Thin Ring Research Articles

Design and analysis of a modified segmented cladding fiber with large mode area

This paper proposes a novel segmented cladding fiber structure for large mode area properties. In this structure a thin ring is placed between the high index core and nonuniform cladding. It is called Single-Ring Segmented-Cladding Fiber (SR-SCF). The novel fiber offers the possibility of single-mode(SM) operation from 1µm to 1.7µm with a large core diameter. With illustrations, the fiber has a better SM operation than segmented-cladding fiber (SCF) is demonstrated. A large effective area of 1000µm2 is achieved. The SM operation with very high suppression of the higher order modes can arise by 76%. Moreover, mode spacing between the adjacent modes (LP01 and LP11) is also improved significantly. Besides, the bending property is analyzed. It is found that the fiber is insensitive to bending angle ranging from −180° to 180° at bending radius of 30cm. The proposed fiber will play an important role in developing high power fiber laser, fiber amplifier and high power delivery application.

Vibrations of tori with hollow elliptical cross-section from a three-dimensional theory

Natural frequencies of a toroidal shells of revolution with hollow elliptical cross-section are determined by the Ritz method from a three-dimensional (3-D) theory while traditional shell theories are mathematically two-dimensional (2-D). The Legendre polynomials, which are mathematically orthonomal, are used instead of ordinary algebraic polynomials as admissible functions. The present analysis is based upon the circular cylindrical coordinates while the toroidal coordinates have been used in general. Potential and kinetic energies of the torus are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the torus. Comparisons are made between the frequencies from the present 3-D method, a 2-D thin shell theory, and thin and thick ring theories. The present method is applicable to very thick toroidal shells as well as thin ones.

EFFECT OF LATERAL FRICTION IN THE VOLUMETRIC RESPONSE OF HIGHLY COMPACTED CLAY SAMPLES SUBMITTED TO OEDOMETRIC TEST

The use of oedometer test to determine the volumetric response of soil samples dates from the beginnings of soil mechanics. Currently, the use of the test has been focused in the study of natural samples that are trimmed in thin wall rings, which do not generate initial stress states that could perturb the volumetric response of the sample. However, due to the increasing interest in studing highly compacted swelling soils, in the case of engineered barriers for nuclear waste disposal, this test has been conducted on samples directly compacted in the oedometer ring. This practice introduces an initial stress state that affects the volumetric response due to frictional effects. In this paper, some results of hydration tests on compacted swelling clay are presented to point out such effects, permitting to show the relevance of the way the samples are prepared, which is the goal of this work.

In Memoriam: Dr. Clive L. Dym (1942–2016)

In Memoriam: Dr. Clive L. Dym (1942–2016)

Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring

We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro-)vacuum exact solutions of Einstein's equations, we first considered the Majumdar--Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach--Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do {\em not} involve rotation and the negative value is achieved due to the {\em electric}-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather non-trivial landscapes {\em outside} the horizon.

ZONAL TOROIDAL HARMONIC EXPANSIONS OF EXTERNAL GRAVITATIONAL FIELDS FOR RING-LIKE OBJECTS

We present an expression of the external gravitational field of a general ring-like object with axial and plane symmetries such as oval toroids or annular disks with an arbitrary density distribution. The main term is the gravitational field of a uniform, infinitely thin ring representing the limit of zero radial width and zero vertical height of the object. The additional term is derived from a zonal toroidal harmonic expansion of a general solution of Laplace's equation outside the Brillouin toroid of the object. The special functions required are the point value and the first-order derivative of the zonal toroidal harmonics of the first kind, namely, the Legendre function of the first kind of half integer degree and an argument that is not less than unity. We developed a recursive method to compute them from two pairs of seed values explicitly expressed by some complete elliptic integrals. Numerical experiments show that appropriately truncated expansions converge rapidly outside the Brillouin toroid. The truncated expansion can be evaluated so efficiently that, for an oval toroid with an exponentially damping density profile, it is 3000–10,000 times faster than the two-dimensional numerical quadrature. A group of the Fortran 90 programs required in the new method and their sample outputs are available electronically.

