Extreme Curvature Research Articles

Growing and critical ovalization for sharp-notched 6061-T6 aluminum alloy tubes under cyclic bending

In this paper, we present results from experiments dealing ovalization in 6061-T6 aluminum alloy tubes which have been notched and subjected to cyclic bending are presented. It was discovered that the tubes continuously ovalized to a critical quantity when they buckled. Tubes with a smooth surface and five different notch depths were considered. The ovalization–curvature curve exhibited a symmetrical and ratcheting increase with the number of bending cycles. Deeper notch depths caused greater ovalizations. In addition, the trend of the ovalization at negative extreme curvature and number of bending cycles relationship was distinguished into three stages. Finally, the empirical form proposed by Lee, Hung, and Pan in 2010 was employed for describing the above-mentioned correlation in the first two stages. It was found that the experimental and simulated data agreed quite well.

Inherently-Forced Tensile Strain in Nanodiamond-Derived Onion-like Carbon: Consequences in Defect-Induced Electrochemical Activation.

We analyzed the nanodiamond-derived onion-like carbon (OLC) as function of synthesis temperature (1000~1400 °C), by high-resolution electron microscopy, electron energy loss spectroscopy, visible-Raman spectroscopy, ultraviolet photoemission spectroscopy, impedance spectroscopy, cyclic voltammetry and differential pulse voltammetry. The temperature dependences of the obtained properties (averaged particle size, tensile strain, defect density, density of states, electron transfer kinetics, and electrochemical oxidation current) unanimously coincided: they initially increased and saturated at 1200 °C. It was attributed to the inherent tensile strains arising from (1) the volume expansion associated with the layer-wise diamond-to-graphite transformation of the core, which caused forced dilation of the outer shells during their thermal synthesis; (2) the extreme curvature of the shells. The former origin was dominant over the latter at the outermost shell, of which the relevant evolution in defect density, DOS and electron transfer kinetics determined the electrochemical performances. In detection of dopamine (DA), uric acid (UA) and ascorbic acid (AA) using the OLC as electrode, their oxidation peak currents were enhanced by factors of 15~60 with annealing temperature. Their limit of detection and the linear range of detection, in the post-treatment-free condition, were as excellent as those of the nano-carbon electrodes post-treated by Pt-decoration, N-doping, plasma, or polymer.

Dissecting seipin function: the localized accumulation of phosphatidic acid at ER/LD junctions in the absence of seipin is suppressed by Sei1p(ΔNterm) only in combination with Ldb16p.

BackgroundSeipin is required for the correct assembly of cytoplasmic lipid droplets. In the absence of the yeast seipin homolog Sei1p (formerly Fld1p), droplets are slow to bud from the endoplasmic reticulum, lack the normal component of proteins on their surface, are highly heterogeneous in size and shape, often bud into the nucleus, and promote local proliferation of the endoplasmic reticulum in which they become tangled. But the mechanism by which seipin catalyzes lipid droplet formation is still uncertain.ResultsSeipin prevents a localized accumulation of phosphatidic acid (PA puncta) at ER-droplet junctions. PA puncta were detected with three different probes: Opi1p, Spo20p(51–91) and Pah1p. A system of droplet induction was used to show that PA puncta were not present until droplets were formed; the puncta appeared regardless of whether droplets consisted of triacylglycerol or steryl ester. Deletion strains were used to demonstrate that a single phosphatidic acid-producing enzyme is not responsible for the generation of the puncta, and the puncta remain resistant to overexpression of enzymes that metabolize phosphatidic acid, suggesting that this lipid is trapped in a latent compartment. Suppression of PA puncta requires the first 14 amino acids of Sei1p (Nterm), a domain that is also important for initiation of droplet assembly. Consistent with recent evidence that Ldb16p and Sei1p form a functional unit, the PA puncta phenotype in the ldb16Δ sei1Δ strain was rescued by human seipin. Moreover, PA puncta in the sei1Δ strain expressing Sei1pΔNterm was suppressed by overexpression of Ldb16p, suggesting a functional interaction of Nterm with this protein. Overexpression of both Sei1p and Ldb16p, but not Sei1p alone, is sufficient to cause a large increase in droplet number. However, Ldb16p alone increases triacylglycerol accumulation in the ldb16Δ sei1Δ background.ConclusionWe hypothesize that seipin prevents formation of membranes with extreme curvature at endoplasmic reticulum/droplet junctions that would attract phosphatidic acid. While Ldb16p alone can affect triacylglycerol accumulation, proper droplet formation requires the collaboration of Sei1p and Ldb16.Electronic supplementary materialThe online version of this article (doi:10.1186/s12860-015-0075-3) contains supplementary material, which is available to authorized users.

