Vertex-Facet Incidences of Unbounded Polyhedra

How much of the combinatorial structure of a pointed polyhedron is contained in its vertex-facet incidences? Not too much, in general, as we demonstrate by examples. However, one can tell from the incidence data whether the polyhedron is bounded. In the case of a polyhedron that is simple and "simplicial," i.e., a d-dimensional polyhedron that has d facets through each vertex and d vertices on each facet, we derive from the structure of the vertex-facet incidence matrix that the polyhedron is necessarily bounded. In particular, this yields a characterization of those polyhedra that have circulants as vertex-facet incidence matrices.Comment: LaTeX2e, 14 pages with 4 figure

Confinement of the Sun's interior magnetic field: some exact boundary-layer solutions

High-latitude laminar confinement of the Sun's interior magnetic field is shown to be possible, as originally proposed by Gough and McIntyre (1998) but contrary to a recent claim by Brun and Zahn (A&A 2006). Mean downwelling as weak as 2x10^-6cm/s -- gyroscopically pumped by turbulent stresses in the overlying convection zone and/or tachocline -- can hold the field in advective-diffusive balance within a confinement layer of thickness scale ~ 1.5Mm ~ 0.002 x (solar radius) while transmitting a retrograde torque to the Ferraro-constrained interior. The confinement layer sits at the base of the high-latitude tachocline, near the top of the radiative envelope and just above the `tachopause' marking the top of the helium settling layer. A family of exact, laminar, frictionless, axisymmetric confinement-layer solutions is obtained for uniform downwelling in the limit of strong rotation and stratification. A scale analysis shows that the flow is dynamically stable and the assumption of laminar flow realistic. The solution remains valid for downwelling values of the order of 10^-5cm/s but not much larger. This suggests that the confinement layer may be unable to accept a much larger mass throughput. Such a restriction would imply an upper limit on possible internal field strengths, perhaps of the order of hundreds of gauss, and would have implications also for ventilation and lithium burning. The solutions have interesting chirality properties not mentioned in the paper owing to space restrictions, but described at http://www.atmos-dynamics.damtp.cam.ac.uk/people/mem/papers/SQBO/solarfigure.htmlComment: 6 pages, 3 figures, to appear in conference proceedings: Unsolved Problems in Stellar Physic

Critically rotating stars in binaries - an unsolved problem -

In close binaries mass and angular momentum can be transferred from one star to the other during Roche-lobe overflow. The efficiency of this process is not well understood and constitutes one of the largest uncertainties in binary evolution. One of the problems lies in the transfer of angular momentum, which will spin up the accreting star. In very tight systems tidal friction can prevent reaching critical rotation, by locking the spin period to the orbital period. Accreting stars in systems with orbital periods larger than a few days reach critical rotation after accreting only a fraction of their mass, unless there is an effective mechanism to get rid of angular momentum. In low mass stars magnetic field might help. In more massive stars angular momentum loss will be accompanied by strong mass loss. This would imply that most interacting binaries with initial orbital periods larger than a few days evolve very non-conservatively. In this contribution we wish to draw attention to the unsolved problems related to mass and angular momentum transfer in binary systems. We do this by presenting the first results of an implementation of spin up by accretion into the TWIN version of the Eggleton stellar evolution code.Comment: 5 pages, 1 figure, to appear in the proceedings of the conference "Unsolved Problems in Stellar Physics", Cambridge, 2-6 July 200

A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh-Benard convection

Experimental measurements of properties of the large-scale circulation (LSC) in turbulent convection of a fluid heated from below in a cylindrical container of aspect ratio one are presented and used to test a model of diffusion in a potential well for the LSC. The model consists of a pair of stochastic ordinary differential equations motivated by the Navier-Stokes equations. The two coupled equations are for the azimuthal orientation theta_0, and for the azimuthal temperature amplitude delta at the horizontal midplane. The dynamics is due to the driving by Gaussian distributed white noise that is introduced to represent the action of the small-scale turbulent fluctuations on the large-scale flow. Measurements of the diffusivities that determine the noise intensities are reported. Two time scales predicted by the model are found to be within a factor of two or so of corresponding experimental measurements. A scaling relationship predicted by the model between delta and the Reynolds number is confirmed by measurements over a large experimental parameter range. The Gaussian peaks of probability distributions p(delta) and p(\dot\theta_0) are accurately described by the model; however the non-Gaussian tails of p(delta) are not. The frequency, angular change, and amplitude bahavior during cessations are accurately described by the model when the tails of the probability distribution of $\delta$ are used as experimental input.Comment: 17 pages, 17 figure

Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

For rapidly rotating turbulent Rayleigh–Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one, whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like Ra1/4Ek2/3 where the Ekman number Ek decreases with increasing rotation rate

Plume motion and large-scale circulation in a cylindrical Rayleigh-B\'enard cell

We used the time correlation of shadowgraph images to determine the angle $\Theta$ of the horizontal component of the plume velocity above (below) the center of the bottom (top) plate of a cylindrical Rayleigh-B\'enard cell of aspect ratio $\Gamma \equiv D/L = 1$ ($D$ is the diameter and $L \simeq 87$ mm the height) in the Rayleigh-number range $7\times 10^7 \leq R \leq 3\times 10^{9}$ for a Prandtl number $\sigma = 6$. We expect that $\Theta$ gives the direction of the large-scale circulation. It oscillates time-periodically. Near the top and bottom plates $\Theta(t)$ has the same frequency but is anti-correlated.Comment: 4 pages, 6 figure

Distribution and Conservation Status of the Rusty Gravedigger, Cambarus miltus, a Poorly Known Gulf Coastal Crayfish

Cambarus (Lacunicambarus) miltus (Rusty Gravedigger Crayfi sh) is a primary burrowing crayfi sh known from a limited portion of the Gulf Coastal region of the United States. The lack of form I males in collections has in the past prevented specieslevel identifi cations and hampered conservation reviews. We conducted an intensive status survey for C. miltus during 2007 and 2008. Our results suggest that the species is much more widespread than previously known and that conservation attention is unwarranted. Preferred habitat for the species is ephemerally fl ooded and thinly wooded fl oodplains of small streams and swamps

Thermocapillary Migration and Interactions of Bubbles and Drops

When a drop or bubble is placed in another fluid and subjected to the action of a temperature gradient, the drop will move. Such motion is a direct consequence of the variation of interfacial tension with temperature, and is termed thermocapillary migration. This paper discusses results from experiments conducted in reduced gravity on the thermocapillary motion of bubbles and drops