Applying MOG to lensing: Einstein rings, Abell 520 and the Bullet Cluster

We investigate gravitational lensing in the context of the MOG modified theory of gravity. Using a formulation of the theory with no adjustable or fitted parameters, we present the MOG equations of motion for slow, nonrelativistic test particles and for ultrarelativistic test particles, such as rays of light. We demonstrate how the MOG prediction for the bending of light can be applied to astronomical observations. Our investigation first focuses on a small set of strong lensing observations where the properties of the lensing objects are found to be consistent with the predictions of the theory. We also present an analysis of the colliding clusters 1E0657-558 (known also as the Bullet Cluster) and Abell 520; in both cases, the predictions of the MOG theory are in good agreement with observation.Comment: 14 pages, 2 figures; final proof before publicatio

Quantum ergodicity for restrictions to hypersurfaces

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple dynamical condition, the restrictions of eigenstates to N are also quantum ergodic.Comment: 22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearit

Experimental Testbeds for ECOSEL: A Market Framework for Private Provision of Forest Ecosystem Services

We attempt to design a market framework (which we call ECOSEL) for private provision of forest ecosystem services. ECOSEL is a non-regulatory framework that uses a voluntary public good provision mechanism (in a form of an auction) in conjunction with a multiobjective optimization algorithm to create a market for forest ecosystem services. It is expected to be attractive to the demand side of the ecosystem service market since only Pareto-efficient bundles of services are offered for auction, and it is expected to be attractive to the supply side as well by creating a source of non-timber income for forest landowners. ECOSEL is capable of flexible response to demand for other relevant dimensions of forest-related environmental amenities such as biodiversity, viewshed or recreational services. Following Roth’s (2002) advice on behavior of economists as “market engineers”, we use both experimental economics to improve the design of the ecosystem services market. Concurrently, we provide experimental evidence on the efficiency and revenue-generating properties of a multi-good subscription game of incomplete information.Environmental Economics and Policy, Marketing,

On the Azimuthal Stability of Shock Waves around Black Holes

Analytical studies and numerical simulations of time dependent axially symmetric flows onto black holes have shown that it is possible to produce stationary shock waves with a stable position both for ideal inviscid and for moderately viscous accretion disks. We perform several two dimensional numerical simulations of accretion flows in the equatorial plane to study shock stability against non-axisymmetric azimuthal perturbations. We find a peculiar new result. A very small perturbation seems to produce an instability as it crosses the shock, but after some small oscillations, the shock wave suddenly transforms into an asymmetric closed pattern, and it stabilizes with a finite radial extent, despite the inflow and outflow boundary conditions are perfectly symmetric. The main characteristics of the final flow are: 1) The deformed shock rotates steadily without any damping. It is a permanent feature and the thermal energy content and the emitted energy vary periodically with time. 2) This behavior is also stable against further perturbations. 3) The average shock is still very strong and well defined, and its average radial distance is somewhat larger than that of the original axially symmetric circular shock. 4) Shocks obtained with larger angular momentum exhibit more frequencies and beating phenomena. 5) The oscillations occur in a wide range of parameters, so this new effect may have relevant observational consequences, like (quasi) periodic oscillations, for the accretion of matter onto black holes. Typical time scales for the periods are 0.01 and 1000 seconds for black holes with 10 and 1 million solar mass, respectively.Comment: 15 pages, 7 figures, accepted by the Astrophysical Journa

Stellar winds, dead zones, and coronal mass ejections

Axisymmetric stellar wind solutions are presented, obtained by numerically solving the ideal magnetohydrodynamic (MHD) equations. Stationary solutions are critically analysed using the knowledge of the flux functions. These flux functions enter in the general variational principle governing all axisymmetric stationary ideal MHD equilibria. The magnetized wind solutions for (differentially) rotating stars contain both a `wind' and a `dead' zone. We illustrate the influence of the magnetic field topology on the wind acceleration pattern, by varying the coronal field strength and the extent of the dead zone. This is evident from the resulting variations in the location and appearance of the critical curves where the wind speed equals the slow, Alfven, and fast speed. Larger dead zones cause effective, fairly isotropic acceleration to super-Alfvenic velocities as the polar, open field lines are forced to fan out rapidly with radial distance. A higher field strength moves the Alfven transition outwards. In the ecliptic, the wind outflow is clearly modulated by the extent of the dead zone. The combined effect of a fast stellar rotation and an equatorial `dead' zone in a bipolar field configuration can lead to efficient thermo-centrifugal equatorial winds. Such winds show both a strong poleward collimation and some equatorward streamline bending due to significant toroidal field pressure at mid-latitudes. We discuss how coronal mass ejections are then simulated on top of the transonic outflows.Comment: scheduled for Astrophys. J. 530 #2, Febr.20 2000 issue. 9 figures (as 6 jpeg and 8 eps files

Mechanical Behavior and Failure Analysis of Prosthetic Retaining Screws after Long‐term Use In Vivo. Part 3: Preload and Tensile Fracture Load Testing

