Cone Axis Research Articles

Complete elliptical ring geometry provides energy and instrument calibration for synchrotron-based two-dimensional X-ray diffraction

A complete calibration method to characterize a static planar two-dimensional detector for use in X-ray diffraction at an arbitrary wavelength is described. This method is based upon geometry describing the point of intersection between a cone's axis and its elliptical conic section. This point of intersection is neither the ellipse centre nor one of the ellipse focal points, but some other point which lies in between. The presented solution is closed form, algebraic and non-iterative in its application, and gives values for the X-ray beam energy, the sample-to-detector distance, the location of the beam centre on the detector surface and the detector tilt relative to the incident beam. Previous techniques have tended to require prior knowledge of either the X-ray beam energy or the sample-to-detector distance, whilst other techniques have been iterative. The new calibration procedure is performed by collecting diffraction data, in the form of diffraction rings from a powder standard, at known displacements of the detector along the beam path.

Diversity of Ancient Conifers: The Jurassic Seed ConeBancroftiastrobus digitatagen. et sp. nov. (Coniferales)

Premise of research. A third genus of anatomically preserved conifer seed cones has been recognized from a Late Jurassic deposit in northeastern Scotland. This cone is described as Bancroftiastrobus digitata Rothwell, Mapes, Stockey et Hilton.Methodology. The cone was sectioned with the classic coal ball peel technique and studied and photographed with transmission light.Pivotal results. Bancroftiastrobus digitata is a cylindrical cone with large, helically arranged ovuliferous scales subtended by short bracts, each bract/scale complex bearing two unwinged inverted seeds on the adaxial surface of the ovuliferous scale. Ovuliferous scales have abaxial plications in the midregion and divide distally, forming up to nine free distal lobes that are vascularized and covered by a dense ramentum of trichomes. The cone axis forms a continuous woody cylinder that surrounds a parenchymatous pith. There are numerous resin canals in the cortex of the cone axis that extend into each bract/scale complex, both abaxial an...

SU‐E‐T‐612: Integral Dose Study of Non‐Coplanar 4pi Radiotherapy

Purpose: To quantify the integral doses of 4π highly non‐coplanar treatment plans and compare them to traditional coplanar IMRT plans. Methods: A systematic study was conducted using an elliptical cylinder, with a major axis length of 35.4 cm and minor axis length of 23.6cm. A 4.5cm diameter spherical tumor was embedded at 4 equally spaced radial locations on the long axis from the center to the periphery. Twenty 6MV conformal non‐coplanar beams were selected in a fashion so that their trajectories would form a circular cone 24° with respect to the cone axis that converged on the tumor. A coplanar plan using twenty evenly spaced conformal 6MV coplanar beams was conducted for comparison. The dose distribution was calculated using the convolution/superposition algorithm. A patient study was also conducted for 10 liver and 12 lung SBRT cases. A column generation algorithm was used to optimize both beam orientations and the fluence map. The dosimetry was compared to clinical plans using 2‐arc volumetric modulated arc therapy (VMAT). Results: For the centrally‐located tumor, non‐coplanar plans delivered up to 37% greater integral dose but the ratio decreased rapidly with the tumor locating more superficially. Approximately the same integral dose resulted from both planning methods at a tumor depth of 10 cm. For the tumor at 6cm depth, the non‐coplanar plan integral dose was approximately 10% lower. Compared to VMAT, the integral dose to the liver and lung SBRT patients were reduced by 17% and 42% using 4π, respectively. Conclusion: Non‐coplanar plans can reduce integral doses as exemplified by both the phantom and patient studies. The effect is most significant with shallower tumors, e.g. the tumor center within 10 cm of a given surface in the simplified phantom model. Actual patient treatments benefit more due to the optimization of the non‐coplanar beam angles.

