Family Of Rays Research Articles

DNA barcoding of chondrichthyans in South African fisheries

South Africa has one of the highest chondrichthyan species diversities in the world, with more than 35% affected by regional fisheries. In order to evaluate the impact of these activities, accurate data on species occurrence is needed. Here, we tested a more robust identification approach of chondrichthyan species in South Africa by sequencing a subsample of specimens (n = 75) collected from different regional fisheries at the mitochondrial cytochrome c oxidase subunit I (COI) gene. Morphological identification of these specimens was evaluated through sequence similarity testing of barcoding sequences available in the Barcode of Life Data (BOLD) database. A total of 23 species from ten families of sharks, skates and rays were identified with an overall agreement of 73% between genetic identification and initial morphological identifications made in the field. Despite some limitations of the COI gene for species identity and the small number of samples analysed in the study, results suggest that a more integrated species identification approach of chondrichthyans can be used to assist conservation of chondrichthyans in South African fisheries.

The fate of the most threatened order of elasmobranchs: Shark-like batoids (Rhinopristiformes) in the Arabian Sea and adjacent waters

Shark-like batoids (Rhinopristiformes) represent of some of the most threatened families of sharks and rays. In certain regions, they are a relatively important component of elasmobranch fisheries, commonly taken as bycatch in gillnets and longlines, but also increasingly targeted for their high value fins and meat. This demand, combined with intense fishing pressure, has resulted in global population declines as well as localized extinctions of many rhinopristoids. Yet, information on the life-history, ecology, and conservation status remains scarce for most species. From 2010–2012, data was opportunistically collected from thirteen rhinopristoid species, including four endemic to the Arabian Sea and adjacent waters, landed from fisheries in the United Arab Emirates or transported from Oman. Four taxa dominated and comprised 92% of total shark-like batoid landings by number, namely Rhynchobatus spp., the Halavi guitarfish (Glaucostegus halavi), bowmouth guitarfish (Rhina ancylostoma), and Bengal guitarfish (Rhinobatos annandalei). Details of the biological characteristics, including size composition and sex ratios, are presented for each species. While there remain identification challenges related to some unresolved taxonomic issues, with several likely undescribed species occurring in the region, the first regional checklist of rhinopristoids is provided. Evidence of significant declines in landings combined with increasing fishing effort over a short time period raises concern about the status and long-term persistence of many species. Increased research to understand the biology, ecology, diversity, and resilience to harvest by fisheries is critical to the effective management of these species and an urgent precautionary approach to their conservation is warranted.

Modeling of Pulse Signals in 3D Propagation Problems of Deep-Water Acoustics Based on the Modified Maslov’s Canonical Operator

Formulae for an asymptotic solution of 3D problems of acoustical pulse signals propagation in the deep sea based on the modified Maslovs canonical operator are presented. The proposed formulae for acoustic pressure are applicable both in the regular case and in the situation when the receiver is located at a focal point of a family of rays. The asymptotics is compared with the solution computed using normal modes theory. It is shown that the derived formulae ensure very high precision of calculation of a pulse signal time series at the receiver point.

Ray-optical Poincaré sphere for structured Gaussian beams

A general family of structured Gaussian beams naturally emerges from a consideration of families of rays. These ray families, with the property that their transverse profile is invariant upon propagation (except for cycling of the rays and a global rescaling), have two parameters, the first giving a position on an ellipse naturally represented by a point on the Poincar\'e sphere (familiar from polarization optics), and the other determining the position of a curve traced out on this Poincar\'e sphere. This construction naturally accounts for the familiar families of Gaussian beams, including Hermite-Gauss, Laguerre-Gauss and Generalized Hermite-Laguerre-Gauss beams, but is far more general. The conformal mapping between a projection of the Poincar\'e sphere and the physical space of the transverse plane of a Gaussian beam naturally involves caustics. In addition to providing new insight into the physics of propagating Gaussian beams, the ray-based approach allows effective approximation of the propagating amplitude without explicit diffraction calculations.

