Error analysis and corrections to pupil diameter measurements with Langley Research Center's oculometer

Factors that can affect oculometer measurements of pupil diameter are: horizontal (azimuth) and vertical (elevation) viewing angle of the pilot; refraction of the eye and cornea; changes in distance of eye to camera; illumination intensity of light on the eye; and counting sensitivity of scan lines used to measure diameter, and output voltage. To estimate the accuracy of the measurements, an artificial eye was designed and a series of runs performed with the oculometer system. When refraction effects are included, results show that pupil diameter is a parabolic function of the azimuth angle similar to the cosine function predicted by theory: this error can be accounted for by using a correction equation, reducing the error from 6% to 1.5% of the actual diameter. Elevation angle and illumination effects were found to be negligible. The effects of counting sensitivity and output voltage can be calculated directly from system documentation. The overall accuracy of the unmodified system is about 6%. After correcting for the azimuth angle errors, the overall accuracy is approximately 2%

Energetic Extremes in Aquatic Locomotion by Coral Reef Fishes

Underwater locomotion is challenging due to the high friction and resistance imposed on a body moving through water and energy lost in the wake during undulatory propulsion. While aquatic organisms have evolved streamlined shapes to overcome such resistance, underwater locomotion has long been considered a costly exercise. Recent evidence for a range of swimming vertebrates, however, has suggested that flapping paired appendages around a rigid body may be an extremely efficient means of aquatic locomotion. Using intermittent flow-through respirometry, we found exceptional energetic performance in the Bluelined wrasse Stethojulis bandanensis, which maintains tuna-like optimum cruising speeds (up to 1 metre s(-1)) while using 40% less energy than expected for their body size. Displaying an exceptional aerobic scope (22-fold above resting), streamlined rigid-body posture, and wing-like fins that generate lift-based thrust, S. bandanensis literally flies underwater to efficiently maintain high optimum swimming speeds. Extreme energetic performance may be key to the colonization of highly variable environments, such as the wave-swept habitats where S. bandanensis and other wing-finned species tend to occur. Challenging preconceived notions of how best to power aquatic locomotion, biomimicry of such lift-based fin movements could yield dramatic reductions in the power needed to propel underwater vehicles at high speed.Funding was provided by the Australian Research Council (to CJF) and the Danish Agency for Science, Technology and Innovation (to JFS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Trends in life cycle greenhouse gas emissions of future light duty electric vehicles

The majority of previous studies examining life cycle greenhouse gas (LCGHG) emissions of battery electric vehicles (BEVs) have focused on efficiency-oriented vehicle designs with limited battery capacities. However, two dominant trends in the US BEV market make these studies increasingly obsolete: sales show significant increases in battery capacity and attendant range and are increasingly dominated by large luxury or high-performance vehicles. In addition, an era of new use and ownership models may mean significant changes to vehicle utilization, and the carbon intensity of electricity is expected to decrease. Thus, the question is whether these trends significantly alter our expectations of future BEV LCGHG emissions. To answer this question, three archetypal vehicle designs for the year 2025 along with scenarios for increased range and different use models are simulated in an LCGHG model: an efficiency-oriented compact vehicle; a high performance luxury sedan; and a luxury sport utility vehicle. While production emissions are less than 10% of LCGHG emissions for today's gasoline vehicles, they account for about 40% for a BEV, and as much as two-thirds of a future BEV operated on a primarily renewable grid. Larger battery systems and low utilization do not outweigh expected reductions in emissions from electricity used for vehicle charging. These trends could be exacerbated by increasing BEV market shares for larger vehicles. However, larger battery systems could reduce per-mile emissions of BEVs in high mileage applications, like on-demand ride sharing or shared vehicle fleets, meaning that trends in use patterns may countervail those in BEV design

Theoretical Parametric Study of the Relative Advantages of Winglets and Wing-Tip Extensions

For identical increases in bending moment, a winglet provides a greater gain in induced efficiency than tip extension. Winglet toe angle allows design trades between efficiency and root moment. A winglet shows the greatest benefit when the wing loads are heavy near the tip. Washout diminishes the benefit of either tip modification, and the gain in induced efficiency becomes a function of lift coefficient; thus, heavy wing loadings obtain the greatest benefit from a winglet, and low-speed performance is enhanced even more than cruise performance. Both induced efficiency and bending moment increase with winglet length and outward cant. The benefit of a winglet relative to a tip extension is greatest for a nearly vertical winglet. Root bending moment is proportional to the minimum weight of bending material required in the wing; thus, it is a valid index of the impact of tip modifications on a new wing design

Two generalizations of the PRV conjecture

Let G be a complex connected reductive group. The PRV conjecture, which was proved independently by S. Kumar and O. Mathieu in 1989, gives explicit irreducible submodules of the tensor product of two irreducible G-modules. This paper has three aims. First, we simplify the proof of the PRV conjecture, then we generalize it to other branching problems. Finally, we find other irreducible components of the tensor product of two irreducible G-modules that appear for "the same reason" as the PRV ones

The three-quark static potential in perturbation theory

We study the three-quark static potential in perturbation theory in QCD. A complete next-to-leading order calculation is performed in the singlet, octets and decuplet channels and the potential exponentiation is demonstrated. The mixing of the octet representations is calculated. At next-to-next-to-leading order, the subset of diagrams producing three-body forces is identified in Coulomb gauge and its contribution to the potential calculated. Combining it with the contribution of the two-body forces, which may be extracted from the quark-antiquark static potential, we obtain the complete next-to-next-to-leading order three-quark static potential in the colour-singlet channel.Comment: 36 pages, 11 figures, version published in Phys.Rev.

Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

Connectivity and a Problem of Formal Geometry

Let $P=\mathbb P^m(e)\times\mathbb P^n(h)$ be a product of weighted projective spaces, and let $\Delta_P$ be the diagonal of $P\times P$. We prove an algebraization result for formal-rational functions on certain closed subvarieties $X$ of $P\times P$ along the intersection $X\cap\Delta_P$.Comment: 9 pages, to appear in the Proceedings volume "Experimental and Theoretical Methods in Algebra, Geometry and Topology", series Springer Proceedings in Mathematics & Statistic

Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in Inventiones Mathematica