Vertebrate Ichnopathology: Pathologies Inferred from Dinosaur Tracks and Trackways from the Mesozoic

Literature concerning dinosaur footprints or trackways exhibiting abnormal gait or morphology reflecting pathology (ichnopathology) is rare. We report on a number of Jurassic and Cretaceous occurrences of theropod footprints from western North America with unusual morphologies interpreted herein as examples of inferred pathologies, or ichnopathologies. The majority of ichnopathologies are primarily manifested in the digit impressions and include examples of swelling, extreme curvature, dislocation or fracture, and amputation. A number of occurrences are single tracks on ex situ blocks with substantial deformation (inferred dislocation or fracture), or absence of a single digit impression. Two occurrences are from in situ natural mould trackways, one of which is a lengthy trackway of a presumed allosauroid with no noticeable deformation of the digits or feet but with strong inward rotation of the left footprint toward the midline and a pronounced, waddling limp. The other is a tyrannosaurid trackway consisting of three footprints (one right, two left) with the two left prints exhibiting repetitive ichnopathology of a partially missing Digit II impression.

Roles of multiple-proton transfer pathways and proton-coupled electron transfer in the reactivity of the bis-FeIV state of MauG

The high-valent state of the diheme enzyme MauG exhibits charge-resonance (CR) stabilization in which the major species is a bis-Fe(IV) state with one heme present as Fe(IV)=O and the other as Fe(IV) with axial heme ligands provided by His and Tyr side chains. In the absence of its substrate, the high-valent state is relatively stable and returns to the diferric state over several minutes. It is shown that this process occurs in two phases. The first phase is redistribution of the resonance species that support the CR. The second phase is the loss of CR and reduction to the diferric state. Thermodynamic analysis revealed that the rates of the two phases exhibited different temperature dependencies and activation energies of 8.9 and 19.6 kcal/mol. The two phases exhibited kinetic solvent isotope effects of 2.5 and 2.3. Proton inventory plots of each reaction phase exhibited extreme curvature that could not be fit to models for one- or multiple-proton transfers in the transition state. Each did fit well to a model for two alternative pathways for proton transfer, each involving multiple protons. In each case the experimentally determined fractionation factors were consistent with one of the pathways involving tunneling. The percent of the reaction that involved the tunneling pathway differed for the two reaction phases. Using the crystal structure of MauG it was possible to propose proton-transfer pathways consistent with the experimental data using water molecules and amino acid side chains in the distal pocket of the high-spin heme.

Energy problem in the Einstein–Cartan theory

The Einstein–Cartan–Kibble–Sciama equations are presented in the following form: the codifferential of the differential of a tetrad is the tetrad current with the ordinary conservation law. This form is an analogue of the form for non-Abelian quantum field theory. A canonical gauge tetrad is proposed for six two-directions with extreme sectional Riemannian curvature. A nonlocal conservation law for the contracted Bianchi identities is presented. The physical and geometric meaning of the Gibbons-Hawking Lagrangian and surface term are proposed. Application of the tetrad current concept is illustrated for the Schwarzschild and de Sitter metrics.

