Embedding Stacked Polytopes on a Polynomial-Size Grid

A stacking operation adds a $d$-simplex on top of a facet of a simplicial $d$-polytope while maintaining the convexity of the polytope. A stacked $d$-polytope is a polytope that is obtained from a $d$-simplex and a series of stacking operations. We show that for a fixed $d$ every stacked $d$-polytope with $n$ vertices can be realized with nonnegative integer coordinates. The coordinates are bounded by $O(n^{2\log(2d)})$, except for one axis, where the coordinates are bounded by $O(n^{3\log(2d)})$. The described realization can be computed with an easy algorithm. The realization of the polytopes is obtained with a lifting technique which produces an embedding on a large grid. We establish a rounding scheme that places the vertices on a sparser grid, while maintaining the convexity of the embedding.Comment: 22 pages, 10 Figure

Molecular line study of the very young protostar IRAM 04191 in Taurus: Infall, rotation, and outflow

We present a detailed millimeter line study of the circumstellar environment of the low-luminosity Class 0 protostar IRAM 04191+1522 in the Taurus molecular cloud. New line observations demonstrate that the ~14000 AU radius protostellar envelope is undergoing both extended infall and fast, differential rotation. Radiative transfer modeling of multitransition CS and C34S maps indicate an infall velocity v_inf ~ 0.15 km/s at r ~ 1500 AU and v_inf ~ 0.1 km/s up to r ~ 11000 AU, as well as a rotational angular velocity Omega ~ 3.9 x 10^{-13} rad/s, strongly decreasing with radius beyond 3500 AU down to a value Omega ~ 1.5-3 x 10^{-14} rad/s at ~ 11000 AU. Two distinct regions, which differ in both their infall and their rotation properties, therefore seem to stand out: the inner part of the envelope (r ~< 2000-4000 AU) is rapidly collapsing and rotating, while the outer part undergoes only moderate infall/contraction and slower rotation. These contrasted features suggest that angular momentum is conserved in the collapsing inner region but efficiently dissipated due to magnetic braking in the slowly contracting outer region. We propose that the inner envelope is in the process of decoupling from the ambient cloud and corresponds to the effective mass reservoir (~0.5 M_sun) from which the central star is being built. Comparison with the rotational properties of other objects in Taurus suggests that IRAM 04191 is at a pivotal stage between a prestellar regime of constant angular velocity enforced by magnetic braking and a dynamical, protostellar regime of nearly conserved angular momentum. The rotation velocity profile we derive for the inner IRAM 04191 envelope should thus set some constraints on the distribution of angular momentum on the scale of the outer Solar system at the onset of protostar/disk formation.Comment: 23 pages, 16 figures, 1 table, Accepted by Astronomy & Astrophysic

XUV lasing during strong-field assisted transient absorption in molecules

Using ab-initio non-Born-Oppenheimer simulations, we demonstrate amplification of XUV radiation in a high-harmonic generation type process using the example of the hydrogen molecular ion. A small fraction of the molecules is pumped to a dissociative Rydberg state from which IR-assisted XUV amplification is observed. We show that starting at sufficiently high IR driving field intensities the ground state molecules become quasi-transparent for XUV radiation, while due to stabilization gain from Rydberg states is maintained, thus leading to lasing from strongly driven Rydberg states. Further increase of the IR intensity even leads to gain by initially unexcited molecules, which are quickly excited by the driving IR pulse

Excess gamma-rays in the direction of the rho Ophiuchi cloud: An exotic object?

The COS-B X-ray data in the direction of the rho Oph dark cloud show an extended structure; at the same time, the region of highest intensity has a spatial distribution compatible with a localized source; 2CG353+16 which is designated Oph gamma. The possibility of an excess gamma ray flux over what is expected on the basis of the interaction of average density cosmic rays with an estimated cloud mass of 2 to 4 000 M is still open, pending an extended CO survey matching the gamma ray data. Estimates for this excess factor are in the range 2 to 4. While the cloud mass may be underestimated, it should be noted that an excess of the same order appears to be present in the nearby Oph-Sag area, well surveyed in CO with the Columbia dish. Possible reasons for a gamma ray excess, in view of two recent observational developments: an Einstein X-ray survey and a VLA radio survey, both covering the approx 2 deg diameter Oph gamma error box. Current interpretations link the gamma ray excess to the cloud gas, in which some active agent is present: stellar winds, or interaction with the North Polar Spur

Kinky Brane Worlds

We present a toy model for five-dimensional heterotic M-theory where bulk three-branes, originating in 11 dimensions from M five-branes, are modelled as kink solutions of a bulk scalar field theory. It is shown that the vacua of this defect model correspond to a class of topologically distinct M-theory compactifications. Topology change can then be analysed by studying the time evolution of the defect model. In the context of a four-dimensional effective theory, we study in detail the simplest such process, that is the time evolution of a kink and its collision with a boundary. We find that the kink is generically absorbed by the boundary thereby changing the boundary charge. This opens up the possibility of exploring the relation between more complicated defect configurations and the topology of brane-world models.Comment: 31 pages, Latex, 6 eps-figure