The avian egg exhibits extraordinary diversity in size, shape and color, and has a key role in avian adaptive radiations. Despite extensive work, our understanding of the underlying principles that guide the “design” of the egg as a load-bearing structure remains incomplete, especially over broad taxonomic scales. Here we define a dimensionless number C, a function of egg weight, stiffness and dimensions, to quantify how stiff an egg is with respect to its weight after removing geometry-induced rigidity. We analyze eggs of 463 bird species in 36 orders across five orders of magnitude in body mass, and find that C number is nearly invariant for most species, including tiny hummingbirds and giant elephant birds. This invariance or “design guideline” dictates that evolutionary changes in shell thickness and Young’s modulus, both contributing to shell stiffness, are constrained by changes in egg weight. Our analysis illuminates unique reproductive strategies of brood parasites, kiwis, and megapodes, and quantifies the loss of safety margin for contact incubation due to artificial selection and environmental toxins. Our approach provides a mechanistic framework for a better understanding of the mechanical design of the avian egg, and may provide clues to the evolutionary origin of contact incubation of amniote eggs.
We studied highly L1 0-ordered FePtAg-C nanogranular film as a potential high-density storage medium in thermally assisted magnetic recording (TAR). A 6.4-nm-thick FePtAg-C film with a perpendicular coercivity of 37 kOe and an average grain size of 6.161.8 nm was fabricated on oxidized silicon substrate with a 10 nm MgO interlayer at 450 C. The time-dependence measurement of remnant coercivity showed the energy barrier of E b ¼ 7.6 eV $300 k B T at room temperature, meaning the excellent thermal stability for long-term data storage. Static tester experiments on this film using a TAR head demonstrate the feasibility of recording at an areal density of $450 Gbits/in. 2 .
Failure of hollow trees in urban areas is a worldwide concern, and it can be caused by different mechanisms, i.e. bending stresses or flattening-related failures. Here we derive a new analytical expression for predicting the bending moment for tangential cracking, and compare the breaking moment of various failure modes, including Brazier buckling, tangential cracking, shear failure and conventional bending failure, as a function of t/R ratio, where t and R are the trunk wall thickness and trunk radius, respectively, of a hollow tree. We use Taiwan red cypress as an example and show that its failure modes and the corresponding t/R ratios are: Brazier buckling (Mode I), tangential cracking followed by longitudinal splitting (Mode II) and conventional bending failure (Mode III) for 0 < t/R < 0.06, 0.06 < t/R < 0.27 and 0.27 < t/R < 1, respectively. The exact values of those ratios may vary within and among species, but the variation is much smaller than individual mechanical properties. Also, shear failure, another type of cracking due to maximum shear stress near the neutral axis of the tree trunk, is unlikely to occur since it requires much larger bending moments. Hence, we conclude that tangential cracking due to cross-sectional flattening, followed by longitudinal splitting, is dominant for hollow trunks. Our equations are applicable to analyse straight hollow tree trunks and plant stems, but are not applicable to those with side openings or those with only heart decay. Our findings provide insights for those managing trees in urban situations and those managing for conservation of hollow-dependent fauna in both urban and rural settings.
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