Scale invariant thermodynamics of a toroidally trapped Bose gas

We consider a system of bosonic atoms in an axially symmetric harmonic trap augmented with a two dimensional repulsive Gaussian optical potential. We find an expression for the grand free energy of the system for configurations ranging from the harmonic trap to the toroidal regime. For large tori we identify an accessible regime where the ideal gas thermodynamics of the system are found to be independent of toroidal radius. This property is a consequence of an invariant extensive volume of the system that we identify analytically in the regime where the toroidal potential is radially harmonic. In considering corrections to the scale invariant transition temperature, we find that the first order interaction shift is the dominant effect in the thermodynamic limit, and is also scale invariant. We also consider adiabatic loading from the harmonic to toroidal trap configuration, which we show to have only a small effect on the condensate fraction of the ideal gas, indicating that loading into the scale invariant regime may be experimentally practical.Comment: 10 pages, 3 figures, to appear in Phys. Rev. A, typos corrected, references added, rewritten to emphasize generalized volume. Results unchange

A VON LIEBIG MODEL FOR WATER AND NITROGEN CROP RESPONSE

The century-old “law of the minimum” proposed by von Liebig was tested using five independent sets of crop response data on wheat, corn, cotton, silage, and sugar beets. The rival models were polynomial functions reported in the literature as the most suitable models for interpreting those data. Overall, the von Liebig model performed very well. While the nonnested hypothesis test was inconclusive with regard to silage and sugar beets, the von Liebig model rejected the polynomial specifications for wheat, corn and cotton.Crop Production/Industries,

On Flux Quantization in F-Theory II: Unitary and Symplectic Gauge Groups

We study the quantization of the M-theory G-flux on elliptically fibered Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic gauge groups. We seek and find its relation to the Freed-Witten quantization of worldvolume fluxes on 7-branes in type IIB orientifold compactifications on Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles on which to calculate the periods of the second Chern class of the fourfolds, we find that there is a half-integral shift in the quantization of G-flux whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold. This correspondence of quantizations holds for all unitary and symplectic gauge groups, except for SU(3), which behaves mysteriously. We also perform our analysis in the case where, in addition to the aforementioned gauge groups, there is also a 'flavor' U(1)-gauge group.Comment: 33 pages, 4 figure

The SEALS Yardsticks for Ontology Management

This paper describes the rst SEALS evaluation campaign over ontology engineering tools (i.e., the SEALS Yardsticks for Ontology Management). It presents the dierent evaluation scenarios dened to evaluate the conformance, interoperability and scalability of these tools, and the test data used in these scenarios

Spectral weight redistribution in strongly correlated bosons in optical lattices

We calculate the single-particle spectral function for the one-band Bose-Hubbard model within the random phase approximation (RPA). In the strongly correlated superfluid, in addition to the gapless phonon excitations, we find extra gapped modes which become particularly relevant near the superfluid-Mott quantum phase transition (QPT). The strength in one of the gapped modes, a precursor of the Mott phase, grows as the QPT is approached and evolves into a hole (particle) excitation in the Mott insulator depending on whether the chemical potential is above (below) the tip of the lobe. The sound velocity of the Goldstone modes remains finite when the transition is approached at a constant density, otherwise, it vanishes at the transition. It agrees well with Bogoliubov theory except close to the transition. We also calculate the spatial correlations for bosons in an inhomogeneous trapping potential creating alternating shells of Mott insulator and superfluid. Finally, we discuss the capability of the RPA approximation to correctly account for quantum fluctuations in the vicinity of the QPT.Comment: 14 pages, 12 figure

Luminosity Function of High-Mass X-ray Binaries and Anisotropy in the Distribution of Active Galactic Nuclei toward the Large Magellanic Cloud

In 2003-2012, the INTEGRAL observatory has performed long-term observations of the Large Magellanic Cloud (LMC). At present, this is one of the deepest hard X-ray (20-60 keV) surveys of extragalactic fields in which more than 20 sources of different natures have been detected. We present the results of a statistical analysis of the population of high-mass X-ray binaries in the LMC and active galactic nuclei (AGNs) observed in its direction. The hard X-ray luminosity function of high-mass X-ray binaries is shown to be described by a power law with a slope alpha~1.8, that in agreement with the luminosity function measurements both in the LMC itself, but made in the soft X-ray energy band, and in other galaxies. At the same time, the number of detected AGNs toward the LMC turns out to be considerably smaller than the number of AGNs registered in other directions, in particular, toward the source 3C 273. The latter confirms the previously made assumption that the distribution of matter in the local Universe is nonuniform.Comment: 5 pages, 5 figures, will be published in Astronomy Letters, 2012, Vol. 38, No. 8, p. 492--49

Sympathetic Cooling of Lithium by Laser-cooled Cesium

We present first indications of sympathetic cooling between two neutral, optically trapped atomic species. Lithium and cesium atoms are simultaneously stored in an optical dipole trap formed by the focus of a CO$_2$ laser, and allowed to interact for a given period of time. The temperature of the lithium gas is found to decrease when in thermal contact with cold cesium. The timescale of thermalization yields an estimate for the Li-Cs cross-section.Comment: 4 pages, proceedings of ICOLS 200

Observation of the Pairing Gap in a Strongly Interacting Fermi Gas

We study fermionic pairing in an ultracold two-component gas of $^6$Li atoms by observing an energy gap in the radio-frequency excitation spectra. With control of the two-body interactions via a Feshbach resonance we demonstrate the dependence of the pairing gap on coupling strength, temperature, and Fermi energy. The appearance of an energy gap with moderate evaporative cooling suggests that our full evaporation brings the strongly interacting system deep into a superfluid state.Comment: 18 pages, 3 figure

Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds

We compactify four-dimensional N=1 gauged supergravity theories on a circle including fluxes for shift-symmetric scalars. Four-dimensional Taub-NUT gravitational instantons universally correct the three-dimensional superpotential in the absence of fluxes. In the presence of fluxes these Taub-NUT instanton contributions are no longer gauge-invariant. Invariance can be restored by gauge instantons on top of Taub-NUT instantons. We establish the embedding of this scenario into M-theory. Circle fluxes and gaugings arise from a restricted class of M-theory four-form fluxes on a resolved Calabi-Yau fourfold. The M5-brane on the base of the elliptic fourfold dualizes into the universal Taub-NUT instanton. In the presence of fluxes this M5-brane is anomalous. We argue that anomaly free contributions arise from involved M5-brane geometries dual to gauge-instantons on top of Taub-NUT instantons. Adding a four-dimensional superpotential to the gravitational instanton corrections leads to three-dimensional Anti-de Sitter vacua at stabilized compactification radius. We comment on the possibility to uplift these M-theory vacua, and to tunnel to four-dimensional F-theory vacua.Comment: 47 pages, 2 figure