The evolution of energy in flow driven by rising bubbles

We investigate by direct numerical simulations the flow that rising bubbles cause in an originally quiescent fluid. We employ the Eulerian-Lagrangian method with two-way coupling and periodic boundary conditions. In order to be able to treat up to 288000 bubbles, the following approximations and simplifications had to be introduced: (i) The bubbles were treated as point-particles, thus (ii) disregarding the near-field interactions among them, and (iii) effective force models for the lift and the drag forces were used. In particular, the lift coefficient was assumed to be 1/2, independent of the bubble Reynolds number and the local flow field. The results suggest that large scale motions are generated, owing to an inverse energy cascade from the small to the large scales. However, as the Taylor-Reynolds number is only in the range of 1, the corresponding scaling of the energy spectrum with an exponent of -5/3 cannot develop over a pronounced range. In the long term, the property of local energy transfer, characteristic of real turbulence, is lost and the input of energy equals the viscous dissipation at all scales. Due to the lack of strong vortices the bubbles spread rather uniformly in the flow. The mechanism for uniform spreading is as follows: Rising bubbles induce a velocity field behind them that acts on the following bubbles. Owing to the shear, those bubbles experience a lift force which make them spread to the left or right, thus preventing the formation of vertical bubble clusters and therefore of efficient forcing. Indeed, when the lift is artifically put to zero in the simulations, the flow is forced much more efficiently and a more pronounced energy accumulates at large scales is achieved.Comment: 9 pages, 7 figure

Crustal structure beneath the Trondelag Platform and adjacent areas of the Mid-Norwegian margin, as derived from wide-angle seismic and potential field data

The outer mid-Norwegian margin is characterized by strong breakup magmatism and has been extensively surveyed. The crustal structure of the inner continental shelf, however, is less studied, and its relation to the onshore geology, Caledonian structuring, and breakup magmatism remains unclear. Two Ocean Bottom Seismometer profiles were acquired across the Trøndelag Platform in 2003, as part of the Euromargins program. Additional-land stations recorded the marine shots. The P-wave data were modeled by ray-tracing, supported by gravity modeling. Older multi-channel seismic data allowed for interpretation of stratigraphy down to the top of the Triassic. Crystalline basement velocity is ~6 km s-1 onshore. Top basement is difficult to identify offshore, as velocities (5.3-5.7 km s-1) intermediate between typical crystalline crust and Mesozoic sedimentary strata appear 50-80 km from the coast. This layer thickens towards the Klakk-Ytreholmen Fault Complex and predates Permian and later structur-ing. The velocities indicate sedimentary rocks, most likely Devonian. Onshore late- to post-Caledonian detachments have been proposed to extend offshore, based on the magnetic anomaly pattern. We do not find the expected correlation between upper basement velocity structure and detachments. However, there is a distinct, dome-shaped lower-crustal body with a velocity of 6.6-7.0 km s-1. This is thickest under the Froan Basin, and the broad magnetic anomaly used to delineate the detachments correlates with this. The proposed offshore continuation of the detachments thus appears- unreliable. While we find indications of high density and velocity (~7.2 km s-1) lower crust under the Rås Basin, similar to the proposed igneous underplating of the outer margin, this is poorly constrained near the end of our profiles. The gravity field indicates that this body may be continuous from the pre-breakup basement structures of the Utgard High to the Frøya High, suggesting that it could be an island arc or oceanic terrane-accreted during the Caledonian orogeny. Thus, we find no clear evidence of early Cenozoic igneous underplating of the inner part of the shelf

WHAM Observations of H-alpha Emission from High Velocity Clouds in the M, A, and C Complexes

The first observations of the recently completed Wisconsin H-Alpha Mapper (WHAM) facility include a study of emission lines from high velocity clouds in the M, A, and C complexes, with most of the observations on the M I cloud. We present results including clear detections of H-alpha emission from all three complexes with intensities ranging from 0.06 R to 0.20 R. In every observed direction where there is significant high velocity H I gas seen in the 21 cm line we have found associated ionized hydrogen emitting the H-alpha line. The velocities of the H-alpha and 21 cm emission are well correlated in every case except one, but the intensities are not correlated. There is some evidence that the ionized gas producing the H-alpha emission envelopes the 21 cm emitting neutral gas but the H-alpha "halo", if present, is not large. If the H-alpha emission arises from the photoionization of the H I clouds, then the implied Lyman continuum flux F_{LC} at the location of the clouds ranges from 1.3 to 4.2 x 10^5 photons cm^{-2} s^{-1}. If, on the other hand, the ionization is due to a shock arising from the collision of the high-velocity gas with an ambient medium in the halo, then the density of the pre-shocked gas can be constrained. We have also detected the [S II] 6716 angstrom line from the M I cloud and have evidence that the [S II] to H-alpha ratio varies with location on the cloud.Comment: 32 pages, 18 figures, to appear in ApJ (Sept. 10, 1998

