Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.

New characterizations for hyperbolic cylinders in anti-de Sitter spaces

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H-1(n+1) with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders H-m(c(1)) x Hn-m(c(2)), 1 <= m <= n - 1, as the only such hypersurfaces with (n - 1) principal curvatures with the same sign everywhere. In particular we prove that a complete maximal spacelike hypersurface in H-1(5) with negative constant Gauss-Kronecker curvature is isometric to H-1(c(1)) x H-3(c(2)). (C) 2012 Elsevier Inc. All rights reserved.

Effect of Si addition on Ca- and P-impregnated implant surfaces with nanometer-scale roughness: an experimental study in dogs

Objectives: To investigate the effect of Si addition on a nanometer-scale roughness Ca and P implant surfaces in a canine tibia model by biomechanical and histomorphometric evaluations. Material and methods: The implant surfaces comprised a resorbable media CaP microblasted (control) and a CaP resorbable media + silica-boost microblasted (experimental) surfaces. Surfaces were characterized by scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and optical interferometry (IFM) down to the nanometric level. The animal model involved the bilateral placement of control (n = 24) and experimental surface (n = 24) implants along the proximal tibiae of six dogs, remaining in vivo for 2 or 4 weeks. After euthanization, half of the specimens were torquedto- interface failure, and the other half was subjected to histomorphologic and bone-to-implant contact (BIC) evaluation. Torque and BIC statistical evaluation was performed by the Friedman test at 95% level of significance, and comparisons between groups was performed by the Dunn test. Results: IFM and SEM observations depicted comparable roughness parameters for both implant surfaces on the micrometer and nanometer scales. XPS analysis revealed similar chemical composition, except for the addition of Si on the experimental group. Torque-to-interface failure and BIC mean values showed no significant differences (P = 0.25 and 0.51, respectively) at both 2- and 4-week evaluation points for experimental and control groups. Early bone healing histomorphologic events were similar between groups. Conclusions: The experimental surface resulted in not significantly different biomechanical fixation and BIC relative to control. Both surfaces were biocompatible and osseoconductive.

Biomechanical and histologic evaluation of non-washed resorbable blasting media and alumina-blasted/acid-etched surfaces

Objectives: To compare the biomechanical fixation and histomorphometric parameters between two implant surfaces: non-washed resorbable blasting media (NWRBM) and alumina-blasted/acid-etched (AB/AE), in a dog model. Material and methods: The surface topography was assessed by scanning electron microscopy, optical interferometry and chemistry by X-ray photoelectron spectroscopy (XPS). Six beagle dogs of similar to 1.5 years of age were utilized and each animal received one implant of each surface per limb (distal radii sites). After a healing period of 3 weeks, the animals were euthanized and half of the implants were biomechanically tested (removal torque) and the other half was referred to nondecalcified histology processing. Histomorphometric analysis considered bone-to-implant contact (BIC) and bone area fraction occupancy (BAFO). Following data normality check with the Kolmogorov-Smirnov test, statistical analysis was performed by paired t-tests at 95% level of significance. Results: Surface roughness parameters Sa (average surface roughness) and Sq (mean root square of the surface) were significantly lower for the NWRBM compared with AB/ AE. The XPS spectra revealed the presence of Ca and P in the NWRBM. While no significant differences were observed for both BIC and BAFO parameters (P>0.35 and P>0.11, respectively), a significantly higher level of torque was observed for the NWRBM group (P = 0.01). Bone morphology was similar between groups, which presented newly formed woven bone in proximity with the implant surfaces. Conclusion: A significant increase in early biomechanical fixation was observed for implants presenting the NWRBM surface.

Issues on the mean stress effect in fretting fatigue of a 7050-T7451 Al alloy posed by new experimental data

The aims of this work are: (i) to produce new experimental data for fretting fatigue considering the presence of a mean bulk stress and (ii) to assess two design methodologies against failure by fretting fatigue. Tests on a cylinder–flat contact configuration were conducted using a fretting apparatus mounted on a servo-hydraulic machine. The material used for both the pads and fatigue specimen was an aeronautical 7050-T7451 Al alloy. The experimental program was designed with all relevant parameters, apart from the mean bulk load (always applied before the contact loads), kept constant. The mean bulk stress varied from compressive to tensile values while maintaining a high peak pressure in order to encourage crack initiation. Two methodologies against fretting fatigue are proposed and confronted against the experimental data. The non-local stress-based methodology considers the evaluation of a critical plane fatigue criterion at the center of a process zone located beneath the contacting surfaces. The results showed that it correctly predicts crack initiation, but was not capable to provide successful prediction of the integrity of the specimens. Alternatively, we considered a crack arrest criterion which has the potential to provide a more complete description about the integrity of the specimens.