Optical microlithography on oblique and multiplane surfaces using diffractive phase masks

Micropatterning on oblique and multiplane surfaces remains a challenge in microelectronics, microelectromechanics, and photonics industries. We describe the use of numerically optimized diffractive phase masks to project microscale patterns onto photoresist-coated oblique and multiplane surfaces. Intriguingly, we were able to pattern a surface at 90 deg to the phase mask, which suggests the potential of our technique to pattern onto surfaces of extreme curvature. Further studies show that mask fabrication error of below 40-nm suffices to conserve pattern fidelity. A resolution of 3 μm and a depth-of-focus of 55 μm are essentially dictated by the design parameters, the mask generation tool, and the exposure system. The presented method can be readily extended for simple and inexpensive three-dimensional micropatterning.

Evolution and dynamics of a fold-thrust belt: the Sulaiman Range of Pakistan

We present observations and models of the Sulaiman Range of western Pakistan that shed new light on the evolution and deformation of fold-thrust belts. Earthquake source inversions show that the seismic deformation in the range is concentrated in the thick pile of sediments overlying the underthrusting lithosphere of the Indian subcontinent. The slip vectors of the earthquakes vary in strike around the margin of the range, in tandem with the shape of the topography, suggesting that gravitational driving forces arising from the topography play an important role in governing the deformation of the region. Numerical models suggest that the active deformation, and the extreme plan-view curvature of the range, are governed by the presence of weak sediments in a pre-existing basin on the underthrusting Indian Plate. These sediments affect the stress-state in the over-riding mountain range and allow for the rapid propagation of the nose of the range and the development of extreme curvature and laterally varying surface gradients.

Extreme curvature and extreme flexure analysis for fracture characterization from 3D seismic data: New analytical algorithms and geologic implications

Fracture characterization is fundamental to the reliable prediction of fractured reservoirs; however, it is difficult and expensive to obtain detailed fracture information required for reservoir prediction due to the lack of direct observational data in the subsurface. Here we develop seismic analysis methods to characterize fractured reservoirs based on reflection geometry related to bending and shearing of reservoir formations. Among various geometric attributes, we focus on extreme curvature and extreme flexure that are considered effective at detecting fractures. Extreme curvature refers to the signed absolute maximum curvature at a specific azimuth where the curve shape is the tightest, whereas extreme flexure refers to the signed absolute maximum gradient of curvature at a specific azimuth where the curve shape changes the most. We implement new algorithms based on analytical equations to calculate extreme curvature and extreme flexure along with the corresponding azimuth from 3D seismic data. Results from 3D seismic surveys demonstrate that the new algorithms help resolve structural details that are otherwise not easily discernible from regular amplitude and conventional attributes. Most importantly, the algorithms hold the potential to volumetrically detect and visualize fractures in an automatic and quantitative manner. We conclude that extreme curvature and extreme flexure attributes have important geologic implications for predicting fundamental fracture properties that are critical to fractured reservoir characterization in the subsurface.

CONSTRAINING COSMOLOGICAL PARAMETERS WITH IMAGE SEPARATION STATISTICS OF GRAVITATIONALLY LENSED SDSS QUASARS: MEAN IMAGE SEPARATION AND LIKELIHOOD INCORPORATING LENS GALAXY BRIGHTNESS

Recent large scale surveys such as Sloan Digital Sky Survey have produced homogeneous samples of multiple-image gravitationally lensed quasars with well-defined selection effects. Statistical analysis on these can yield independent constraints on cosmological parameters. Here we use the image separation statistics of lensed quasars from Sloan Digital Sky Survey Quasar Lens Search (SQLS) to derive constraints on cosmological parameters. Our analysis does not require knowledge of the magnification bias, which can only be estimated from the detailed knowledge on the quasar luminosity function at all redshifts, and includes the consideration for the bias against small image separation quasars due to selection against faint lens galaxy in the follow-up observations for confirmation. We first use the mean image separation of the lensed quasars as a function of redshift to find that cosmological models with extreme curvature are inconsistent with observed lensed quasars. We then apply the maximum likelihood test to the statistical sample of 16 lensed quasars that have both measured redshift and magnitude of lens galaxy. The likelihood incorporates the probability that the observed image separation is realized given the luminosity of the lens galaxy in the same manner as Im et al. (1997). We find that the 95% confidence range for the cosmological constant (i.e., the vacuum energy density) is <TEX>$0.72{\leq}{\Omega}_{\Lambda}{\leq}1.0$</TEX> for a flat universe. We also find that the equation of state parameter can be consistent with -1 as long as the matter density <TEX>${\Omega}_m{\leq}0.4$</TEX> (95% confidence range). We conclude that the image separation statistics incorporating the brightness of lens galaxies can provide robust constraints on the cosmological parameters.

