Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates

 The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of M?bius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex generated by the unknown point and the four known points. Substitution of M?bius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4. contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gau? (1842), A. Schreiber (1908) and A.␣Ansermet (1910). Received: 05 March 1996; Accepted: 15 October 1996     

Die Radialgeschwindigkeit des Am Sternes 68 Tau

The radial velocity of the star 68 Tau is searched in dependence on the light variation period. No variations have been proved. The mean radial velocity of 22 spectra is 40.4 km/sec ± 0.7 km/sec.     

Stable carbon isotope variations in northwest Europe during the last glacial–interglacial transition

Stable carbon isotope data that span part of the last glacial–interglacial transition (ca. 14-9 ka ¹⁴C BP; ca. 15–11 ka cal. BP), and which derive from organ-specific plant macrofossils recovered from two lake sediment profiles in the UK and one in Norway, are compared. The recorded temporal variations show similar trends, which, over a millennial time-scale appear to parallel the main drift in δ¹⁸O as determined for the GRIP ice-core. It is postulated that some smaller scale variations in the δ¹³C profiles may reflect the shorter term oscillations in δ¹⁸O values evident in the GRIP record, although this is less certain. Overall, however, the results suggest that stable carbon isotope measurements based on organ-specific terrestrial plant macrofossils may provide (i) a means for establishing correlations between terrestrial successions and (ii) additional paleoenvironmental information, as the apparent ‘shadowing’ of the GRIP record indicates a common forcing mechanism for both Greenland δ¹⁸O and northwest European δ¹³C variations. From the evidence available we suggest that the recorded δ¹³C variations reflect fluctuations in air temperature and/or changes in water vapour pressure in the atmosphere. © 1997 John Wiley & Sons, Ltd.     

Experiments on steady buoyancy transfer through turbulent fluid layers separated by density interfaces

A laboratory experiment was performed to investigate mixing across a density interface which separates two turbulent fluid layers and coexists with a stabilizing buoyancy flux. It was found that the buoyancy flux (q₀) across the interface and through the turbulent layers (of depth D) becomes steady and constant in magnitude in the vertical direction, only when , where u is the horizontal r.m.s. velocity at the base of the mixed layers. The results suggest that mixing across the density interface is controlled by a dynamically important buoyancy gradient induced in the turbulent layers and that parameters such as the bulk Richardson number, , where Δb is the interfacial buoyancy jump, are of secondary importance. Measurements are used to infer the mixing mechanism at the interface, the mixing efficiency of stratified fluids and the entrainment law. Some geophysical applications of the results are also discussed.     

Resolving mechanisms of toxicity while pursuing ecotoxicological relevance?

In this age of modern biology, aquatic toxicological research has pursued mechanisms of action of toxicants. This has provided potential tools for ecotoxicologic investigations. However, problems of biocomplexity and issues at higher levels of biological organization remain a challenge. In the 1980s and 1990s and continuing to a lesser extent today, organisms residing in highly contaminated field sites or exposed in the laboratory to calibrated concentrations of individual compounds were carefully analyzed for their responses to priority pollutants. Correlation of biochemical and structural analyses in cultured cells and tissues, as well as the in vivo exposures led to the production and application of biomarkers of exposure and effect and to our awareness of genotoxicity and its chronic manifestations, such as neoplasms, in wild fishes. To gain acceptance of these findings in the greater environmental toxicology community, “validation of the model” versus other, better-established often rodent models, was necessary and became a major focus. Resultant biomarkers were applied to heavily contaminated and reference field sites as part of effects assessment and with investigations following large-scale disasters such as oil spills or industrial accidents.

Over the past 15 years, in the laboratory, small aquarium fish models such as medaka (Oryzias latipes), zebrafish (Danio rerio), platyfish (Xiphophorus species), fathead minnow (Pimephales promelas), and sheepshead minnow (Cyprinodon variegatus) were increasingly used establishing mechanisms of toxicants. Today, the same organisms provide reliable information at higher levels of biological organization relevant to ecotoxicology. We review studies resolving mechanisms of toxicity and discuss ways to address biocomplexity, mixtures of contaminants, and the need to relate individual level responses to populations and communities.     

