7,327 research outputs found
In Re the Marlborough Sounds foreshore and seabed : the effects of the Maori Land Court decision on the Crown, Maori and the public of New Zealand
Square character degree graphs yield direct products
If is a solvable group, we take to be the character degree
graph for with primes as vertices. We prove that if is a
square, then must be a direct product
Gravity currents in a porous medium at an inclined plane
We consider the release from a point source of relatively heavy fluid into a
porous saturated medium above an impermeable slope. We consider the case where
the volume of the resulting gravity current increases with time like
and show that for , at short times the current spreads
axisymmetrically, with radius , while at long times it
spreads predominantly downslope. In particular, for long times the downslope
position of the current scales like while the current extends a distance
across the slope. For , this situation is reversed
with spreading occurring predominantly downslope for short times. The governing
equations admit similarity solutions whose scaling behaviour we determine, with
the full similarity form being evaluated by numerical computations of the
governing partial differential equation. We find that the results of these
analyses are in good quantitative agreement with a series of laboratory
experiments. Finally, we briefly discuss the implications of our work for the
sequestration of carbon dioxide in aquifers with a sloping, impermeable cap.Comment: 10 pages, 6 figures - revised versio
The Growth and Structure of Double - Diffusive Cells Adjacent to a Side - Wall in a Salt - Stratified Environment
August 15-21, 2004 Measurements are reported of the rate of horizontal extension of the cells in tanks of different lengths with a range of initial salinity gradients and cooling rates (which determine the vertical height of each cell). A simple model for the cell evolution is developed. It predicts that cell growth is dependent on tank length. The mean rate of increase of cell length decreases linearly in time, as does the density gradient inside the cells, supported by both temperature and salinity gradients. The results are found to agree quantitatively with the measurements
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