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

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

The C23A system, an exmaple of quantitative control of plant growth associated with a data base

The architecture of the C23A (Chambers de Culture Automatique en Atmosphere Artificielles) system for the controlled study of plant physiology is described. A modular plant growth chambers and associated instruments (I.R. CO2 analyser, Mass spectrometer and Chemical analyser); network of frontal processors controlling this apparatus; a central computer for the periodic control and the multiplex work of processors; and a network of terminal computers able to ask the data base for data processing and modeling are discussed. Examples of present results are given. A growth curve analysis study of CO2 and O2 gas exchanges of shoots and roots, and daily evolution of algal photosynthesis and of the pools of dissolved CO2 in sea water are discussed

Electron hydrodynamics dilemma: whirlpools or no whirlpools

In highly viscous electron systems such as, for example, high quality graphene above liquid nitrogen temperature, a linear response to applied electric current becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena including negative nonlocal resistance and current whirlpools. It has also been shown that, although both effects originate from high electron viscosity, a negative voltage drop does not principally require current backflow. In this work, we study the role of geometry on viscous flow and show that confinement effects and relative positions of injector and collector contacts play a pivotal role in the occurrence of whirlpools. Certain geometries may exhibit backflow at arbitrarily small values of the electron viscosity, whereas others require a specific threshold value for whirlpools to emerge

Infall models of Class 0 protostars

We have carried out radiative transfer calculations of infalling, dusty envelopes surrounding embedded protostars to understand the observed properties of the recently identified ``Class 0'' sources. To match the far-infrared peaks in the spectral energy distributions of objects such as the prototype Class 0 source VLA 1623, pure collapse models require mass infall rates \sim10^{-4}\msunyr$^{-1}$. The radial intensity distributions predicted by such infall models are inconsistent with observations of VLA 1623 at sub-mm wavelengths, in agreement with the results of Andre et al. (1993) who found a density profile of $\rho \propto r^{-1/2}$ rather than the expected $\rho \propto r^{-3/2}$ gradient. To resolve this conflict, while still invoking infall to produce the outflow source at the center of VLA 1623, we suggest that the observed sub-mm intensity distribution is the sum of two components: an inner infall zone, plus an outer, more nearly constant-density region. This explanation of the observations requires that roughly half the total mass observed within 2000 AU radius of the source lies in a region external to the infall zone. The column densities for this external region are comparable to those found in the larger Oph A cloud within which VLA 1623 is embedded. The extreme environments of Class 0 sources lead us to suggest an alternative or additional interpretation of these objects: rather than simply concluding with Andre et al. that Class 0 objects only represent the earliest phases of protostellar collapse, and ultimately evolve into older ``Class I'' protostars, we suggest that many Class 0 sources could be the protostars of very dense regions. (Shortened)Comment: 22 pages, including 3 PostScript figures, accepted for publication in The Astrophysical Journa