U.S. International Trade: Trends and Forecasts

[Excerpt] This report provides an overview of the current status, trends, and forecasts for U.S. import and export flows as well as certain balances. The purpose of this report is to provide current data and brief explanations for the various types of trade flows along with a brief discussion of trends that may require attention or point to the need for policy changes. The use of trade policy as an economic or strategic tool is beyond the scope of this report but can be found in various other CRS reports. Further detail on trade in specific commodities, with particular countries or regions, or for different time periods, can be obtained from the Department of Commerce, U.S. International Trade Commission, or by contacting the authors of this report

Stable Fractional Vortices in the Cyclic States of Bose-Einstein Condensates

We propose methods to create fractional vortices in the cyclic state of an F = 2 spinor Bose-Einstein condensate by manipulating its internal spin structure using pulsed microwave and laser fields. The stability of such vortices is studied as a function of the rotation frequency of the confining harmonic trap both in pancake and cigar shaped condensates. We find a range of parameters for which the so-called 1/3-vortex state is energetically favorable. Such fractional vortices could be created in condensates of 87Rb atoms using current experimental techniques facilitating probing of topological defects with non-Abelian statistics.Comment: 5 pages, 2 figure

Avoided intersections of nodal lines

We consider real eigen-functions of the Schr\"odinger operator in 2-d. The nodal lines of separable systems form a regular grid, and the number of nodal crossings equals the number of nodal domains. In contrast, for wave functions of non integrable systems nodal intersections are rare, and for random waves, the expected number of intersections in any finite area vanishes. However, nodal lines display characteristic avoided crossings which we study in the present work. We define a measure for the avoidance range and compute its distribution for the random waves ensemble. We show that the avoidance range distribution of wave functions of chaotic systems follow the expected random wave distributions, whereas for wave functions of classically integrable but quantum non-separable wave functions, the distribution is quite different. Thus, the study of the avoidance distribution provides more support to the conjecture that nodal structures of chaotic systems are reproduced by the predictions of the random waves ensemble.Comment: 12 pages, 4 figure

Quantum turbulence at finite temperature: the two-fluids cascade

To model isotropic homogeneous quantum turbulence in superfluid helium, we have performed Direct Numerical Simulations (DNS) of two fluids (the normal fluid and the superfluid) coupled by mutual friction. We have found evidence of strong locking of superfluid and normal fluid along the turbulent cascade, from the large scale structures where only one fluid is forced down to the vorticity structures at small scales. We have determined the residual slip velocity between the two fluids, and, for each fluid, the relative balance of inertial, viscous and friction forces along the scales. Our calculations show that the classical relation between energy injection and dissipation scale is not valid in quantum turbulence, but we have been able to derive a temperature--dependent superfluid analogous relation. Finally, we discuss our DNS results in terms of the current understanding of quantum turbulence, including the value of the effective kinematic viscosity

Regulation of the cerebral circulation: bedside assessment and clinical implications

The regulation of the cerebral circulation relies on the complex interplay between cardiovascular, respiratory, and neural physiology. In health, these physiologic systems act to maintain an adequate cerebral blood flow (CBF) through modulation of hydrodynamic parameters; the resistance of cerebral vessels, and the arterial, intracranial, and venous pressures. In critical illness, however, one or more of these parameters can be compromised raising the possibility of disturbed CBF regulation and its pathophysiologic sequelae. The rigorous assessment of the cerebral circulation requires not only measuring CBF and its hydrodynamic determinants but also assessing the stability of CBF in response to changes in arterial pressure (cerebral autoregulation), the reactivity of CBF to a vasodilator (CO₂ reactivity for example), and the dynamic regulation of arterial pressure (baroreceptor sensitivity). Ideally, cerebral circulation monitors in critical care should be continuous, physically robust, allow for both regional and global CBF assessment, and be conducive to application at the bedside. The regulation of the cerebral circulation is impaired not only in primary neurologic conditions that affect the vasculature such as subarachnoid haemorrhage and stroke, but also in conditions that affect the regulation of intracranial pressure (such as traumatic brain injury and hydrocephalus) or arterial blood pressure (sepsis, or cardiac dysfunction). Importantly, this impairment is often associated with poor patient outcome. At present, the assessment of the cerebral circulation is primarily used as a research tool to elucidate pathophysiology or prognosis. However, when combined with other physiologic signals and online analytical techniques, cerebral circulation monitoring has the appealing potential to not only prognosticate patients, but also direct critical care management.JD is supported by a Woolf Fisher scholarship (NZ). MC is partially supported by the NIHR

Vortex lattices in a stirred Bose-Einstein condensate

We stir with a focused laser beam a Bose-Einstein condensate of $^{87}$Rb atoms confined in a magnetic trap. We observe the formation of a single vortex for a stirring frequency exceeding a critical value. At larger rotation frequencies we produce states of the condensate for which up to eleven vortices are simultaneously present. We present measurements of the decay of a vortex array once the stirring laser beam is removed

Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

The radial curvature of an end that makes eigenvalues vanish in the essential spectrum II

Under the quadratic-decay-conditions of the radial curvatures of an end, we shall derive growth estimates of solutions to the eigenvalue equation and show the absence of eigenvalues.Comment: "$\ge$" in the conditions $(*_4)$ and $(*_5)$ should be replaced by "$>$". $\gamma \ge \frac{n-1}{2}(b-a)$ in the conclusion of Theorem 1.3 should be replaced by $\gamma > \frac{n-1}{2}(b-a)$; trivial miss-calculatio