Structure properties of 226{}^{226}Th and 256,258,260{}^{256,258,260}Fm fission fragments: mean field analysis with the Gogny force

The constrained Hartree-Fock-Bogoliubov method is used with the Gogny interaction D1S to calculate potential energy surfaces of fissioning nuclei ${}^{226}$Th and ${}^{256,258,260}$Fm up to very large deformations. The constraints employed are the mass quadrupole and octupole moments. In this subspace of collective coordinates, many scission configurations are identified ranging from symmetric to highly asymmetric fragmentations. Corresponding fragment properties at scission are derived yielding fragment deformations, deformation energies, energy partitioning, neutron binding energies at scission, neutron multiplicities, charge polarization and total fragment kinetic energies.Comment: 15 pages, 23 figures, accepted for publication in Phys. Rev. C (2007

A generalization of the Lyndon--Hochschild--Serre spectral sequence with applications to group cohomology and decompositions of groups

We set up a Grothendieck spectral sequence which generalizes the Lyndon--Hochschild--Serre spectral sequence for a group extension K\mono G\epi Q by allowing the normal subgroup $K$ to be replaced by a subgroup, or family of subgroups which satisfy a weaker condition than normality. This is applied to establish a decomposition theorem for certain groups as fundamental groups of graphs of Poincar\'e duality groups. We further illustrate the method by proving a cohomological vanishing theorem which applies for example to Thompson's group $F$.Comment: 22 page

Weakly nonlinear ion sound waves in gravitational systems

Ion sound waves are studied in a plasma subject to gravitational field. Such systems are interesting by exhibiting a wave growth that is a result of energy flux conservation in inhomogeneous systems. The increasing wave amplitude gives rise to an enhanced interaction between waves and plasma particles that can be modeled by a modified Korteweg-de Vries equation. Analytical results are compared with numerical Particle-in-Cell simulations of the problem. Our code assumes isothermally Boltzmann distributed electrons while the ion component is treated as a collection of individual particles interacting through collective electric fields. Deviations from quasi neutrality are allowed for.Comment: 30 pages, 9 figure

Zero area singularities in general relativity and inverse mean curvature flow

First we restate the definition of a Zero Area Singularity, recently introduced by H. Bray. We then consider several definitions of mass for these singularities. We use the Inverse Mean Curvature Flow to prove some new results about the mass of a singularity, the ADM mass of the manifold, and the capacity of the singularity.Comment: 13 page

A closer look at a coronal loop rooted in a sunspot umbra

Extreme UV (EUV) and X-ray loops in the solar corona connect regions of enhanced magnetic activity, but they are not usually rooted in the dark umbrae of sunspots because the strong magnetic field found there suppresses convection. This means that the Poynting flux of magnetic energy into the upper atmosphere is not significant within the umbra as long as there are no light bridges or umbral dots. Here we report a rare observation of a coronal loop rooted in the dark umbra of a sunspot without any traces of light bridges or umbral dots. We used the slit-jaw images and spectroscopic data from IRIS and concentrate on the line profiles of O IV and Si IV that show persistent strong redshifted components in the loop rooted in the umbra. Using the ratios of O IV, we can estimate the density and thus investigate the mass flux. The coronal context and temperature diagnostics of these observations is provided through the EUV channels of AIA. The coronal loop, embedded within cooler downflows, hosts supersonic downflows. The speed of more than 100 km s$^{-1}$ is on the same order of magnitude in the transition region lines of O IV and Si IV, and is even seen at comparable speed in the chromospheric Mg II lines. At a projected distance of within $1"$ of the footpoint, we see a shock transition to smaller downflow speeds of about 15 km s$^{-1}$ being consistent with mass conservation across a stationary isothermal shock. We see no direct evidence for energy input into the loop because the loop is rooted in the dark uniform part of the umbra with no light bridges or umbral dots near by. Thus one might conclude that we are seeing a siphon flow driven from the footpoint at the other end of the loop. However, for a final result data of similar quality at the other footpoint are needed, but this is too far away to be covered by the IRIS field of view.Comment: Accepted for publication in Astronomy and Astrophysics (abridged abstract

The angular momentum of a magnetically trapped atomic condensate

For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this paper we investigate the relationship between the values of the sum/difference angular momentums for an atomic condensate inside a magnetic trap and the associated gauge potential induced by the adiabatic approximation. Our result provides significant new insight into the vorticity of magnetically trapped atomic quantum gases.Comment: 4 pages, 1 figure

Existence and stability of solitons for the nonlinear Schr\"odinger equation on hyperbolic space

We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space.Comment: New: As noted in Banica-Duyckaerts (arXiv:1411.0846), Section 5 should read that for sufficiently large mass, sub-critical problems can be solved via energy minimization for all d \geq 2 and as a result Cazenave-Lions results can be applied in Section 6 with the same restriction. These requirements were addressed by the subsequent work with Metcalfe and Taylor in arXiv:1203.361