A new robust enantiornithine bird from the Lower Cretaceous of China with scansorial adaptations

ABSTRACTWe describe a new enantiornithine bird, Fortunguavis xiaotaizicus, gen. et sp. nov, from the Lower Cretaceous lacustrine deposits of the Jiufotang Formation in northeastern China. The new taxon has a strongly dorsoventrally bowed furcula indicating that enantiornithines evolved furcular morphologies in parallel with ornithuromorphs. The new specimen has very robust limbs compared with other enantiornithines and has an unique foot morphology with metatarsal II much shorter than metatarsal IV, robust pedal digits, and strongly recurved pedal unguals. Although recurved unguals characterize Enantiornithes, the extreme curvature present in Fortunguavis suggests scansorial specialization in this species. These features hint at a unique ecology for this taxon and further increase the known diversity of body plans in Early Cretaceous enantiornithines.SUPPLEMENTAL DATA—Supplemental materials are available for this article for free at http://www.tandfonline.com/UJVP.

Nonisocentric Treatment Strategy for Breast Radiation Therapy: A Proof of Concept Study

To propose a nonisocentric treatment strategy as a special form of station parameter optimized radiation therapy, to improve sparing of critical structures while preserving target coverage in breast radiation therapy. To minimize the volume of exposed lung and heart in breast irradiation, we propose a novel nonisocentric treatment scheme by strategically placing nonconverging beams with multiple isocenters. As its name suggests, the central axes of these beams do not intersect at a single isocenter as in conventional breast treatment planning. Rather, the isocenter locations and beam directions are carefully selected, in that each beam is only responsible for a certain subvolume of the target, so as to minimize the volume of irradiated normal tissue. When put together, the beams will provide an adequate coverage of the target and expose only a minimal amount of normal tissue to radiation. We apply the nonisocentric planning technique to 2 previously treated clinical cases (breast and chest wall). The proposed nonisocentric technique substantially improved sparing of the ipsilateral lung. Compared with conventional isocentric plans using 2 tangential beams, the mean lung dose was reduced by 38% and 50% using the proposed technique, and the volume of the ipsilateral lung receiving ≥ 20 Gy was reduced by a factor of approximately 2 and 3 for the breast and chest wall cases, respectively. The improvement in lung sparing is even greater compared with volumetric modulated arc therapy. A nonisocentric implementation of station parameter optimized radiation therapy has been proposed for breast radiation therapy. The new treatment scheme overcomes the limitations of existing approaches and affords a useful tool for conformal breast radiation therapy, especially in cases with extreme chest wall curvature.

Most Extreme Curvature and its Application to Seismic Structural Interpretation

Curvature, as a newly developing structural attribute, closely related to the bending of geologic body and received extensive attention of the researchers in recent years. Most positive curvature and most negative curvature in particular are widely used in fault detection and fracture prediction. In this paper, most extreme curvature was introduced into structural interpretation. Compared with the conventional curvature attributes, the advantage of most extreme curvature in fault detection was highlighted in this study. It not only clearly shown the property of fault, but also precisely indicated the location of fault plane and its variation along the strike by the dramatic change in curvature values. These findings contribute to better structural interpretation of 3D seismic data and are of great significance to hydrocarbon exploration.