Stanley's conjecture for critical ideals

Let S=K[x_1,x_2,...,x_n] be a polynomial ring in n variables over a field K. Stanley's conjecture holds for the modules I and S/I, when I is a critical monomial ideal. We calculate the Stanley depth of S/I when I is a canonical critical monomial ideal. For non critical monomial ideals we show the existence of a Stanley ideal with the same depth and Hilbert function.Comment: 5 page

Tidal Streams as Probes of the Galactic Potential

We explore the use of tidal streams from Galactic satellites to recover the potential of the Milky Way. Our study is motivated both by the discovery of the first lengthy stellar stream in the halo (\cite{it98}) and by the prospect of measuring proper motions of stars brighter than 20th magnitude in such a stream with an accuracy of $\sim 4\mu as/$yr, as will be possible with the Space Interferometry Mission (SIM). We assume that the heliocentric radial velocities of these stars can be determined from supporting ground-based spectroscopic surveys, and that the mass and phase-space coordinates of the Galactic satellite with which they are associated will also be known to SIM accuracy. Using results from numerical simulations as trial data sets, we find that, if we assume the correct form for the Galactic potential, we can predict the distances to the stars as a consequence of the narrow distribution of energy expected along the streams. We develop an algorithm to evaluate the accuracy of any adopted potential by requiring that the satellite and stars recombine within a Galactic lifetime when their current phase-space coordinates are integrated backwards. When applied to a four-dimensional grid of triaxial logarithmic potentials, with varying circular velocities, axis ratios and orientation of the major-axis in the disk plane, the algorithm can recover the parameters used for the Milky Way in a simulated data set to within a few percent using only 100 stars in a tidal stream.Comment: Revised version - original algorithm generalised to be applicable to any potential shape. LaTeX, 12 pages including 3 figures. To be published in ApJ Letter

Modulating the Properties of Azulene‐Containing Polymers through Controlled Incorporation of Regioisomers

Two libraries of random conjugated polymers are presented that incorporate varying ratios of regioisomeric azulene units connected via the 5‐membered or 7‐membered ring in combination with bithiophene or fluorene comonomers. It is demonstrated that the optoelectronic and stimuli‐responsive properties of the materials can be systematically modulated by tuning the relative percentage of each azulene building block in the polymer backbone. Significantly, these materials exhibit stimuli‐responsive behavior in the solid state with spin‐coated thin films undergoing rapid and reversible color switching. Ultimately, this work introduces a new design strategy in which the optoelectronic properties of conjugated polymers can be modulated by varying only the regiochemistry of the constituent building blocks along a polymer chain

The Magellanic Stream and the density of coronal gas in the Galactic halo

The properties of the Magellanic Stream constrain the density of coronal gas in the distant Galactic halo. We show that motion through ambient gas can strongly heat Stream clouds, driving mass loss and causing evaporation. If the ambient gas density is too high, then evaporation occurs on unreasonably short timescales. Since heating dominates drag, tidal stripping appears to be responsible for producing the Stream. Requiring the survival of the cloud MS IV for 500 Myr sets an upper limit on the halo gas density n_H< 10^{-5} cm^{-3} at 50 kpc, roughly a factor of 10 lower than that estimated from the drag model of Moore & Davis (1994). Implications for models of the evolution of gas in galaxy halos are discussed.Comment: 4 pages, 1 figure, in press, ApJ

Topology of Neutral Hydrogen Within the Small Magellanic Cloud

In this paper, genus statistics have been applied to an HI column density map of the Small Magellanic Cloud in order to study its topology. To learn how topology changes with the scale of the system, we provide the study of topology for column density maps at varying resolution. To evaluate the statistical error of the genus we randomly reassign the phases of the Fourier modes while keeping the amplitudes. We find, that at the smallest scales studied ($40 {pc}\leq\lambda\leq 80 {pc}$) the genus shift is in all regions negative, implying a clump topology. At the larger scales ($110 {pc}\leq\lambda\leq 250 {pc}$) the topology shift is detected to be negative in 4 cases and positive (``swiss cheese'' topology) in 2 cases. In 4 regions there is no statistically significant topology shift at large scales