Summary Recent interest has arisen in the possibility that changes in the Earth's inertia tensor accompanying earthquakes may provide the excitation for the ‘Chandler’ wobble of the rotation axis. We present a simple procedure for calculating these changes based on the elastic reciprocal theorem and Volterra's formula. In particular, if t is the shear stress created in the slip direction on a prospective fault surface when a perfect, unfaulted sphere is steadily rotated at unit angular velocity about some axis, then the change in moment of inertia about that same axis is shown to be twice the work of τ when carried through the actual slip displacement which occurs in faulting. It is shown that changes of products of inertia may be computed in a similarly simple way. The method is applied to two homogeneous Earth models, the relation to previous treatments is discussed, and it is noted that inertia changes accompanying less-catastrophic mass movements may be calculated in a similar way. The development in the body of the paper is in the context of classical linear elasticity. An Appendix extends the reciprocal theorem and Volterra's formula, and hence the basis for similar inertia change calculations, to the linearized incremental deformation of self-gravitating, initially stressed elastic systems, such as real-Earth models.
An inexpensive fabrication technique for transferring the edges of a patterned mask layer into an underlying, thin metal film is found in controlled undercutting by isotropic wet etching. This technique generates structures with critical dimensions as small as 50 nm (see Figure) in a thin film of chromium or aluminum and it is useful for structures that do not require multiple-level registration and that are tolerant of defects.
Recent results on fluid–structure interaction for plates subject to high intensity air shocks are employed to assess the performance of all-metal sandwich plates compared to monolithic solid plates of the same material and mass per area. For a planar shock wave striking the plate, the new results enable the structural analysis to be decoupled from an analysis of shock propagation in the air. The study complements prior work on the role of fluid–structure interaction in the design and assessment of sandwich plates subject to water shocks. Square honeycomb and folded plate core topologies are considered. Fluid–structure interaction enhances the performance of sandwich plates relative to solid plates under intense air shocks, but not as significantly as for water blasts. The paper investigates two methods for applying the loading to the sandwich plate—responses are contrasted for loads applied as a time-dependent pressure history versus imposition of an initial velocity.
Patolsky et al. (Reports, 25 August 2006, p. 1100) used silicon nanowires to record action potentials in rat neuronal axons and found increases in conductance of about 85 nanosiemens. We point out that the data correspond to voltage changes of about -85 millivolts on the nanowire and that conceivable mechanisms of axon-nanowire interaction lead to signals that are opposite in sign or smaller by orders of magnitude.
A study is carried out of the problem of a penny-shaped crack in an infinite body of power-law material subject to general remote axisymmetric stressing conditions. The plane strain version of the problem is also examined. The material is incompressible and is characterized by small strain deformation theory with a pure power relation between stress and strain. The solutions presented also apply to power-law creeping materials and to a class of strain-rate sensitive hardening materials. Both numerical and analytical procedures are employed to obtain the main results. A perturbation solution obtained by expanding about the trivial state in which the stress is everywhere parallel to the crack leads to simple formulas which are highly accurate even when the remote stress is perpendicular to the crack.
No abstract is provided for this article.
A near-tip asymptotic analysis is given for the stress and deformation field near the tip of crack propagating dynamically under anti-plane shear in an ideally plastic single crystal. A paricular class of orientations of the crack relative to the crystals is considered so that the yield is so simple diamond shape (relative to directions along perpendicular to the crack) in the plane of the anti-plane shear stresses. The near-tip solution is shown to consists of sectors which carry constant stresses, at yield levels, corresponding to adjacent vertices on the diamond-shaped yield locus, and which are joined along an elastic-plastic shock discontinuity. All plastic flow in the near-tip region occurs in the shock. Plastic strains and particle velocity are finite at the crack tip. The plastic strain is proportional to the elastic strain at onset of yielding and is inversely proportional to the elastic Mach number associated with the speed of crack growth.
No abstract is provided for this article.
The relationship between various diet quality indices and risk of type 2 diabetes (T2D) remains unsettled. We compared associations of 4 diet quality indices--the Alternate Mediterranean Diet Index, Healthy Eating Index 2010, Alternate Healthy Eating Index 2010, and the Dietary Approaches to Stop Hypertension (DASH) Index--with reported T2D in the Women's Health Initiative, overall, by race/ethnicity, and with/without adjustment for overweight/obesity at enrollment (a potential mediator). This cohort (n = 101,504) included postmenopausal women without T2D who completed a baseline food frequency questionnaire from which the 4 diet quality index scores were derived. Higher scores on the indices indicated a better diet. Cox regression was used to estimate multivariate hazard ratios for T2D. Pearson coefficients for correlation among the indices ranged from 0.55 to 0.74. Follow-up took place from 1993 to 2013. During a median 15 years of follow-up, 10,815 incident cases of T2D occurred. For each diet quality index, a 1-standard-deviation higher score was associated with 10%-14% lower T2D risk (P < 0.001). Adjusting for overweight/obesity at enrollment attenuated but did not eliminate associations to 5%-10% lower risk per 1-standard-deviation higher score (P < 0.001). For all 4 dietary indices examined, higher scores were inversely associated with T2D overall and across racial/ethnic groups. Multiple forms of a healthful diet were inversely associated with T2D in these postmenopausal women.
void half-length, v is the speed of propagation of the void tip, ..cap omega.. is the atomic volume, and v* is a temperature dependent material parameter. An iterative solution for void shape which depends on a/sup 3/v/..cap omega..v* is derived also. By assuming the grain boundary flux to be distributed in such a manner that the grains separate as rigid bodies, the similarity and iterative shapes are linked to the applied stress, and the resulting growth models compared with the limiting cases of equilibrium and crack-like growth. The comparison indicates that void growth can be represented by a two-part solution where either the linearized equilibrium or the similarity model applies for small a/sup 3/v/..cap omega..v*, and the crack-like model applies for larger a/sup 3/v/..cap omega..v*. An analysis is included of relaxation times associated with a variety of diffusion mechanisms which are useful in determining the dominant mechanisms of matter transport.