THREE-DIMENSIONAL, OFF-LATTICE MONTE CARLO KINETICS SIMULATIONS OF INTERSTELLAR GRAIN CHEMISTRY AND ICE STRUCTURE

The first off-lattice Monte Carlo kinetics model of interstellar dust-grain surface chemistry is presented. The positions of all surface particles are determined explicitly, according to the local potential minima resulting from the pair-wise interactions of contiguous atoms and molecules, rather than by a pre-defined lattice structure. The model is capable of simulating chemical kinetics on any arbitrary dust-grain morphology, as determined by the user-defined positions of each individual dust-grain atom. A simple method is devised for the determination of the most likely diffusion pathways and their associated energy barriers for surface species. The model is applied to a small, idealized dust grain, adopting various gas densities and using a small chemical network. Hydrogen and oxygen atoms accrete onto the grain, to produce H2O, H2, O2 and H2O2. The off-lattice method allows the ice structure to evolve freely; ice mantle porosity is found to be dependent on the gas density, which controls the accretion rate. A gas density of 2 x 10^{4} cm^{-3}, appropriate to dark interstellar clouds, is found to produce a fairly smooth and non-porous ice mantle. At all densities, H2 molecules formed on the grains collect within the crevices that divide nodules of ice, and within micropores (whose extreme inward curvature produces strong local potential minima). The larger pores produced in the high-density models are not typically filled with H2. Direct deposition of water molecules onto the grain indicates that amorphous ices formed in this way may be significantly more porous than interstellar ices that are formed by surface chemistry.

Arabidopsis CURVATURE THYLAKOID1 Proteins Modify Thylakoid Architecture by Inducing Membrane Curvature

Chloroplasts of land plants characteristically contain grana, cylindrical stacks of thylakoid membranes. A granum consists of a core of appressed membranes, two stroma-exposed end membranes, and margins, which connect pairs of grana membranes at their lumenal sides. Multiple forces contribute to grana stacking, but it is not known how the extreme curvature at margins is generated and maintained. We report the identification of the CURVATURE THYLAKOID1 (CURT1) protein family, conserved in plants and cyanobacteria. The four Arabidopsis thaliana CURT1 proteins (CURT1A, B, C, and D) oligomerize and are highly enriched at grana margins. Grana architecture is correlated with the CURT1 protein level, ranging from flat lobe-like thylakoids with considerably fewer grana margins in plants without CURT1 proteins to an increased number of membrane layers (and margins) in grana at the expense of grana diameter in overexpressors of CURT1A. The endogenous CURT1 protein in the cyanobacterium Synechocystis sp PCC6803 can be partially replaced by its Arabidopsis counterpart, indicating that the function of CURT1 proteins is evolutionary conserved. In vitro, Arabidopsis CURT1A proteins oligomerize and induce tubulation of liposomes, implying that CURT1 proteins suffice to induce membrane curvature. We therefore propose that CURT1 proteins modify thylakoid architecture by inducing membrane curvature at grana margins.

Semiautomatic morphometric land surface segmentation of an arid mountainous area using DEM and self-organizing maps

In this study, the land surface in an arid mountainous area in southwestern Iran, Jooyom, was segmented by self-organizing maps, using an unsupervised method. The classification was performed using a digital elevation model with 10-m resolution and window size of 17 × 17. Twenty-two morphometric layers were calculated using elevation derivatives with first, second, and third orders. The morphometric layers then were ranked and the optimum numbers of parameters and classes were selected with an optimum index factor and Davies–Bouldin index methods. It was found that the most effective parameters in classification of the area were differential curvature, slope insolation, rotor, aspect, cross-sectional curvature, total ring curvature, extreme curvature, vertical curvature, and unsphericity. The study area was segmented into six classes of negative contact, pitty-thalweg valley, gently eastward and westward sloping transversely concave and convex plains, sloping or slopy pass, and peaky ridges. The average parameters of each class confirmed their gravity, debris, and wash behavior of the surface slopes. The relative coverage percent of each formation in each class showed that the Asmari formation with highest coverage of classes 5 and 6 and Mole member marl limestone with the highest coverage of class 1 have the smallest maturity and highest maturity between formations, respectively. The maturities of each formation based on coverage percentages of different classes agreed with their corresponding hypsometric integral indexes. Furthermore, the distribution of classes in watersheds on mountain flanks confirmed the existence of tectonic tilting in this area.

