Finite element differential forms on cubical meshes

We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the serendipity finite elements and the rectangular BDM elements. In three dimensions they include a recent generalization of the serendipity spaces, and new H(curl) and H(div) finite element spaces. Spaces in the family can be combined to give finite element subcomplexes of the de Rham complex which satisfy the basic hypotheses of the finite element exterior calculus, and hence can be used for stable discretization of a variety of problems. The construction and properties of the spaces are established in a uniform manner using finite element exterior calculus.Comment: v2: as accepted by Mathematics of Computation after minor revisions; v3: this version corresponds to the final version for Math. Comp., after copyediting and galley proof

Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations

Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this problem for the Einstein--Christoffel (EC) symmetric hyperbolic formulation of Einstein's equations linearized around flat spacetime. First, we prescribe simple boundary conditions that make the problem well posed and preserve the constraints. Next, we indicate boundary conditions for a system that extends the linearized EC system by including the momentum constraints and whose solution solves Einstein's equations in a bounded domain

A Dipole on the Sky: Predictions for Hypervelocity Stars from the Large Magellanic Cloud

We predict the distribution of hypervelocity stars (HVSs) ejected from the Large Magellanic Cloud (LMC), under the assumption that the dwarf galaxy hosts a central massive black hole (MBH). For the majority of stars ejected from the LMC the orbital velocity of the LMC has contributed a significant fraction of their galactic rest frame velocity, leading to a dipole density distribution on the sky. We quantify the dipole using spherical harmonic analysis and contrast with the monopole expected for HVSs ejected from the Galactic Center. There is a tendril in the density distribution that leads the LMC which is coincident with the well-known and unexplained clustering of HVSs in the constellations of Leo and Sextans. Our model is falsifiable, since it predicts that Gaia will reveal a large density of HVSs in the southern hemisphere.Comment: 6 pages, ApJ (Letters), in pres

Mathematicians take a stand

We survey the reasons for the ongoing boycott of the publisher Elsevier. We examine Elsevier's pricing and bundling policies, restrictions on dissemination by authors, and lapses in ethics and peer review, and we conclude with thoughts about the future of mathematical publishing.Comment: 5 page

Colliding stellar winds in the eclipsing Wolf-Rayet binary V444 Cygni

High resolution spectra of V444 Cygni have been obtained using the International Ultraviolet Explorer Satellite. These spectra span both eclipses and include one observation at third quadrature. Together with seven archival spectra, they provide reasonably complete phase coverage for the system. The variations in the P Cygni profiles of the He(II) and N(IV) lines, imply the existence of a low density region in the WR wind. This region occupies a relatively narrow range of orbital phase coinciding with the highest terminal velocities observed in C IV. These data are interpreted to be evidence of an interaction region separating the winds of the O-star and Wolf-Rayet star

Explaining the observed velocity dispersion of dwarf galaxies by baryonic mass loss during the first collapse

In the widely adopted LambdaCDM scenario for galaxy formation, dwarf galaxies are the building blocks of larger galaxies. Since they formed at relatively early epochs when the background density was relatively high, they are expected to retain their integrity as satellite galaxies when they merge to form larger entities. Although many dwarf spheroidal galaxies (dSphs) are found in the galactic halo around the Milky Way, their phase space density (or velocity dispersion) appears to be significantly smaller than that expected for satellite dwarf galaxies in the LambdaCDM scenario. In order to account for this discrepancy, we consider the possibility that they may have lost a significant fraction of their baryonic matter content during the first infall at the Hubble expansion turnaround. Such mass loss arises naturally due to the feedback by relatively massive stars which formed in their centers briefly before the maximum contraction. Through a series of N-body simulations, we show that the timely loss of a significant fraction of the dSphs initial baryonic matter content can have profound effects on their asymptotic half-mass radius, velocity dispersion, phase-space density, and the mass fraction between residual baryonic and dark matter.Comment: 6 pages, 6 figures, accepted for publication in the Ap