Comparison of Cone Model Parameters for Halo Coronal Mass Ejections

Halo coronal mass ejections (HCMEs) are a major cause of geomagnetic storms, hence their three-dimensional structures are important for space weather. We compare three cone models: an elliptical-cone model, an ice-cream-cone model, and an asymmetric-cone model. These models allow us to determine three-dimensional parameters of HCMEs such as radial speed, angular width, and the angle [γ] between sky plane and cone axis. We compare these parameters obtained from three models using 62 HCMEs observed by SOHO/LASCO from 2001 to 2002. Then we obtain the root-mean-square (RMS) error between the highest measured projection speeds and their calculated projection speeds from the cone models. As a result, we find that the radial speeds obtained from the models are well correlated with one another (R > 0.8). The correlation coefficients between angular widths range from 0.1 to 0.48 and those between γ-values range from −0.08 to 0.47, which is much smaller than expected. The reason may be the different assumptions and methods. The RMS errors between the highest measured projection speeds and the highest estimated projection speeds of the elliptical-cone model, the ice-cream-cone model, and the asymmetric-cone model are 376 km s−1, 169 km s−1, and 152 km s−1. We obtain the correlation coefficients between the location from the models and the flare location (R > 0.45). Finally, we discuss strengths and weaknesses of these models in terms of space-weather application.

Pararaucaria carriisp. nov., Anatomically Preserved Evidence for the Conifer Family Cheirolepidiaceae in the Northern Hemisphere

A cylindrical permineralized conifer seed cone has been identified from the Officer Member of the Trowbridge Formation, near Izee, in east-central Oregon. The cone is preserved in a Middle Jurassic (Callovian) marine calcium carbonate concretion, associated with araucarian seed cones, conifer twigs and wood, cycad seeds, fern rachides, and lycopodialean remains and was prepared by the cellulose acetate peel technique. The specimen is abraded, 2.8 cm long and 1.3 cm wide, and consists of a cone axis with helically arranged bract/scale complexes, with a large ovuliferous scale and a broad, flattened bract. The bract/scale trace arises as a cylindrical unit from the cone axis, in which the bract and scale traces are separated by ground tissue. The traces separate immediately in the cortex to form a crescent-shaped bract trace and a horseshoe-shaped scale trace with associated sclerenchyma bands that form two triangular bundles toward the distal end of the scale. Ovuliferous scale tissue covers one inverted seed per scale, forming a pocket that contains the seed. Seeds are attached at the chalaza to the inside of the pocket. Seed integuments have an outer epidermis of isodiametric cells with dark contents; one or two layers of palisade cells, occasionally appearing in I-beam configuration; and several inner layers of randomly arranged cells. The nucellus is adnate to the integument, to near the apex, where it forms a cellular mound of tissue. Cylindrical cones with helically arranged bract/scale complexes, bract and scale free to the base, one seed per scale enclosed in a pocket, and triangular sclerenchyma bands are characteristic of the genus Pararaucaria, which recently has been placed in the extinct conifer family Cheirolepidiaceae. This third species extends the known range of Pararaucaria from the Southern Hemisphere to the Northern Hemisphere and emphasizes that the association of araucarian and pararaucarian conifers extended over a wide geographic area during the Jurassic.

Formation and Structure of Steady Oblique and Conical Detonation Waves

The formation and structure of oblique detonation waves initiated by semi-infinite wedges and cones are presented. For wedge or cone angles less than the deflection angle required for an oblique Chapman–Jouguet (CJ) detonation, different wave structures have been previously reported. Using the method of characteristics and numerical simulations, it is shown that, for such low wedge or cone angles, a CJ oblique detonation is eventually initiated following an induction process. It its thus demonstrated that shock-induced combustion with the reaction front remaining uncoupled to the oblique shock in the far field is not a valid solution. Simulations with semi-infinite cones reveal that the effect of the front curvature around the cone axis allows oblique detonations to be formed at angles lower than that of a planar CJ oblique detonation.

