On concentrated loads and Green's functions in elastostatics

This investigation is concerned with the notion of concentrated loads in classical elastostatics and related issues. Following a limit treatment of problems involving concentrated internal and surface loads, the orders of the ensuing displacements and stress singularities, as well as the stress resultants of the latter, are determined. These conclusions are taken as a basis for an alternative direct formulation of concentrated-load problems, the completeness of which is established through an appropriate uniqueness theorem. In addition, the present work supplies a reciprocal theorem and an integral representation-theorem applicable to singular problems of the type under consideration. Finally, in the course of the analysis presented here, the theory of Green's functions in elastostatics is extended.

Dynamical models for the Earth's geoid

The Earth's largest geoid anomalies occur at the lowest spherical harmonic degrees, or longest wavelengths, and are primarily the result of mantle convection. Thermal density contrasts due to convection are partially compensated by boundary deformations due to viscous flow whose effects must be included in order to obtain a dynamically consistent model for the geoid. These deformations occur rapidly with respect to the timescale for convection, and we have analytically calculated geoid response kernels for steady-state, viscous, incompressible, self-gravitating, layered Earth models which include the deformation of boundaries due to internal loads. Both the sign and magnitude of geoid anomalies depend strongly upon the viscosity structure of the mantle as well as the possible presence of chemical layering.

Correlations of various global geophysical data sets with the observed geoid can be used to construct theoretical geoid models which constrain the dynamics of mantle convection. Surface features such as topography and plate velocities are not obviously related to the low-degree geoid, with the exception of subduction zones which are characterized by geoid highs (degrees 4-9). Recent models for seismic heterogeneity in the mantle provide additional constraints, and much of the low-degree (2-3) geoid can be attributed to seismically inferred density anomalies in the lower mantle. The Earth's largest geoid highs are underlain by low density material in the lower mantle, thus requiring compensating deformations of the Earth's surface. A dynamical model for whole mantle convection with a low viscosity upper mantle can explain these observations and successfully predicts more than 80% of the observed geoid variance.

Temperature variations associated with density anomalies in the man tie cause lateral viscosity variations whose effects are not included in the analytical models. However, perturbation theory and numerical tests show that broad-scale lateral viscosity variations are much less important than radial variations; in this respect, geoid models, which depend upon steady-state surface deformations, may provide more reliable constraints on mantle structure than inferences from transient phenomena such as postglacial rebound. Stronger, smaller-scale viscosity variations associated with mantle plumes and subducting slabs may be more important. On the basis of numerical modelling of low viscosity plumes, we conclude that the global association of geoid highs (after slab effects are removed) with hotspots and, perhaps, mantle plumes, is the result of hot, upwelling material in the lower mantle; this conclusion does not depend strongly upon plume rheology. The global distribution of hotspots and the dominant, low-degree geoid highs may correspond to a dominant mode of convection stabilized by the ancient Pangean continental assemblage.

The analysis of the transient temperature distribution of double-slab Nd:YAG laser medium

A novel double-slab Nd:YAG laser, which uses face-pumped slab medium cooled by liquid with different temperatures on both sides, is proposed. The thermal distortion of wavefront caused by the non-uniform temperature distribution in the laser gain media can be self-compensated. According to the method of operation, the models of the temperature distribution and stress are presented, and the analytic solutions for the model are derived. Furthermore, the numerical simulations with pulse pumping energy of 10 J and repetition frequencies of 500 and 1000 Hz are calculated respectively for Nd:YAG laser medium. The simulation results show that the temperature gradient remains the approximative linearity, and the heat stress is within the extreme range. Then the absorption coefficient is also discussed. The result indicates that the doping concentration cannot be too large for the high repetition frequency laser. It has been proved that the high repetition frequency, high laser beam quality, and high average output power of the order of kilowatt of Nd: YAG slab laser can be achieved in this structure.

Visualization by High Resolution Immunoelectron Microscopy of the Transient Receptor Potential Vanilloid-1 at Inhibitory Synapses of the Mouse Dentate Gyrus

We have recently shown that the transient receptor potential vanilloid type 1 (TRPV1), a non-selective cation channel in the peripheral and central nervous system, is localized at postsynaptic sites of the excitatory perforant path synapses in the hippocampal dentate molecular layer (ML). In the present work, we have studied the distribution of TRPV1 at inhibitory synapses in the ML. With this aim, a preembedding immunogold method for high resolution electron microscopy was applied to mouse hippocampus. About 30% of the inhibitory synapses in the ML are TRPV1 immunopositive, which is mostly localized perisynaptically (similar to 60% of total immunoparticles) at postsynaptic dendritic membranes receiving symmetric synapses in the inner 1/3 of the layer. This TRPV1 pattern distribution is not observed in the ML of TRPV1 knock-out mice. These findings extend the knowledge of the subcellular localization of TRPV1 to inhibitory synapses of the dentate molecular layer where the channel, in addition to excitatory synapses, is present.

Contrasting abundance and residency patterns of two sympatric populations of transient killer whales (Orcinus orca) in the northern Gulf of Alaska

Two sympatric populations of “transient” (mammal-eating) killer whales were photo-identified over 27 years (1984–2010) in Prince William Sound and Kenai Fjords, coastal waters of the northern Gulf of Alaska (GOA). A total of 88 individuals were identified during 203 encounters with “AT1” transients (22 individuals) and 91 encounters with “GOA” transients (66 individuals). The median number of individuals identified annually was similar for both populations (AT1=7; GOA=8), but mark-recapture estimates showed the AT1 whales to have much higher fidelity to the study area, whereas the GOA whales had a higher exchange of individuals. Apparent survival estimates were generally high for both populations, but there was a significant reduction in the survival of AT1 transients after the Exxon Valdez oil spill in 1989, with an abrupt decline in estimated abundance from a high of 22 in 1989 to a low of seven whales at the end of 2010. There was no detectable decline in GOA population abundance or survival over the same period, but abundance ranged from just 6 to 18 whales annually. Resighting data from adjacent coastal waters and movement tracks from satellite tags further indicated that the GOA whales are part of a larger population with a more extensive range, whereas AT1 whales are resident to the study area.