Numerical Study of the Instability and Flow Transition in a Vortex-Ring/Wall Interaction

Instability and fl w transition of a vortex ring impinging on a wall were investig ated by means of large-eddy simulation for two vortex core thicknesses corresponding to thin and thick vortex rings. Various fundamental mechanisms dictating the fl w behaviours, such as evolution of vortical structures, instability and breakdown of vortex rings, development of modal energies, and transition from laminar to turbulent state, have been studied systematically . Analysis of the enstrophy of wrapping vortices and turbulent kinetic energy (TKE) in fl w fiel indicates that the formation and evolution of wrapping vortices are closely associated with the fl w transition to turbulent state. It is found that the temporal development of wrapping vortices and the growth rate of axial fl w generated around the circumference of the core region for the thin ring are faster than those for the thick ring. The azimuthal instabilities of primary and secondary vortex rings are analysed and the development of modal energies reveals the fl w transition to turbulent state. The law of energy decay follows a characteristic k 5=3 law, indicating that the vortical fl w has become turbulent. The results obtained in this study provide physical insight into the understanding of the instability mechanisms relevant to the vortical fl w evolution.

Dynamic stability of biaxially strained thin sheets under high strain-rates: response to local perturbations

This work pertains to the stability of structures under rapid loading rates when inertia is taken into account. In contrast to the widely used approach in the relevant literature, which is based on the method of modal analysis to determine the structure’s fastest growing eigenmode—meaningful only for cases where the velocity of the perfect structure is significantly lower than the associated characteristic wave propagation speeds—the present study analyzes the time-dependent response to spatially localized perturbations of the transient (time-dependent) states of these structures, in order to understand the initiation of the corresponding failure mechanisms. We are motivated by the experimental studies of Zhang and Ravi-Chandar (Int J Fract 142:183-217, 2006), Int J Fract 163:41-65, (2010) on the high strain-rate expansion of thin rings and tubes, which show no evidence of a dominant wavelength in their failure mode and no influence of strain-rate sensitivity on the necking strains. Recently, Ravi-Chandar and Triantafyllidis (Int J Solids Struct 58:301-308, 2014) studied the dynamic stability of an incompressible, nonlinearly elastic bar at different strain-rates by following the evolution of localized small perturbations introduced at different times. The same approach is followed here for the biaxial stretching of thin plates, where we follow the time evolution of spatially localized perturbations and their interactions. The nonlinear time evolution of a such a perturbation is studied numerically and it is shown that these structures are stable until the time when the condition for the loss of ellipticity is reached. An analytical method, based on linearization, is used to define the size of the influence zone of a point-wise perturbation and we study its dependence on constitutive laws and loading conditions.

Vibration Analysis of Toroidal Shells with Hollow Circular Cross-Section Having Variable Thickness

AbstractA three-dimensional (3D) Ritz method of analysis is presented for determining the free vibration frequencies of completely free, toroidal shells of revolution with hollow circular cross-section having variable thickness. Displacement components ur, uθ, and uz in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in θ, and ordinary algebraic polynomials in the r and z directions. Strain and kinetic energies of the torus are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the torus. Comparisons are made between the frequencies from the present 3D Ritz method, a 3D finite-element method, experimental methods, and thin and thick ring theories.

Analyzing Out-of-Plane Vibration of a Rotating Ring with Wave Propagation

Wave propagation is introduced to analyze out-of-plane vibration problem of a rotating ring. Harmonic wave solutions are found for the coupled equations of the axial and torsional motion. Wavenumber spectra and phase velocity map are obtained, and the ratio of axial displacement to torsional displacement and the cut-off frequencies are determined. Examples for the free vibration of the uniform rotating thin ring are given to illustrate the validity of the wave propagation. This research will be valuable in the application of a solid cage in high speed roller bearing.

Ultrasound and gross anatomy of the brachial plexus and major nerves of the forelimb. An anesthetic approach using the domestic rabbit (Oyctolagus cuniculus) as an experimental model1.

To update the gross and sonographic anatomy and propose landmarks to perform ultrasound-guided (US-guided) axillary brachial plexus block (BPB) in rabbits. Forty New Zeeland's rabbit (NZR) cadavers were dissected and the nerves were trimmed, identified, measured, and photographed. Additionally, in twenty NZRs, sonographic images of brachial plexus (BP) were performed through a simple-resolution ultrasound device. The US-guided block was achieved through a minimum volume of lidocaine necessary to surround the BP roots. The effectiveness of the brachial plexus block was assessed on sensitivity and motor functions. The BP resulted from connections between the ventral branches of the last four cervical spinal nerves and the first thoracic spinal nerve. In the axillary sonoanatomy, the BP appeared as an agglomerate of small, round hypoechoic structures surrounded by a thin hyperechoic ring. The amount of time and the minimum volume required to perform was 4.3 ± 2.3 min and 0.8 ± 0.3ml, respectively. The gross and sonographic anatomy of the BP showed uncommon morphological variations. Moreover, from sonographic landmarks, we showed complete reproducibility of the axillary US-guided brachial plexus block with simple resolution equipment and small volume of anesthetics required.