Acute Manipulation of Diacylglycerol Reveals Roles in Nuclear Envelope Assembly &amp; Endoplasmic Reticulum Morphology

The functions and morphology of cellular membranes are intimately related and depend not only on their protein content but also on the repertoire of lipids that comprise them. In the absence of in vivo data on lipid asymmetry in endomembranes, it has been argued that motors, scaffolding proteins or integral membrane proteins rather than non-lamellar bilayer lipids such as diacylglycerol (DAG), are responsible for shaping of organelles, local membrane curvature and fusion. The effects of direct alteration of levels of such lipids remain predominantly uninvestigated. Diacylglycerol (DAG) is a well documented second messenger. Here we demonstrate two additional conserved functions of DAG: a structural role in organelle morphology, and a role in localised extreme membrane curvature required for fusion for which proteins alone are insufficient. Acute and inducible DAG depletion results in failure of the nuclear envelope (NE) to reform at mitosis and reorganisation of the ER into multi-lamellar sheets as revealed by correlative light and electron microscopy and 3D reconstructions. Remarkably, depleted cells divide without a complete NE, and unless rescued by 1,2 or 1,3 DAG soon die. Attenuation of DAG levels by enzyme microinjection into echinoderm eggs and embryos also results in alterations of ER morphology and nuclear membrane fusion. Our findings demonstrate that DAG is an in vivo modulator of organelle morphology in mammalian and echinoderm cells, indicating a fundamental role conserved across the deuterostome superphylum.

The Pyrenean Hercynian Keirogen and the Cantabrian Orocline as genetically coupled structures

The two most enigmatic structures of the western European Hercynian orogenic system are the (late Palaeozoic parts of the) Pyrenean mountain range and the extremely tight (in some estimates more than 180°) Cantabrian Orocline, the innermost section of the Ibero-Armorican Arc. They have developed coevally in close proximity to one another and any hypothesis proposed to explain the evolution of the western European Hercynides must explain both in terms of a single model. The Pyrenees have both a peculiar position in the Hercynian architecture and a strange evolution if viewed from the viewpoint of the development of orogens. They sit on the ‘hinterland’, south of the main orogenic body, the ‘innermost’ edge of which is marked by the south-vergent Montaigne Noire Helvetic-type nappes11The orogenic polarity used in this paper for the Hercynides is that they are, in toto and in contradiction to most existing models of a doubly-facing orogen, a solely north-facing (west and south-west in Iberia) orogen (see Robardet, 2002, 2003), although they have numerous and major elements, especially in their southern parts, that verge southwards.. They have a possible minor and local early shortening (D1) accompanied by Barrovian metamorphism followed by a major ESE–WNW-directed stretching that created a pervasive flat foliation and recumbent gneissic nappes of the first genre (D2) accompanied by a major Buchan-type metamorphism. This latter phase also displays porphyroblasts indicating dextral motion along the range. It was followed by later shortening nearly 90° to the stretching creating mostly upright structures with an E–W striking foliation and a following crenulation cleavage also with indication of continuing right-handed slip along the entire system (D3 and its subphases). The Visean to Bashkirian ‘flysches’ developed from north to south across the entire mountain range plus its bounding plains to the north and south and no flysch production accompanied any later deformation. All the major structures of the late Palaeozoic range face upwards. Such an architecture and sequence of events create a picture that is odd in terms of an orogenic development leading one to suspect the presence here of what John F. Dewey called ‘spoof orogeny’, but seems in accord with a keirogen that created, in addition to extension, a high geothermal gradient and associated Buchan-type HT/LP metamorphism. It was during the later episodes of the strike-slip in the Pyrenees that the Cantabrian Orocline formed. It seems clear that a westerly escaping fragment between the Pyrenean keirogen and the left-later shear systems of inner Iberia indented the formerly N–S Iberian segment of the Hercynides and produced the extreme curvature of the orogen similar to the tectonic evolution of the Appenninic/Alpine/Dinaride Orocline around the Apulian indenter (Argand's African promontory), the Carpathian/Balkan Orocline around the Moesian indenter, Hazara and the Assam Oroclines22The Hazara and the Assam oroclines are so tight that they have been classified also as syntaxes by Suess. But not all syntaxes are also oroclines: For example, the NE Greenland syntaxis joins two branches of early Palaeozoic orogens that formed along margins that meet at a right angle. The active Aleutian and the Kuril/Kamchatka arcs also meet at a syntaxis that is not an orocline. Oroclines are also different from simple deflections (Bucher, 1933, fig. 18; note here, however, that the fixist Bucher used at least four oroclines, namely those of Calabria, western Alps, Carpathians and the Balkans, and only one true deflection, the Alpine-Carpathian passage, to illustrate the concept of deflection in this figure; also in the same figure his concept of syntaxis is entirely wrong) that form around curved margins. Oroclines must show strain indicating bending synchronously with or postdating orogeny. around the Indian indenter (Argand's Indian promontory). Such a model is not in itself inconsistent with models involving lithospheric delamination, but I find it hard to see how the highest supracrustal sedimentary rocks in the core of the Cantabrian Orocline could have been preserved if a lithosphere-detaching thickening had taken place here. Contrary to the earlier models of lithospheric detachment by thickening, even much of Tibet still preserves its thick lithospheric root.

