A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity

It has recently been shown that for a Cauchy stress response induced by a strictly rank-one convex hyperelastic energy potential, a homogeneous Cauchy stress tensor field cannot correspond to a non-homogeneous deformation if the deformation gradient has discrete values, i.e. if the deformation is piecewise affine linear and satisfies the Hadamard jump condition. In this note, we expand upon these results and show that they do not hold for arbitrary deformations by explicitly giving an example of a strictly rank-one convex energy and a non-homogeneous deformation such that the induced Cauchy stress tensor is constant. In the planar case, our example is related to another previous result concerning criteria for generalized convexity properties of conformally invariant energy functions, which we extend to the case of strict rank-one convexity

Head-up displays - A study of their applicability in civil aviation

Benefits and problems of using head-up displays in commercial and general aviation aircraf

Additive factors and stages of mental processes in task networks.

To perform a task a subject executes mental processes. An experimental manipulation, such as a change in stimulus intensity, is said to selectively influence a process if it changes the duration of that process leaving other process durations unchanged. For random process durations a definition of a factor selectively influencing a process by increments is given in terms of stochastic dominance (also called “the usual stochastic order”. A technique for analyzing reaction times, Sternberg\u27s Additive Factor Method, assumes all the processes are in series. When all processes are in series, each process is called a stage. With the Additive Factor Method, if two experimental factors selectively influence two different stages by increments, the factors will have additive effects on reaction time. An assumption of the Additive Factor Method is that if two experimental factors interact, then they influence the same stage. We consider sets of processes in which some pairs of processes are sequential and some are concurrent (i. e., the processes are partially ordered). We propose a natural definition of a stage for such sets of processes. For partially ordered processes, with our definition of a stage, if two experimental factors selectively influence two different processes by increments, each within a different stage, then the factors have additive effects. If each process selectively influenced by increments is in the same stage, then an interaction is possible, although not inevitable

Paleomagnetism of Jurassic Rocks in the Western Sierra Nevada Metamorphic Belt and its Bearing on the Structural Evolution of the Sierra Nevada Block

The western metamorphic belt of the Sierra Nevada consists of two eugeosynclinal terranes separated by the Melones and Sonora faults. Subvertical, bedded Mesozoic volcanic rocks metamorphosed to low greenschist facies predominate to the west, whereas Paleozoic metamorphic rocks of higher grade and greater structural complexity predominate to the east. In order to study the structural development of the faults, 121 samples of basalt and diabase were collected for paleomagnetic analysis from three Jurassic formations, the Logtown Ridge and Penon Blanco formations west of the Melones fault and the Sonora dike swarm to the east of the Sonora fault. A northwesterly, downward directed magnetization occurs in each unit. Three fold tests and a conglomerate test on the two formations west of the faults show that the magnetization is secondary, postdating Nevadan (Late Jurassic) folding and is probably coeval with peak metamorphism. An average of five paleomagnetic poles from the Sierra Nevada, three derived from the secondary magnetizations given herein and two previously published, all of probable Kimmeridgian age, yields λ′=67.2°N, ϕ′=161.2°E, and α95 =6.5°. Southeasterly magnetizations also occur in the Logtown Ridge Formation and Sonora dike swarm. Directions from the Sonora dikes are approximately antipodal to the secondary directions and are reversed; magnetizations from the Logtown Ridge Formation yield similar results only if corrected for the tilt of bedding. The Logtown Ridge magnetizations (tilt-corrected) yield a pole position near to that expected for North America. The data from the Sonora dikes require a tilt correction of 25°-30° toward the south-southwest about a horizontal axis parallel to the regional structure in order to yield a North American pole position. We conclude that the eastern wall rocks of the Melones and Sonora faults have been rotated 25°-30° in response to Nevadan deformation in contrast to the western wall rocks, which have been rotated about 90°

Magnitude of crustal extension across the northern Basin and Range province: constraints from paleomagnetism

The magnitude of crustal extension across the northern Basin and Range province is a matter of longstanding controversy; estimates range from 10 to 300%. Recently published estimates of extension across the southern Basin and Range province (36[deg]N) are in the range of 80-100%. Thus, the larger values suggested for the northern part of the province (40[deg]N) seem to require substantial counterclockwise rotation of the Sierra Nevada during Tertiary extension. Paleomagnetic data from the range, however, limit rotation to 4 +/- 10[deg] at the 95% confidence level. These limits, combined with estimates of extension near the Garlock fault, allow severe constraints to be placed on the magnitude of extension across more northerly parts of the province. We conclude that the maximum extension at 40[deg]N is about 50% and that values of 39 +/- 12% (188 +/- 43 km) are likely.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25578/1/0000122.pd

Marine Volcaniclastic Record of Early Arc Evolution in the Eastern Ritter Range Pendant, Central Sierra Nevada, California

Marine volcaniclastic rocks in the Sierra Nevada preserve a critical record of silicic magmatism in the early Sierra Nevada volcanic arc, and this magmatic record provides precise minimum age constraints on subduction inception and tectonic evolution of the early Mesozoic Cordilleran convergent margin at this latitude. New zircon Pb/U ages from the Ritter Range pendant and regional correlations indicate arc inception no later than mid‐Triassic time between 37 and 38°N. The regional first‐order felsic magma eruption rate as recorded by marine volcanic arc rocks was episodic, with distinct pulses of ignimbrite emplacement at ca. 221 to 216 Ma and 174 to 167 Ma. Ignimbrites range from dacite to rhyolite in bulk composition, and are petrographically similar to modern arc‐type, monotonous intermediate dacite or phenocryst‐poor, low‐silica rhyolite. Zircon trace element geochemistry indicates that Jurassic silicic melts were consistently Ti‐ and light rare earth‐enriched and U‐depleted in comparison to Triassic melts of the juvenile arc, suggesting Jurassic silicic melts were hotter, drier, and derived from distinct lithospheric sources not tapped in the juvenile stage of arc construction. Pulses of ignimbrite deposition were coeval with granodioritic to granitic components of the underlying early Mesozoic Sierra Nevada batholith, suggesting explosive silicic volcanism and batholith construction were closely coupled at one‐ to two‐million‐year time scales

The EU’s stability-democracy dilemma in the context of the problematic accession of the Western Balkan states

The accession of the remaining six Western Balkan states into the EU is shrouded in much uncertainty. Despite Croatia finally traversing the difficult path to eventual membership in 2013, not one of the remaining Western Balkan countries can claim to be on a definite pathway to membership today. An increasingly prevalent argument is that the EU’s engagement with its neighbourhoods has faltered because its strategies have been undermined by an inherent stability-democracy dilemma. This article examines the EU’s engagement with the Western Balkans and finds that although the EU tried to transcend this dilemma, in reality, a tension between stability and democracy was present with the former generally receiving more attention in policymaking. This led to not only a lack of tangible democratization amongst the Western Balkan states, but further uncertainty about their accession prospects. By 2018, it was clear that the EU’s engagement with the Western Balkans needed a rethink, resulting in a new approach: the ‘Six Flagship Initiatives’. However, given the apprehensiveness of some member states (especially France) coupled with the presence of outsiders such as Russia and China in the area, the accession prospects of the six non-EU Western Balkan states remains blurred