Geometric Analysis of Bifurcation and Symmetry Breaking in a Gross-Pitaevskii equation

Gross-Pitaevskii and nonlinear Hartree equations are equations of nonlinear Schroedinger type, which play an important role in the theory of Bose-Einstein condensation. Recent results of Aschenbacher et. al. [AFGST] demonstrate, for a class of 3- dimensional models, that for large boson number (squared L^2 norm), N, the ground state does not have the symmetry properties as the ground state at small N. We present a detailed global study of the symmetry breaking bifurcation for a 1-dimensional model Gross-Pitaevskii equation, in which the external potential (boson trap) is an attractive double-well, consisting of two attractive Dirac delta functions concentrated at distinct points. Using dynamical systems methods, we present a geometric analysis of the symmetry breaking bifurcation of an asymmetric ground state and the exchange of dynamical stability from the symmetric branch to the asymmetric branch at the bifurcation point.Comment: 22 pages, 7 figure

New and Developing Research on Disparities in Discipline

This briefing paper describes the results of new research in the area of disciplinary disparities, and identifies remaining gaps in the literature that can guide researchers and funders of research. The brief is organized into two sections:1) What Have we Learned? Key New Research Findings describes research from leading scholars across the nation commissioned by The Center for Civil Rights Remedies at UCLA's Civil Rights Project with the support of the Collaborative, findings from projects supported by the Collaborative Funded Research Grant Program, and other new research on disproportionality in school discipline in the peer-reviewed literature.2) Future Research Needs describes gaps that remain in the research base. Although there has been considerable new knowledge generated in recent years, significant gaps remain, especially in identifying and evaluating intervention strategies that reduce inequity in discipline for all students

On the Optical -- X-ray correlation from outburst to quiescence in Low Mass X-ray Binaries: the representative cases of V404 Cyg and Cen X-4

Low mass X-ray binaries (LMXBs) show evidence of a global correlation of debated origin between X-ray and optical luminosity. We study for the first time this correlation in two transient LMXBs, the black hole V404 Cyg and the neutron star Cen X-4, over 6 orders of magnitude in X-ray luminosity, from outburst to quiescence. After subtracting the contribution from the companion star, the Cen X-4 data can be described by a single power law correlation of the form $L_{opt}\propto\,L_{X}^{0.44}$, consistent with disk reprocessing. We find a similar correlation slope for V404 Cyg in quiescence (0.46) and a steeper one (0.56) in the outburst hard state of 1989. However, V404 Cyg is about $160-280$ times optically brighter, at a given $3-9$ keV X-ray luminosity, compared to Cen X-4. This ratio is a factor of 10 smaller in quiescence, where the normalization of the V404 Cyg correlation also changes. We show that once the bolometric X-ray emission is considered and the known main differences between V404 Cyg and Cen X-4 are taken into account (a larger compact object mass, accretion disk size, and the presence of a strong jet contribution in the hard state for the black hole system) the two systems lie on the same correlation. In V404 Cyg, the jet dominates spectrally at optical-infrared frequencies during the hard state, but makes a negligible contribution in quiescence, which may account for the change in its correlation slope and normalization. These results provide a benchmark to compare with data from the 2015 outburst of V404 Cyg and, potentially, other transient LMXBs as well.Comment: Accepted on ApJ, 12 pages, 4 figures, 4 table

Technical Transfer in the British Optical Industry 1888-1914: The Case of Barr and Stroud

A case study of the British Scientific Instrument Makers Barr and Stroud

Petrography and bulk composition of Miller Range 05035: a new lunar VLT gabbro

Miller Range (MIL) 05035 is a crystalline lunar mare gabbroic meteorite collected in Antarctica in 2005 [1]. It is an important new sample in the lunar meteorite (LM) collection as it is only one of ~8 to be classified as basaltic in nature. MIL 05035 is coarsely grained with large pyroxene grains ( 8mm) subophitically enclosing plagioclase grains ( 6mm), and accessory ilmenite, spinel, silica and sulphide phases

Flat-top oscillons in an expanding universe

Oscillons are extremely long lived, oscillatory, spatially localized field configurations that arise from generic initial conditions in a large number of non-linear field theories. With an eye towards their cosmological implications, we investigate their properties in an expanding universe. We (1) provide an analytic solution for one dimensional oscillons (for the models under consideration) and discuss their generalization to 3 dimensions, (2) discuss their stability against long wavelength perturbations and (3) estimate the effects of expansion on their shapes and life-times. In particular, we discuss a new, extended class of oscillons with surprisingly flat tops. We show that these flat topped oscillons are more robust against collapse instabilities in (3+1) dimensions than their usual counterparts. Unlike the solutions found in the small amplitude analysis, the width of these configurations is a non-monotonic function of their amplitudes.Comment: v2-matches version published in Phys. Rev D. Updated references and minor modification to section 4.