing regions of the country developed by the AFPC for policy analysis.Agribusiness, Agricultural and Food Policy, Livestock Production/Industries,