Three-dimensional inverse problem of geometrical optics: a mathematical comparison between Fermat's principle and the eikonal equation.

In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c1,g(x,y,z)=c2), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.

Hamilton’s optics

Building on work by Fermat and Huygens, Hamilton transformed the study of geometrical optics in his very first paper, presented when still in his teens. His ‘characteristic function’ was an analytical way to describe wavefronts, and in his hands a powerful tool to look at families of rays rather than isolated ones. His prediction of internal and external conical refraction in some crystals and its spectacular verification in a few months established his reputation among his contemporaries. This formulation of optics uncovered many general properties, not easy to see in the conventional method of tracing individual rays. The deepest outcome of his early optical work was a parallel view of the mechanics of particles, which played a fundamental role in the birth of quantum mechanics and continues to be the standard framework for classical mechanics up to the present time.

Billiard transformations of parallel flows: A periscope theorem

We consider the following problem: given two parallel and identically oriented bundles of light rays in n-dimensional Euclidean space and given a diffeomorphism between the rays of the former bundle and the rays of the latter one, is it possible to realize this diffeomorphism by means of several mirror reflections? We prove that a 2-mirror realization is possible if and only if the diffeomorphism is the gradient of a function. We further prove that any orientation reversing diffeomorphism of domains in the plane is locally the composition of two gradient diffeomorphisms, and therefore can be realized by 4 mirror reflections of light rays in 3-space, while an orientation preserving diffeomorphism can be realized by 6 reflections. In general, we prove that an (orientation reversing or preserving) diffeomorphism of wave fronts of two normal families of light rays in 3-space can be realized by 6 or 7 reflections.

What Is the Fate of Amputee Sawfish?

The sawfishes (Pristidae) are the most threatened of all of the world's shark and ray families, which is largely due to overfishing (Dulvy et al. 2014). There are five extant species of sawfish, all of which possess an enlarged, tooth-lined rostrum (or saw), which has unfortunately been central to their widespread global decline, due to the saw rendering them extremely susceptible to net entanglement (Faria et al. 2013; Dulvy et al. 2014; Whitty et al. 2014). Individuals may suffer mortality during entanglement or be euthanized or desawed prior to net removal for either operator safety or to simplify removal of the sawfish from the net.

The works of William Rowan Hamilton in geometrical optics and the Malus–Dupin theorem

The works of William Rowan Hamilton in Geometrical Optics are presented, with emphasis on the Malus-Dupin theorem. According to that theorem, a family of light rays depending on two parameters can be focused to a single point by an optical instrument made of reflecting or refracting surfaces if and only if, before entering the optical instrument, the family of rays is rectangular (\emph{i.e.}, admits orthogonal surfaces). Moreover, that theorem states that a rectangular system of rays remains rectangular after an arbitrary number of reflections through, or refractions across, smooth surfaces of arbitrary shape. The original proof of that theorem due to Hamilton is presented, along with another proof founded in symplectic geometry. It was the proof of that theorem which led Hamilton to introduce his \emph{characteristic function} in Optics, then in Dynamics under the name \emph{action integral}

Irreducibility of the Gorenstein loci of Hilbert schemes via ray families

We analyse the Gorenstein locus of the Hilbert scheme of $d$ points on $\mathbb{P}^n$ i.e. the open subscheme parameterising zero-dimensional Gorenstein subschemes of $\mathbb{P}^n$ of degree $d$. We give new sufficient criteria for smoothability and smoothness of points of the Gorenstein locus. In particular we prove that this locus is irreducible when $d\leq 13$ and find its components when $d = 14$. The proof is relatively self-contained and it does not rely on a computer algebra system. As a by--product, we give equations of the fourth secant variety to the $d$-th Veronese reembedding of $\mathbb{P}^n$ for $d\geq 4$.

