52,591 research outputs found
The Transversal Relative Equilibria of a Hamiltonian System with Symmetry
We show that, given a certain transversality condition, the set of relative
equilibria \mcl E near p_e\in\mcl E of a Hamiltonian system with symmetry
is locally Whitney-stratified by the conjugacy classes of the isotropy
subgroups (under the product of the coadjoint and adjoint actions) of the
momentum-generator pairs of the relative equilibria. The dimension
of the stratum of the conjugacy class (K) is , where
Z(K) is the center of K, and transverse to this stratum \mcl E is locally
diffeomorphic to the commuting pairs of the Lie algebra of . The
stratum \mcl E_{(K)} is a symplectic submanifold of P near p_e\in\mcl E if
and only if is nondegenerate and K is a maximal torus of G. We also show
that there is a dense subset of G-invariant Hamiltonians on P for which all the
relative equilibria are transversal. Thus, generically, the types of
singularities that can be found in the set of relative equilibria of a
Hamiltonian system with symmetry are those types found amongst the
singularities at zero of the sets of commuting pairs of certain Lie subalgebras
of the symmetry group.Comment: 18 page
A model for evolution and extinction
We present a model for evolution and extinction in large ecosystems. The
model incorporates the effects of interactions between species and the
influences of abiotic environmental factors. We study the properties of the
model by approximate analytic solution and also by numerical simulation, and
use it to make predictions about the distribution of extinctions and species
lifetimes that we would expect to see in real ecosystems. It should be possible
to test these predictions against the fossil record. The model indicates that a
possible mechanism for mass extinction is the coincidence of a large
coevolutionary avalanche in the ecosystem with a severe environmental
disturbance.Comment: Postscript (compressed etc. using uufiles), 16 pages, with 15
embedded figure
Lakshmi Planum: A distinctive highland volcanic province
Lakshmi Planum, a broad smooth plain located in western Ishtar Terra and containing two large oval depressions (Colette and Sacajawea), has been interpreted as a highland plain of volcanic origin. Lakshmi is situated 3 to 5 km above the mean planetary radius and is surrounded on all sides by bands of mountains interpreted to be of compressional tectonic origin. Four primary characteristics distinguish Lakshmi from other volcanic regions known on the planet, such as Beta Regio: (1) high altitude, (2) plateau-like nature, (3) the presence of very large, low volcanic constructs with distinctive central calderas, and (4) its compressional tectonic surroundings. Building on the previous work of Pronin, the objective is to establish the detailed nature of the volcanic deposits on Lakshmi, interpret eruption styles and conditions, sketch out an eruption history, and determine the relationship between volcanism and the tectonic environment of the region
Secondary flow spanwise deviation model for the stators of NASA middle compressor stages
A model of the spanwise variation of deviation for stator blades is presented. Deviation is defined as the difference between the passage mean flow angle and the metal angle at the outlet of a blade element of an axial compressor stage. The variation of deviation is taken as the difference above or below that predicted by blade element, (i.e., two-dimensional) theory at any spanwise location. The variation of deviation is dependent upon the blade camber, solidity and inlet boundary layer thickness at the hub or tip end-wall, and the blade channel aspect ratio. If these parameters are known or can be calculated, the model provides a reasonable approximation of the spanwise variation of deviation for most compressor middle stage stators operating at subsonic inlet Mach numbers
An ultra-low frequency electromagnetic wave force mechanism for the ionosphere
Ultra-low frequency electromagnetic wave force mechanism for ionospheric anomalie
An Expansion Term In Hamilton's Equations
For any given spacetime the choice of time coordinate is undetermined. A
particular choice is the absolute time associated with a preferred vector
field. Using the absolute time Hamilton's equations are
+ (\delta H_{c})/(\delta \pi)=\dot{q}\Theta = V^{a}_{.;a}N\equiv exp(-\int\Theta d \ta)\pi^{N}\pi^N$. Briefly the possibility of a non-standard sympletic form
and the further possibility of there being a non-zero Finsler curvature
corresponding to this are looked at.Comment: 10 page
Mineral Trioxide Aggregate Material Use in Endodontic Treatment: A Review of the Literature
Objective
The purpose of this paper was to review the composition, properties, biocompatibility, and the clinical results involving the use of mineral trioxide aggregate (MTA) materials in endodontic treatment. Methods
Electronic search of scientific papers from January 1990 to August 2006 was accomplished using PubMed and Scopus search engines (search terms: MTA, GMTA, WMTA, mineral AND trioxide AND aggregate). Results
Selected exclusion criteria resulted in 156 citations from the scientific, peer-reviewed dental literature. MTA materials are derived from a Portland cement parent compound and have been demonstrated to be biocompatible endodontic repair materials, with its biocompatible nature strongly suggested by its ability to form hydroxyappatite when exposed to physiologic solutions. With some exceptions, MTA materials provide better microleakage protection than traditional endodontic repair materials using dye, fluid filtration, and bacterial penetration leakage models. In both animal and human studies, MTA materials have been shown to have excellent potential as pulp-capping and pulpotomy medicaments but studies with long-term follow-up are limited. Preliminary studies suggested a favorable MTA material use as apical and furcation restorative materials as well as medicaments for apexogenesis and apexification treatments; however, long-term clinical studies are needed in these areas. Conclusion
MTA materials have been shown to have a biocompatible nature and have excellent potential in endodontic use. MTA materials are a refined Portland cement material and the substitution of Portland cement for MTA products is presently discouraged. Existing human studies involving MTA materials are very promising, however, insufficient randomized, double-blind clinical studies of sufficient duration exist involving MTA for all of its clinical indications. Further clinical studies are needed in these areas
On the elastic approximation to the vacancy formation energy in metals
Isotropic elastic continuum model application to calculate energy and entropy of vacancy formation in metal crystal
Hydrogen film cooling of a small hydrogen-oxygen thrust chamber and its effect on erosion rates of various ablative materials
An experimental investigation was conducted to determine what arrangement of film-coolant-injection orifices should be used to decrease the erosion rates of small, high temperature, high pressure ablative thrust chambers without incurring a large penalty in combustion performance. All of the film cooling was supplied through holes in a ring between the outer row of injector elements and the chamber wall. The best arrangement, which had twice the number of holes as there were outer row injection elements, was also the simplest. The performance penalties, presented as a reduction in characteristic exhaust velocity efficiency, were 0.8 and 2.8 percentage points for the 10 and 20 percent cooling flows, respectively, The best film-coolant injector was then used to obtain erosion rates for 19 ablative materials. The throat erosion rate was reduced by a factor of 2.5 with a 10 percent coolant flow. Only the more expensive silica phenolic materials had low enough erosion rates to be considered for use in the nozzle throat. However, some of the cheaper materials might qualify for use in other areas of small nozzles with large throat diameters where the higher erosion rates are more acceptable
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