Taxation within electricity auctions with dominant firm

This paper gives an additional contribution to the literature on environmental policy under imperfect competition. It aims at exploring how imperfect competition can affect the performance of environmental policy. The focus is on pollution taxes and power generation which is a particularly interesting case for three reasons. First it is one of the most important environmentally regulated markets. Second the demand for electricity varies cyclically over time (for example on hourly basis). Third the pricing mechanism is a multi-period and multi-unit first price auctions. The main finding of the analysis is that, looking at the entire demand cycle, it is very unlikely (virtually impossible) that under imperfect competition taxation could increase emissions although, according to a part of the current literature, in principle pollution may increase in the short-run within specific cycle periods. Moreover this may happen under specific and unlikely conditions although, unlike what this literature suggests, large asymmetry of firms and extreme curvature of demand are not strictly necessary.

Rajiform locomotion: three-dimensional kinematics of the pectoral fin surface during swimming by freshwater stingray Potamotrygon orbignyi

Rajiform locomotion in fishes is dominated by distinctive undulations of expanded pectoral fins. Unlike other fishes, which typically interact with the fluid environment via multiple fins, undulating rays modulate a single control surface, the pectoral disc, to perform pelagic locomotion, maneuvering and other behaviors. Complex deformations of the broad, flexible pectoral fins occur as the undulating wave varies in three dimensions; pectoral fin kinematics and changes in waveform with swimming speed cannot be fully quantified by two-dimensional analyses of the fin margin. We present the first three-dimensional analysis of undulatory rajiform locomotion in a batoid, the freshwater stingray Potamotrygon orbignyi. Using three cameras (250 frames s(-1)), we gathered three-dimensional excursion data from 31 points on the pectoral fin during swimming at 1.5 and 2.5 disc lengths s(-1), describing the propulsive wave and contrasting waveforms between swimming speeds. Only a relatively small region of the pectoral fin (~25%) undulates with significant amplitude (>0.5 cm). Stingrays can maintain extreme lateral curvature of the distal fin margin in opposition to induced hydrodynamic loads, 'cupping' the edge of the pectoral fin into the flow, with potential implications for drag reduction. Wave amplitude increases across both anteroposterior and mediolateral fin axes. Along the anteroposterior axis, amplitude increases until the wave reaches mid-disc and then remains constant, in contrast to angulliform patterns of continuous amplitude increase. Increases in swimming speed are driven by both wave frequency and wavespeed, though multivariate analyses reveal a secondary role for amplitude.