Reconstruction of reflector images using the C-SAFT method with account for the anisotropy of the material of the test object

A modification of the combined SAFT (C-SAFT) method for reconstructing reflector images in a test object, which consists of several regions with different acoustic properties, in particular, anisotropy properties, is proposed. A method for the direct construction of a family of rays, which exit from the point where a transmitter is positioned, is used to calculate the ray trajectories with consideration for the anisotropy. After the family of rays is constructed, it is possible to analyze their attribution to a certain acoustic scheme and to approximate the calculated delays on the spatial grid of the region of iterest (ROI). This will allow one to calculate the pulse travel time from a transmitter to any point of the ROI and back to the receiver and to use the C-SAFT method for reconstructing reflector images. During processing of echo signals that were calculated in the CIVA program, the efficiency of the proposed method was demonstrated. Accounting for the anisotropy in a model experiment increased the focusing quality when reconstructing images of side-drilled holes in a specimen with a repair weld.

Reconstruction of images of reflectors using the correlation method at an arbitrary number of reflections of an ultrasonic pulse from the boundary of a test object that consists of regions with different acoustic properties

An algorithm for reconstructing images of reflectors from echo signals that propagate in a test object, which consists of several regions with different acoustic properties, is considered. The ray trajectories are calculated using the method of direct construction of the family of rays that escape from the point where a transmitter is located but not the Fermat variational principle. After the family of rays is constructed, their belonging to a certain acoustic scheme can be analyzed and the approximation of the calculated delays on the spatial mesh of the image reconstruction region (IRR) can be performed. This will allow the reconstruction of both the pulse travel time from the transmitter to any point in the IRR and back to the receiver and the attenuation of the pulse amplitude caused by the divergence, reflection, and refraction effects at the boundaries of the regions that constitute the test object. Numerical and model experiments show the working capacity of the proposed algorithm for reconstructing reflector images.

Singularities in a teacup

Standard presentations of optics concentrate on ideal systems made for imaging which bring all rays from a point source to one focus. But, in Nature, or in realistic optical systems with defects, rays do not behave precisely in this way. Rather than the focus simply being blurred, the rays, after reflection or refraction, form beautiful and rather universal patterns of bright lines known as caustics. Mathematically speaking, a family of rays is best viewed as a surface in a higher-dimensional space where we keep track of both the position and direction of rays. The intensity enhancement on approaching the caustic line is a singularity, arising from projection of a smooth surface from higher dimensions to lower dimensions. The universal features of such singularities, which arise in many contexts beyond optics, formed a major theme of Vladimir Arnold’s work after 1965, when he was exposed to Rene Thom’s vision of ‘catastrophe theory’. Arnold and his school made seminal contributions to singularity theory.

Raman and the mirage revisited: confusions and a rediscovery

Raman argued that in a continuously varying layered medium, such as air above a hot road, a ray that bends so as to become horizontal must remain so, implying that the reflection familiar in the mirage cannot be explained by geometrical optics. This is a mistake, as standard ray curvature arguments demonstrate. But a simple limiting process, in which the smoothly varying refractive index is approximated by a stack of thin discrete layers, is not quite straightforward because it involves a curious singularity, related to the level ray envisaged by Raman. In contrast to individual rays, families of rays possess caustic (focal) singularities. These can be calculated explicitly for two families of rays that are relevant to the mirage. Only exceptionally does the locus of reflection (lowest points on the rays) coincide with the caustics. Caustics correspond to the ‘vanishing line’, representing the limiting height of objects that can be seen by reflection. For these two families, the waves that decorating mirage caustics are described by the universal Airy function, and can be calculated exactly.

Gross Features of Nuclear Interactions around 1015eV through Observation of Gamma Ray Families

A systematic analysis is made on the 106 ϒ-ray families with visible energy in the range of 100∼300 TeV observed in the Chacaltaya emulsion chamber experiment. A new method called ‘decascading’ is introduced to pick up a cluster of ϒ-rays and electrons in a family, so that the cluster is an air cascade from one parent ϒ-ray. The application of ‘decascading’ method to the family data gives information on original ϒ-rays produced at the atmospheric nuclear interactions. The results are compared with expected ones from the simulation calculation on the base of H-quantum model, and with data from the target interactions at lower energy range (ΣEϒ=20 ∼100 TeV). The conclusion is that the characteristics of nuclear interactions at the concerned family energy range (E0≃1,000 TeV) are in accordance with those at the target interaction range (E0≃100 TeV), with increased ratio of frequencies of a heavy fire-ball (SH-quantum) to a small and usual fire-ball (H-quantum).