Plasma parameters and electromagnetic forces induced by the magneto hydro dynamic interaction in a hypersonic argon flow experiment

This work proposes an experimental analysis on the magneto hydro dynamic (MHD) interaction induced by a magnetic test body immersed into a hypersonic argon flow. The characteristic plasma parameters are measured. They are related to the voltages arising in the Hall direction and to the variation of the fluid dynamic properties induced by the interaction. The tests have been performed in a hypersonic wind tunnel at Mach 6 and Mach 15. The plasma parameters are measured in the stagnation region in front of the nozzle of the wind tunnel and in the free stream region at the nozzle exit. The test body has a conical shape with the cone axis in the gas flow direction and the cone vertex against the flow. It is placed at the nozzle exit and is equipped with three permanent magnets. In the configuration adopted, the Faraday current flows in a closed loop completely immersed into the plasma of the shock layer. The electric field and the pressure variation due to MHD interaction have been measured on the test body walls. Microwave adsorption measurements have been used for the determination of the electron number density and the electron collision frequency. Continuum recombination radiation and line radiation emissions have been detected. The electron temperature has been determined by means of the spectroscopic data by using different methods. The electron number density has been also determined by means of the Stark broadening of Hα and the Hβ lines. Optical imaging has been utilized to visualize the pattern of the electric current distribution in the shock layer around the test body. The experiments show a considerable effect of the electromagnetic forces produced by the MHD interaction acting on the plasma flow around the test body. A comparison of the experimental data with simulation results shows a good agreement.

The seed cone Eathiestrobus gen. nov.: Fossil evidence for a Jurassic origin of Pinaceae

Pinaceae and nonpinoid species are sister groups within the conifer clade as inferred from molecular systematic comparisons of living species and therefore should have comparable geological ages. However, the fossil record for the nonpinoid lineage of extant conifer families is Triassic, nearly 100 million years older than the oldest widely accepted Lower Cretaceous record for Pinaceae. An anatomically preserved fossil conifer seed cone described here extends the stratigraphic range of Pinaceae nearly 30 million years, thus reducing the apparent discrepancy between evidence from the fossil record and inferences from systematic studies of living species. Material was prepared as serial thin sections by the cellulose acetate peel technique, mounted on microscope slides, and viewed and photographed using transmitted light. A large cylindrical cone consisting of bract-scale complexes that diverge from the cone axis in a helical phyllotaxis has bracts and scales that separate from each other in the midregion and are of equal length and of nearly equal width. The cone has two inverted and winged seeds that are attached to the adaxial surface of each cone scale and, thus, represents an early member of the Pinaceae. Eathiestrobus mackenziei gen. et sp. nov. extends the fossil record for well-documented members of the family Pinaceae from the Lower Cretaceous to the Kimmeridgian Stage of the Upper Jurassic. This species also clarifies the set of characters that are diagnostic for seed cones of Pinaceae and reveals possible plesiomorphic characters for seed cones of the family.

Vortex Stabilization of Market Equilibrium in Theory and in Practice of Economics

Rotary movements of the object around the position of equilibrium is the most common type of dynamics in nature. The way of plotting trajectory resembles winding a line onto a cone of revolution or some other solid of revolution. The state of equilibrium, which is usually not reached by the system, is marked with the cone axis. The trajectory can move away from the state of equilibrium, or get closer to it. A similar behavior is observed in many two-dimensional economic models, both linear, and nonlinear. The simplest example is a linear cobweb model, where ‐ depending on slopes of linear demand function and linear function of supply ‐ price and quantity make a broken line with a growing, constant or decreasing amplitude around the equilibrium point. In nonlinear models, trajectories are more realistic. A natural space for exploring spiral trajectories is a three-dimensional space. Usually, it requires magnifying the model’s dimension by one. Economic vortices are made up by economic vectors of three constituents. It may be price, quantity, and time. Apparently, flat zigzags that can be seen on two-dimensional graphs of cobweb models are orthogonal projections of spinning trajectories. Vortexes created by nonlinear models are much smoother than the vortices created by linear models. The real economic vectors create smooth spiral trajectories, which indicates necessity to employ nonlinear dynamics in economic modeling. The basis for rotary movements are surface areas of solids of revolution of the second degree. The kinematics of solids indicated by market shows that they also rotate in three-dimensional space. It resembles precession movements. In economic dynamics we have at least a double rotation. What rotates are both economic vectors as well as the solids created by them.

