A Unified Conformal Field Theory Description of Paired Quantum Hall States

The wave functions of the Haldane-Rezayi paired Hall state have been previously described by a non-unitary conformal field theory with central charge c=-2. Moreover, a relation with the c=1 unitary Weyl fermion has been suggested. We construct the complete unitary theory and show that it consistently describes the edge excitations of the Haldane-Rezayi state. Actually, we show that the unitary (c=1) and non-unitary (c=-2) theories are related by a local map between the two sets of fields and by a suitable change of conjugation. The unitary theory of the Haldane-Rezayi state is found to be the same as that of the 331 paired Hall state. Furthermore, the analysis of modular invariant partition functions shows that no alternative unitary descriptions are possible for the Haldane-Rezayi state within the class of rational conformal field theories with abelian current algebra. Finally, the known c=3/2 conformal theory of the Pfaffian state is also obtained from the 331 theory by a reduction of degrees of freedom which can be physically realized in the double-layer Hall systems.Comment: Latex, 42 pages, 2 figures, 3 tables; minor corrections to text and reference

Optical-NIR analysis of globular clusters in the IKN dwarf spheroidal: a complex star formation history

Age, metallicity and spatial distribution of globular clusters (GCs) provide a powerful tool to reconstruct major star-formation episodes in galaxies. IKN is a faint dwarf spheroidal (dSph) in the M81 group of galaxies. It contains five old GCs, which makes it the galaxy with the highest known specific frequency (SN=126). We estimate the photometric age, metallicity and spatial distribution of the poorly studied IKN GCs. We search SDSS for GC candidates beyond the HST field of view, which covers half of IKN. To break the age-metallicity degeneracy in the V-I colour we use WHT/LIRIS Ks-band photometry and derive photometric ages and metallicities by comparison with SSP models in the V,I,Ks colour space. IKN GCs' VIKs colours are consistent with old ages ($\geq\!8$ Gyr) and a metallicity distribution with a higher mean than typical for such a dSph ([Fe/H$]\!\simeq\!-1.4_{-0.2}^{+0.6}$ dex). Their photometric masses range ($0.5 <{\cal M_{\rm GC}}<4\times10^5M_\odot$) implies a high mass ratio between GCs and field stars, of $10.6\%$. Mixture model analysis of the RGB field stars' metallicity suggests that 72\% of the stars may have formed together with the GCs. Using the most massive GC-SFR relation we calculate a SFR of $\sim\!10M_\odot/$yr during its formation epoch. We note that the more massive GCs are closer to the galaxy photometric centre. IKN GCs also appear spatially aligned along a line close to the IKN major-axis and nearly orthogonal to the plane of spatial distribution of galaxies in the M81 group. We identify one new IKN GC candidate based on colour and PSF analysis of the SDSS data. The evidence towards i) broad and high metallicity distribution of the field IKN RGB stars and its GCs, ii) high fraction and iii), spatial alignment of IKN GCs, supports a scenario for tidally triggered complex IKN's SFH in the context of interactions with galaxies in the M81 group.Comment: 12 pages, 9 figures, accepted to A&

Coulomb Excitation of 68,70Cu: First Use of Postaccelerated Isomeric Beams

We report on the first low-energy Coulomb excitation measurements with radioactive Iπ=6- beams of odd-odd nuclei 68,70Cu. The beams were produced at ISOLDE, CERN and were post-accelerated by REX-ISOLDE to 2.83  MeV/nucleon. γ rays were detected with the MINIBALL spectrometer. The 6- beam was used to study the multiplet of states (3-, 4-, 5-, 6-) arising from the π2p3/2ν1g9/2 configuration. The 4- state of the multiplet was populated via Coulomb excitation and the B(E2;6-→4-) value was determined in both nuclei. The results obtained illustrate the fragile stability of the Z=28 shell and N=40 subshell closures. A comparison with large-scale shell-model calculations using the 56Ni core shows the importance of the proton excitations across the Z=28 shell gap to the understanding of the nuclear structure in the neutron-rich nuclei with N≈40

Does Atkinson-Wilcox Expansion Converges for any Convex Domain?

2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40.The Atkinson-Wilcox theorem claims that any scattered field in the exterior of a sphere can be expanded into a uniformly and absolutely convergent series in inverse powers of the radial variable and that once the leading coefficient of the expansion is known the full series can be recovered uniquely through a recurrence relation. The leading coefficient of the series is known as the scattering amplitude or the far field pattern of the radiating field. In this work we give a simple characterization of the strictly convex domains, such that a reasonable generalization of the AtkinsonWilcox expansion converges uniformly in the corresponding exterior domain. All these strictly convex domains are spheres

Nuclear star cluster formation in energy-space

In a virialized stellar system, the mean-square velocity is a direct tracer of the energy per unit mass of the system. Here, we exploit this to estimate and compare root-mean-square velocities for a large sample of nuclear star clusters and their host (late- or early-type) galaxies. Traditional observables, such as the radial surface brightness and second-order velocity moment profiles, are subject to short-term variations due to individual episodes of matter infall and/or star formation. The total mass, energy and angular momentum, on the other hand, are approximately conserved. Thus, the total energy and angular momentum more directly probe the formation of galaxies and their nuclear star clusters, by offering access to more fundamental properties of the nuclear cluster-galaxy system than traditional observables. We find that there is a strong correlation, in fact a near equality, between the root-mean-square velocity of a nuclear star cluster and that of its host. Thus, the energy per unit mass of a nuclear star cluster is always comparable to that of its host galaxy. We interpret this as evidence that nuclear star clusters do not form independently of their host galaxies, but rather that their formation and subsequent evolution are coupled. We discuss how our results can potentially be used to offer a clear and observationally testable prediction to distinguish between the different nuclear star cluster formation scenarios, and/or quantify their relative contributions.Comment: 12 pages, 3 figures, 4 tables; accepted for publication in MNRA

Prediction of sanding in subsurface hydrocarbon reservoirs.

Sand production in oil and gas wells can occur if the fluid velocity exceeds a certain value. Due to drilling operations, the mechanical stresses can exceed the load bearing capacity of the rock. As the local stresses exceed certain level, a certain amount of rock is fractured into sand. Then, the sand is carried by the fluid through the wellbore depending on the flow rate. The amount of the solids can be less than a few grams per cubic meter of reservoir fluid or an essential amount. In the later case erosion of the rock and removing sufficient quantities of rock can occur. This can produce subsurface cavities which collapse and destroy the well. When sanding is unavoidable it is necessary to estimate the characteristics of the process. Our aim was to generate a simple one-dimensional local model, which predicts the volume of sanding, the radius and the porosity of the yielded zone. Such model will help the company in the development of complex 3D models