Purpose: The aim of this study was to determine the preload and tensile fracture load values of prosthetic retaining screws after long‐term use in vivo compared to unused screws (controls). Additionally, the investigation addressed whether the preload and fracture load values of prosthetic retaining screws reported by the manufacturer become altered after long‐term use in vivo. Materials and Methods: For preload testing, 10 new screws (controls) from Nobel Biocare (NB) and 73 used retaining screws [58 from NB and 15 from Sterngold (SG)] were subjected to preload testing. For tensile testing, eight controls from NB and 58 used retaining screws (46 from NB and 12 from SG) were subjected to tensile testing. Used screws for both tests were in service for 18–120 months. A custom load frame, load cell, and torque wrench setup were used for preload testing. All 83 prosthetic screws were torqued once to 10 Ncm, and the produced preload value was recorded (N) using an X–Y plotter. Tensile testing was performed on a universal testing machine and the resulting tensile fracture load value was recorded (N). Preload and tensile fracture load values were analyzed with 2‐way ANOVA and Tukey post‐hoc tests. Results: There was a significant difference between preload values for screws from NB and screws from SG (p \u3c 0.001). The preload values for gold alloy screws from NB decreased as the number of years in service increased. There was a significant difference between tensile fracture values for the three groups (gold alloy screws from NB and SG and palladium alloy screws from NB) at p \u3c 0.001. The tensile fracture values for gold alloy screws from NB and SG decreased as the number of years in service increased. Conclusions: In fixed detachable hybrid prostheses, perhaps as a result of galling, the intended preload values of prosthetic retaining screws may decrease with increased in‐service time. The reduction of the fracture load value may be related to the increase of in‐service time; however, the actual determination of this relationship is not possible from this study alone

Mechanical Behavior and Failure Analysis of Prosthetic Retaining Screws after Long‐term Use in vivo. Part 4: Failure Analysis of 10 Fractured Retaining Screws Retrieved from Three Patients

Purpose: The aim of this study was to perform a failure analysis on fractured prosthetic retaining screws after long‐term use in vivo. Additionally, the study addresses the commonly asked question regarding whether complex repeated functional occlusal forces initiate fatigue‐type cracks in prosthetic retaining screws. Materials and Methods: Ten fractured prosthetic retaining screws retrieved from three patients treated with fixed detachable hybrid prostheses were subjected to a failure analysis. In patients 1 and 2, the middle three retaining screws of the prostheses were found fractured at retrieval time after they had been in service for 20 and 19 months, respectively. In patient 3, the middle three and one of the posterior retaining screws were found to be fractured at retrieval after they had been in service for 18 months. Low power stereomicroscopy and high‐power scanning electron microscopy (SEM) were performed to analyze the fractured surfaces of the retaining screws examining fatigue cracks in greater detail. Results: Typical fatigue failure characterized by ratchet mark formation was revealed by light microscopy and SEM for all examined screws. Using low magnification light microscopy, ratchet marks were visible on the fracture surfaces of only two screws. SEM examination revealed all three classical stages of fatigue failure, and it was possible to see the ratchet marks on the fracture surfaces of all specimens, indicating a fatigue zone. The final catastrophic overload fracture appeared fibrous, indicating ductile fracture. The final overload ductile fracture surfaces showed equiaxed dimples, suggesting tensile overload in all examined screws except in two specimens that showed an elongated dimple pattern indicating shear/tearing overload forces. Conclusions: Fracture of prosthetic retaining screws in hybrid prostheses occurs mainly through a typical fatigue mode involving mostly the middle anterior three screws. Fatigue cracks can grow in more than one prosthetic retaining screw, leading to fracture before the patient or clinician determines that any problem exists

Mechanical Behavior and Failure Analysis of Prosthetic Retaining Screws after Long‐Term Use In Vivo. Part 2: Metallurgical and Microhardness Analysis

Abstract Purpose: This study involved testing and analyzing multiple retrieved prosthetic retaining screws after long‐term use in vivo to: (1) detect manufacturing defects that could affect in‐service behavior; (2) characterize the microstructure and alloy composition; and (3) further characterize the wear mechanism of the screw threads. Materials and Methods: Two new (control) screws from Nobel Biocare (NB) and 18 used (in service 18–120 months) retaining screws [12 from NB and 6 from Sterngold (SG)] were: (1) metallographically examined by light microscopy and scanning electron microscopy (SEM) to determine the microstructure; (2) analyzed by energy dispersive X‐ray (EDX) microanalysis to determine the qualitative and semiquantitative average alloy and individual phase compositions; and (3) tested for Vickers microhardness. Results: Examination of polished longitudinal sections of the screws using light microscopy revealed a significant defect in only one Group 4 screw. No significant defects in any other screws were observed. The defect was considered a “seam” originating as a “hot tear” during original casting solidification of the alloy. Additionally, the examination of longitudinal sections of the screws revealed a uniform homogeneous microstructure in some groups, while in other groups the sections exhibited rows of second phase particles. The screws for some groups demonstrated severe deformation of the lower threads and the bottom part of the screw leading to the formation of crevices and grooves. Some NB screws were comprised of Au‐based alloy with Pt, Cu, and Ag as alloy elements, while others (Groups 4 and 19) were Pd‐based with Ga, Cu, and Au alloy elements. The microstructure was homogeneous with fine or equiaxed grains for all groups except Group 4, which appeared inhomogeneous with anomalous grains. SG screws demonstrated a typical dendritic structure and were Au‐based alloy with Cu and Ag alloy elements. There were differences in the microhardness of gold alloy screws from NB and SG as well as palladium alloy screws from NB. Conclusions: Significant differences within NB retaining screws and between NB and SG screws were found for microstructure, major alloy constituents, and microhardness