Vector wave measurements on landmine detection with an array of loudspeakers focused on the ground

An array of 16 loudspeakers, deployed along a segment of the base of a right circular cone, was used to focus sound on soils overlying buried targets lying along the conical axis of the source. Measurements were made at several incident angles tending toward grazing to examine long range detection for humanitarian de-mining applications. Targets and soils were instrumented with triaxial geophone and accelerometer sensors. The transmission of airborne sound into the soils produced vertical and radial vibrations in both the soil and the targets, which included rigid and compliant mine cases. Several waveform transmission types were utilized. The compliant targets provided resonances amenable to optical detection, depending on the acoustic, geometric and environmental parameters, which are discussed. [Work supported by the IRD program at ARL:UT Austin, in cooperation with the National Center for Physical Acoustics.]

Synthesis and magnetic reversal of bi-conical Ni nanostructures

Template synthesis in polyethylene terephthalate (PET) membranes has been used to grow hour glass shaped nickel nanowires with a constriction in the range of tens of nanometers at the center. Anisotropic magnetoresistance measurements have been performed on a single nanowire to follow magnetization reversal of the structure. The results are explained via 3D micromagnetic simulations showing the appearance of a complex vortex state close to the constriction whose propagation depends on the angle between the cone axis and the applied field. The interest of this original growth process for spintronics is discussed.

Analytic treatment of nuclear spin–lattice relaxation for diffusion in a cone model

We consider nuclear spin–lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin–lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole–dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin–lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.

Non-line-of-sight ultraviolet single-scatter propagation model

A universal non-line-of-sight (NLOS) ultraviolet single-scatter propagation model in noncoplanar geometry is proposed to generalize an existing restricted analytical model. This generalized model considers that the transmitter and the receiver cone axes lie in the same plane or different planes, where they can be pointed in arbitrary directions. The model is verified by extensive simulations, showing that the proposed model is consistent with the original NLOS single-scatter propagation model and the Monte Carlo model. The path loss performance is further investigated in terms of different noncoplanar geometric settings and path loss dependence is also analyzed for different factors, including scattering volume size, relative position between the scattering volume and the transceiver, and radiation intensity of the transmitter.

Terahertz surface plasmon polaritons on a conductive right circular cone: Analytical description and experimental verification

We report on an analytical solution of Maxwell's equations for the propagation of surface plasmon polaritons on a right circular cone. The problem was solved for THz frequencies in real metals and was therefore derived using the Leontovich approximation, which is valid for media with small surface impedances. The solution also accounts for both surface plasmon polaritons that are axisymmetric and those that have an angular structure in a plane normal to the cone's axis. This was an important consideration since it is crucial for describing surface phenomena such as surface-enhanced absorption, fluorescence, and Raman scattering. Our findings predict a total reflection of surface plasmon polaritons at the cone's apex, which was experimentally verified by an absence of light emitted from a heated cone's tip into the far-field region.

Mellin and Green operators of the corner calculus

We study spaces of parameter-dependent Mellin plus Green operators occurring as operator-valued symbols of the pseudo-differential calculus on a manifold with corners. Here we mainly focus on holomorphic families in the complex Mellin covariable belonging to the corner axis variable \({t\in\mathbb{R}_{+},}\) while we impose the full asymptotic information with respect to the subordinate cone axis variable \({r\in\mathbb{R}_{+},}\) here in terms of continuous asymptotics.

Proliferating seed cones in Metasequoia glyptostroboidesHu & Cheng (Cupressaceae s.l., Coniferales) elucidate the evolution of seed cones and ovules in Cupressaceae s.l.

AbstractProliferating seed cones are frequent in extant conifers. However, most proliferations are not useful for elucidating evolutionary scenarios, representing only chaotic mutations or a proliferation of the cone axis. In contrast the proliferating cones in Metasequoia studied here do not show a simple modification of a well understood pattern but show a known pattern with features that do not normally appear. A correct interpretation might allow a new hypothesis about the evolution of seed cones and ovules in conifers. In these proliferated Metasequoia seed cones several cone scales carried axillary, leafy short shoots instead of ovules. In most Cupressaceae, the shoot subtending the ovule – the so called seed scale – can no longer be detected. In proliferated seed cones a leafy short shoot replaces the ovules. This kind of proliferation can be regarded as an atavism, assuming that the sterile leaves on this short shoot represent transformed sterile ovules. This hypothesis is supported by the fact that the ovules in the axil of cone scales and the leaves formed on short shoots show a similarly centripetal or acropetal developmental pattern (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A New Species of the Extinct Genus Schizolepis from the Jurassic Daohugou Flora, Inner Mongolia, China with Special Reference to the Fossil Diversity and Evolutionary Implications

