Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II -- Spheroidal Cavity --

We derive a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences and discontinuities occurring at bifurcation points and in the spherical limit, the trace integrals over the action-angle variables are performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell energies are in good agreement with quantum-mechanical results. We find that the births of three-dimensional orbits through the bifurcations of planar orbits in the equatorial plane lead to considerable enhancement of shell effect for superdeformed shapes.Comment: 49 pages, 18 figures, using PTPTeX.cls(included), submitted to Prog. Theor. Phy

Symmetry Breaking and Bifurcations in the Periodic Orbit Theory; 1, Elliptic Billiard

We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all bifurcation points of the short diameter orbit and its repetitions, and possesses the correct limit of the circular billiard at zero eccentricity. Away from the circular limit and the bifurcations, it reduces to the usual (extended) Gutzwiller trace formula which for the leading-order families of periodic orbits is identical to the result of Berry and Tabor. We show that the circular disk limit of the diameter-orbit contribution is also reached through contributions from closed (periodic and non-periodic) orbits of hyperbolic type with an even number of reflections from the boundary. We obtain the Maslov indices depending on deformation and energy in terms of the phases of the complex error and Airy functions. We find enhancement of the amplitudes near the common bifurcation points of both short-diameter and hyperbolic orbits. The calculated semiclassical level densities and shell energies are in good agreement with the quantum mechanical ones

Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials

We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials near their saddlesComment: LaTeX revtex4, 38 pages, 7 PostScript figures, 2 table

Modification of the Ceramic Implant Surfaces from Zirconia by the Magnetron Sputtering of Different Calcium Phosphate Targets: A Comparative Study

In this study, thin calcium phosphate (Ca-P) coatings were deposited on zirconia substrates by radiofrequency (RF) magnetron sputtering using different calcium phosphate targets (calcium phosphate tribasic (CPT), hydroxyapatite (HA), calcium phosphate monobasic, calcium phosphate dibasic dehydrate (DCPD) and calcium pyrophosphate (CPP) powders). The sputtering of calcium phosphate monobasic and DCPD powders was carried out without an inert gas in the self-sustaining plasma mode. The physico-chemical, mechanical and biological properties of the coatings were investigated. Cell adhesion on the coatings was examined using mesenchymal stem cells (MSCs). The CPT coating exhibited the best cell adherence among all the samples, including the uncoated zirconia substrate. The cells were spread uniformly over the surfaces of all samples