Design and Analysis of a Microstructure Ring Fiber for Orbital Angular Momentum Transmission

In this paper, we propose a novel microstructure fiber with annular core for transmitting optical orbital angular momentum (OAM), and the OAM modes are calculated under different structure parameters of the fiber. Compared with the previous hollow step-index ring fiber, the proposed fiber brings higher refractive index contrast between the ring core and the cladding region by using only the single material of silica. The designed fiber can support more well-separated OAM modes with both thin and thick rings. Simulation results show that the novel microstructure ring fiber is promising to be applied in fiber-based OAM multiplexing in order to improve communication capacity.

Pyogenic cerebral abscesses demonstrating facilitated diffusion

ObjectivePyogenic cerebral abscesses are associated with high morbidity and mortality when treatment is delayed. Benign clinical presentation, as well as absence of restricted diffusion on MRI may contribute to missed diagnoses and delays. The authors sought to elucidate characteristics associated with facilitated diffusion on the MRIs of patients with pyogenic abscesses. Patients and methodsThe authors performed a 10-year retrospective review of prospectively attained data for patients undergoing mass resection by a single surgeon. ResultsOur findings show that 3/33 (9%) patients with microbiological diagnoses of cerebral abscesses with a thin ring of contrast enhancement but minimal or no restricted diffusion MRI imaging. All causative organisms were hemolytic streptococci and none of the subjects received antibiotic therapy prior to specimen collection. A trend in these patients was the presence of diabetes and in conjunction with other studies that cite incomplete treatment as being associated with facilitated diffusion, we conjecture that impaired inflammatory responses in some patients may be associated with the absence of restricted diffusion. ConclusionWith this in mind, clinicians must maintain a high index of suspicion when assessing patients with cystic, contrast enhancing masses. A prospective multicenter study to compile imaging along with other patient characteristics may help refine the non-invasive diagnostic criteria for brain abscesses.

Persistent Hall voltages across thin planar charged quantum rings on the surface of a three-dimensional topological insulator

We study theoretically, the electromagnetic response due to localized charge current distributions above a topological insulator (coated with a thin ferromagnetic layer) using the electromagnetic duality symmetry. We show that the localized current induces an electric field which depends on the current —this is a manifestation of the topological magnetoelectric (TME) effect. We also show that if the charge carriers have spin, then they acquire Aharanov-Casher phases which depend on the current. As an application, we consider thin planar charged quantum rings with persistent currents on the surface of a TI and show that the TME manifests itself as persistent Hall voltages across the charged ring. If the spin is also taken into account, then persistent spin Hall voltages develop across the ring.

End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture

We produce the first concrete evidence that violation of the weak cosmic censorship conjecture can occur in asymptotically flat spaces of five dimensions by numerically evolving perturbed black rings. For certain thin rings, we identify a new, elastic-type instability dominating the evolution, causing the system to settle to a spherical black hole. However, for sufficiently thin rings the Gregory-Laflamme mode is dominant, and the instability unfolds similarly to that of black strings, where the horizon develops a structure of bulges connected by necks which become ever thinner over time.

Negative refraction and imaging of acoustic waves in a two-dimensional square chiral lattice structure

The negative refraction behavior and imaging effect for acoustic waves in a kind of two-dimensional square chiral lattice structure are studied in this paper. The unit cell of the proposed structure consists of four zigzag arms connected through a thin circular ring at the central part. The relation of the symmetry of the unit cell and the negative refraction phenomenon is investigated. Using the finite element method, we calculate the band structures and the equi-frequency surfaces of the system, and confirm the frequency range where the negative refraction is present. Due to the rotational symmetry of the unit cell, a phase difference is induced to the waves propagating from a point source through the structure to the other side. The phase difference is related to the width of the structure and the frequency of the source, so we can get a tunable deviated imaging. This kind of phenomenon is also demonstrated by the numerical simulation of two Gaussian beams that are symmetrical about the interface normal with the same incident angle, and the different negative refractive indexes are presented. Based on this special performance, a double-functional mirror-symmetrical slab is proposed for realizing acoustic focusing and beam separation. La réfraction négative et l'imagerie des ondes acoustiques dans une structure périodique chirale bidimensionnelle sont étudiées dans cet article. La cellule élémentaire de la structure considérée comporte quatre bras en zigzag, connectés dans la partie centrale par un fin anneau circulaire. La relation entre la symétrie de la cellule élémentaire et le phénomène de réfraction négative est explorée. À l'aide de la méthode des éléments finis, nous calculons la structure de bande et les surfaces équifréquence du système, ce qui nous permet de confirmer la gamme de fréquence pour laquelle la réfraction négative est obtenue. En raison de la symétrie par rotation de la cellule élémentaire, une différence de phase est introduite pour les ondes émises par un point source et traversant la structure. Cette différence de phase est liée à la largeur de la structure ainsi qu'à la fréquence de la source, ce qui nous permet d'obtenir une image défléchie avec un angle ajustable. Le même phénomène est également démontré par simulation numérique pour deux faisceaux gaussiens incidents, avec des angles symétriques par rapport à la normale à l'interface. Dans ce cas, différents indices de réfraction négatifs sont obtenus. Sur la base de ce comportement spécifique, une dalle présentant une symétrie miroir est proposée pour réaliser la double fonction de focalisation et de séparation de faisceaux acoustiques.