Silica depleted melting of pelites. Petrogenetic grid and application to the Susqueda Aureole, Spain

Metapelitic rocks in the low pressure contact metamorphic aureole around the Susqueda igneous complex, Spain show a number of features that make them an ideal testing ground for the modelling of silica‐undersaturated melting. Rocks in the aureole experienced localized depletion in silica by the segregation of quartz veins during a pre‐anatectic, regional cordierite‐andalusite grade metamorphic event. These rocks were then intruded by gabbroic to dioritic rocks of the Susqueda igneous complex that formed a migmatitic contact metamorphic aureole in the country rocks. This migmatisation event caused quartz‐saturated hornfels and restite formation in rocks that had experienced no quartz vein segregation in the previous regional metamorphic event, but silica‐undersaturated melting in those rocks that were previously depleted in silica. Silica‐undersaturated melting is investigated using a new petrogenetic P–T projection and equilibrium pseudosections calculated in the KFMASH and NCKFMASH systems, respectively. The grid considers quartz absent equilibria and a range of phases that form typically in silica‐undersaturated bulk compositions, for example corundum. It is shown that the quartz‐rich precursors in the Susqueda contact aureole produced about 10% melt during contact metamorphism. However, most of this melt was extracted leaving behind rocks with restitic bulk compositions and minor leucosome segregation. It is suggested that the melt mixed with the host igneous rocks causing an apparent magmatic zoning from diorite in the centre of the complex to tonalite at the margins. In contrast, the quartz‐poor precursors (from which the quartz veins segregated) melted in the silica‐undersaturated field producing a range of assemblages including peritectic corundum and spinel. Melting of the silica‐undersaturated rocks produced only negligible melt and no subsequent melt loss.     

Pillow talk

Three distinct types of pillows and pillow lava sequences with different modes of origin have been recognized in the extrusive sequences comprising the upper parts of ophiolite complexes that represent the mafic portion of the floor of an Early Cretaceous back-arc basin in southern Chile. One type of pillow formed by non-explosive submarine effusion. A second type formed by magmatic intrusion into pre-existing aquagene tuff formed by explosive eruption. The third type of pillow occurs within dikes, forming pillowed dikes, possibly as a result of vapor streaming within a cooling dike. Where studied in southern Chile, aquagene tuffs and intrusive pillows decrease and water-lain pillows increase in relative abundance from north to south. This variation corresponds with a north-to-south decrease in both the relative volume of extrusives to extensional dikes and the range and volume of differentiated rocks, suggesting a southward increase in rate of extension relative to rate of magma supply within the spreading ridges at which the ophiolites formed. In the northern part of the original basin where the rate of extension was small relative to the rate of magma supply, magma remained in magma chambers longer, resulting in a greater range and volume of differentiated rocks. The larger volume of more differentiated, cooler and more viscous magmas, in conjunction with the likelihood of more violent eruption of volatile-rich differentiates, may have been responsible for the large volume of aquagene tuff in the northern part of the original basin. These observations in southern Chile suggest that ophiolites which contain a great abundance of aquagene tuffs and intrusive pillow lavas formed in tectonic environments in which the rate of extension was small relative to the rate of magma supply (island arcs, embryonic marginal basins). Ophiolites with predominantly water-lain pillowed and massive lavas formed in tectonic environments in which the rate of extension was large relative to the rate of magma supply (mid-ocean ridges, mature back-arc basins). Thus geologic field data may supplement geochemical data as a tool in distinguishing the original igneous-tectonic environments in which ophiolites originate.     

Structure Function Analysis of Two-Scale Scalar Ramps. Part II: Ramp Characteristics and Surface Renewal Flux Estimation

Ramp features in the turbulent scalar field are associated with turbulent coherent structures, which dominate energy and mass fluxes in the atmospheric surface layer. Although finer scale ramp-like shapes embedded within larger scale ramp-like shapes can readily be perceived in turbulent scalar traces, their presence has largely been overlooked in the literature. We demonstrate the signature of more than one ramp scale in structure functions of the turbulent scalar field measured from above bare ground and two types of short plant canopies, using structure-function time lags ranging in scale from isotropic to larger than the characteristic coherent structures. Spectral analysis of structure functions was used to characterize different scales of turbulent structures. By expanding structure function analysis to include two ramp scales, we characterized the intermittency, duration, and surface renewal flux contribution of the smallest (i.e., Scale One) and the dominant (i.e., Scale Two) coherent structure scales. The frequencies of the coherent structure scales increase with mean wind shear, implying that both Scale One and Scale Two are shear-driven. The embedded Scale One turbulent structure scale is ineffectual in the surface-layer energy and mass transport process. The new method reported here for obtaining surface renewal-based scalar exchange works well over bare ground and short canopies under unstable conditions, effectively eliminating the α calibration for these conditions and forming the foundation for analysis over taller and more complex surfaces.