Claves taxonomicas para el reconocimiento dentario en taxa del superorden Rajomorphii de Chile (Chondrichthyes, Batoidea)

A series of keys with external and internal dental morphologic features for the identification of each order, family and genus of rays and skates of the bato...

Quality factors of deformed dielectric cavities

An analysis is provided of the degradation that arises in the quality factor of a whispering gallery mode when a circular or spherical dielectric cavity is deformed. The large quality factors of such resonators are important to their use in applications such as sensors, wavelength filters or lasers. Yet a straightforward analysis of the effect of shape deformation on quality factors cannot be given because the underlying complex ray data demanded by a standard eikonal approximation frequently does not exist. In this paper we exploit an approach that has been successfully used elsewhere to describe the strong directional emission of such systems, based on a perturbative treatment of the relevant complex ray families. Applicable when the radial perturbation is formally of the order of a wavelength, the resulting approximation successfully describes changes to the quality factor using the ray geometry in a neighbourhood of a discrete set of escaping rays guiding the directions of maximum emitted intensity.

Taxonomic dental keys for the Chilean taxa of the superorder Rajomorphii (Chondrichthyes, Batoidea)

A series of keys with external and internal dental morphologic features for the identification of each order, family and genus of rays and skates of the batoids known in Chile, are presented. In the case of families Rhinobatidae, Torpedinidae, Narcinidae, Myliobatidae, Mobulidae, Dasyatidae and Urotrygonidae, an identification at the species level is possible. In other cases, due to limitations imposed by the existing knowledge, only discrimination up to genus is allowed. These keys are a complementary tool for the diagnosis of rays suitable for the identification of dental fragments, paleontological discoveries of teeth as well as for jaw teeth. This tool offers a novel taxonomic support, which includes dental features different from those considered nowadays for this superorder.

Differences between emission patterns and internal modes of optical resonators

The evanescent wave field outside an optical resonator is typically strongly directional when the shape deviates even very slightly from being perfectly circular or spherical. In this Rapid Communication we show that the tunneling mechanism underlying escape from such weakly deformed resonators can lead to emission patterns that look quite different to the corresponding internal mode. A direct short-wavelength analysis is not possible because the required complex ray data cannot be found due to the presence of natural boundaries. We show, however, that an approach based on perturbative approximation of the ray families successfully describes this phenomenon. In appropriate limits, the emission pattern allows one effectively to perform a direct observation of solutions of the one-dimensional Schrödinger equation in the complex plane.

Rooms with a view: A novel approach to iterated multidimensional wave conversion

Ray tracing in the presence of linear mode conversion leads to a ‘splitting’ of an incoming ray into two outgoing rays. When the rays are confined to a cavity, the rays can re-enter the conversion region many times, leading to iterated conversion. In this paper, we present new methods for the analysis of this problem. These involve a shift from local to global methods of analysis, and a shift in emphasis from the study of ray evolution in the dispersion surface to the study of the iterated dynamics of rays crossing the conversion surface. The analytical methods are quite general and can be applied in phase spaces of arbitrary dimension. In two spatial dimensions, ( x, y), i.e. with a four-dimensional ray space, ( x, y, k x , k y ), rays are confined to three-dimensional regions called rooms, with one room for each wave type. In these rooms the rays do not cross, but when they intersect the conversion surface a family of converted rays is produced in the other room. The use of rooms allows a full view of the phase space dynamics of the iterated conversion of ray families. A simple two-dimensional model, inspired by the Budden resonance model, is presented as an example of these ideas.