A ring-like concentration of mm-sized particles in Sz 91

Abstract Models of planet formation and disc evolution predict a variety of observables in the dust structure of protoplanetary discs. Here, we present Atacama Large Millimeter/submillimeter Array (ALMA) Band-6 and Band-7 observations of the transition disc Sz 91 showing that the continuum emission at 870 μm, which is dominated by emission from large dust grains, is localized in an optically thin narrow ring. We find that most of the emission (∼95 per cent) is concentrated in a ring located at 110 au from the central star that is only about 44 au wide. In contrast, the 12CO (2–1) emission peaks closer to the star and is detected up to ∼488 au from the star. The concentration of large grains in a ring-like structure while the gas disc extends much further in and further out is in qualitative agreement with predictions of hydrodynamical models of planet–disc interactions including radial drift and gas drag.

Black rings at large D

We study the effective theory of slowly rotating black holes at the infinite limit of the spacetime dimension D. This large D effective theory is obtained by integrating the Einstein equation with respect to the radial direction. The effective theory gives equations for non-linear dynamical deformations of the slowly rotating black hole as effective equations. The effective equations contain the slowly rotating Myers-Perry black hole, slowly boosted black string, non-uniform black string and black ring as stationary solutions. We obtain an analytic solution of the black ring by solving the effective equations. Furthermore, by perturbation analysis of the effective equations, we find a quasinormal mode condition of the black ring in analytic way. As a result we confirm that thin black ring is unstable against non-axisymmetric perturbations. We also include 1/D corrections to the effective equations and discuss the effects by 1/D corrections.

Effects of specimen size on assessment of shrinkage cracking of concrete via elliptical rings: Thin vs. thick

An elliptical ring test method is proposed to replace the circular ring test recommended by ASTM and AASHTO for faster and more reliable assessment of cracking tendency of concrete. Numerical models are also established to simulate stress development and crack initiation/propagation in restrained concrete rings. Cracking age, position and propagation in various rings are obtained from numerical analyses that agree well with experimental results. Elliptical thin rings of certain geometry can shorten the ring test duration as desirable. In thin rings, crack initiation is caused by external restraint effect so that a crack occurs at the inner circumference and propagates towards the outer one. In thick rings, crack initiation is mainly due to the self-restraint effect so that a crack occurs at the outer circumference and propagates towards their inner one. Therefore, thick elliptical concrete rings do not necessarily crack earlier than circular ones as observed from experiment.

A refined one-dimensional rotordynamics model with three-dimensional capabilities

This paper evaluates the vibration characteristics of various rotating structures. The present methodology exploits the one-dimensional Carrera Unified Formulation (1D CUF), which enables one to go beyond the kinematic assumptions of classical beam theories. According to the component-wise (CW) approach, Lagrange-like polynomial expansions (LE) are here adopted to develop the refined displacement theories. The LE elements make it possible to model each structural component of the rotor with an arbitrary degree of accuracy using either different displacement theories or localized mesh refinements. Hamilton׳s Principle is used to derive the governing equations, which are solved by the Finite Element Method. The CUF one-dimensional theory includes all the effects due to rotation, namely the Coriolis term, spin softening and geometrical stiffening. The numerical simulations have been performed considering a thin ring, discs and bladed-deformable shafts. The effects of the number and the position of the blades on the dynamic stability of the rotor have been evaluated. The results have been compared, when possible, with the 2D and 3D solutions that are available in the literature. CUF models appear very practical to investigate the dynamics of complex rotating structures since they provide 2D and quasi-3D results, while preserving the computational effectiveness of one-dimensional solutions.