Abstract: Schizolepis daohugouensis sp. nov. is described from the Jurassic sediments of Daohugou flora, from Ningcheng County, Inner Mongolia Autonomous Region, China. The female cone is slender, cylindrical in shape, seed scale complexes are loosely and helically arranged on the cone axis at intervals of 3–5 mm. The seed scales are bilobed and divided almost from the base; the scales have no evident petiole but an articulation at the region of attachment to the cone axis. Each lobe of the seed scales is oval in shape, widest at the lower middle part; lobes are obtusely pointed with entire margins. Bract scale is fan shaped. Based on the records of Schizolepis, this is the first report of the occurrence of female cone of Schizolepis with the seed scales, the winged seeds and vegetative branches preserved together in the Jurassic deposits. The new discovery provides evidence that confirms the phylogenetic position of Schizolepis to the extant Pinaceae.

Optical anisotropy induced by torsion stresses in LiNbO_3 crystals: appearance of an optical vortex

We report the results of studies of the torsion effect on the optical birefringence in LiNbO(3) crystals. We found that the twisting of those crystals causes a birefringence distribution revealing nontrivial peculiarities. In particular, they have a special point at the center of the cross section perpendicular to the torsion axis where the zero birefringence value occurs. It has also been ascertained that the surface of the spatial birefringence distribution has a conical shape, with the cone axis coinciding with the torsion axis. We revealed that an optical vortex, with a topological charge equal to unity, appears under the torsion of LiNbO(3) crystals. It has been shown that, in contrast to the q plate, both the efficiency of spin-orbital coupling and the orbital momentum of the emergent light can be operated by the torque moment.

Non-line-of-sight single-scatter propagation model for noncoplanar geometries

In this paper, a geometrical propagation model is developed that generalizes the classical single-scatter model under the assumption of first-order scattering and non-line-of-sight (NLOS) communication. The generalized model considers the case of a noncoplanar geometry, where it overcomes the restriction that the transmitter and the receiver cone axes lie in the same plane. To verify the model, a Monte Carlo (MC) radiative transfer model based on a photon transport algorithm is constructed. Numerical examples for a wavelength of 266 nm are illustrated, which corresponds to a solar-blind NLOS UV communication system. A comparison of the temporal responses of the generalized model and the MC simulation results shows close agreement. Path loss and delay spread are also shown for different pointing directions.

Systematics, Phylogenetics, and Reproductive Biology ofFlemingites arcuatussp. nov., an Exceptionally Preserved and Partially Reconstructed Carboniferous Arborescent Lycopsid

Exceptionally preserved lycopsid remains from an ex situ chert–carbonate cobble found on the Yorkshire coast, United Kingdom, are here reconstructed as Flemingites arcuatus sp. nov. Megasporophylls are C shaped and emerge from the cone axis at a relatively acute angle. Megasporangia are adaxial on sporophylls and typically contain four megaspore tetrads. Megaspores are described as Lagenicula wellmanii sp. nov.; they are 1.0–1.7 mm in diameter and have a pronounced gula and numerous vermiform spines with bulbous apices. Archegonia occur in some megaspore apices, and developing oocytes are also rarely preserved. Trilete microspores found in an isolated microsporangium conform to Lycospora orbicula. Leaves and sporophylls are helically arranged and have stomata organized in rows along abaxial grooves. Correlation of these organs allowed the resulting partial plant to be added to an existing cladistic matrix. Analyses confirmed the provisional assignment of F. arcuatus to the stem genus Paralycopodites. Stratigraphic comparisons of the megafossils and spores restrict the likely age of the cobble from the Early Mississippian to the Middle Pennsylvanian. The plants were deposited alongside univalve crustaceans in a swamp environment where preservation was probably enhanced by local volcanic activity. The as yet unlocated lagerstätte appears comparable in quality of preservation with the Lower Devonian Rhynie Chert.