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 $(\mu,\xi)$ of the relative equilibria. The dimension of the stratum of the conjugacy class (K) is $\dim G+2\dim Z(K)-\dim K$, 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 $K/Z(K)$. The stratum \mcl E_{(K)} is a symplectic submanifold of P near p_e\in\mcl E if and only if $p_e$ 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 $- (\delta H_{c})/(\delta q)=\dot{\pi}+\Theta\pi,$+ (\delta H_{c})/(\delta \pi)=\dot{q}$, where$\Theta = V^{a}_{.;a}$is the expansion of the vector field. Thus there is a hitherto unnoticed term in the expansion of the preferred vector field. Hamilton's equations can be used to describe fluid motion. In this case the absolute time is the time associated with the fluid's co-moving vector. As measured by this absolute time the expansion term is present. Similarly in cosmology, each observer has a co-moving vector and Hamilton's equations again have an expansion term. It is necessary to include the expansion term to quantize systems such as the above by the canonical method of replacing Dirac brackets by commutators. Hamilton's equations in this form do not have a corresponding sympletic form. Replacing the expansion by a particle number$N\equiv exp(-\int\Theta d \ta)$and introducing the particle numbers conjugate momentum$\pi^{N}$the standard sympletic form can be recovered with two extra fields N and$\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

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

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