Three-dimensional Ring Research Articles

Design Characteristics of a Three-Dimensional Geometric Aortic Valve Annuloplasty Ring

Design Characteristics of a Three-Dimensional Geometric Aortic Valve Annuloplasty Ring

Green's function for the Laplace–Beltrami operator on a toroidal surface

Green's function for the Laplace–Beltrami operator on the surface of a three-dimensional ring torus is constructed. An integral ingredient of our approach is the stereographic projection of the torus surface onto a planar annulus. Our representation for Green's function is written in terms of the Schottky–Klein prime function associated with the annulus and the dilogarithm function. We also consider an application of our results to vortex dynamics on the surface of a torus.

Low-lying planar isomers of neutral and charged B22 clusters

Using the density functional theory, we investigate low-energy structures of B22 clusters. Our study shows that a 22-atom boron cluster prefers a three-dimensional double ring structure with a diameter of 0.58 nm for all of its charged states. This result combined with previous results of our calculations on B21, and by others on B19, B20 and B24 shows that boron clusters in the size range 19–24 show oscillation between planar and ring structures. Clusters with an odd number of atoms in this size regime tend to form planar structures, while clusters with an even number of atoms prefer three-dimensional ring structures. We have also studied several isomers of cationic and anionic B22 clusters.

La anuloplastia tricúspide: ¿De Vega, flexible o rígida?

AbstractIn 1953 the use of the cardiopulmonary bypass was responsible for the beginning of the history of open-heart surgery and regurgitant lesions of the heart valves could be treated. Kay, in 1965, designed a novel strategy to repair tricuspid insufficiency, but it wasn't until 1972 that de Vega described his technique of selective, adjustable, and permanent annuloplasty. Around the same time, Carpentier invented the ring that bears his name and probably everything seemed to indicate that at least the acquired pathology of the tricuspid valve was on track to be resolved surgically. since then, with multiple suture annuloplasties and numerous types of rings, complete, incomplete, rigid, flexible, and even three-dimensional rings, it may seem that the initial enthusiasm is vanishing.It is possible that neither the initial confidence nor skepticism of today are logical attitudes, because probably the unknown can be cleared by applying the theory of comparing apples and pears.

Wall-less liquid pathways formed with three-dimensional microring arrays

This paper describes a method to construct microfluidic pathways without physical walls—wall-less microchannels. Compared to the previous wall-less microfluidics based on two-dimensional patterns, this method uses three-dimensional ring arrays and two immiscible liquids. The distant rings generate free-standing liquid pathways in order to minimize liquid surfaces contacted to solid walls. In the experimental study, we reduced the liquid-solid interface area per volume to 17.3% of that of the conventional microchannels with squared cross-sections. We envision that this aspect would be significant in micro/nano-fluidics, whose surface-area-to-volume ratio is extremely large.

Three-dimensional ring vortex solitons and their stabilities in Bose-Einstein condensates under magnetic confinement

A three-dimensional study of the ring vortex solitons is conducted for both attractive and repulsive Bose-Einstein condensates subject to harmonic potential confinement. A family of stationary ring vortex solitons, which is defined by the radial excitation number and the winding number of the intrinsic vorticity, are obtained numerically for a given atomic interaction strength. We find that stabilities of the ground and radially excited states of the ring vortex soliton are dependent on the winding number differently. The ground state of the ring vortex soliton with the large winding number is unstable dynamically against random perturbation. The radially excited state of the ring vortex soliton with large winding number corresponds to the increased collapse threshold and therefore can be made stable for sufficiently small atomic interaction strengths. The ground and radially excited states also demonstrate different dynamic evolutions under large atomic interaction strengths. The former exhibits simultaneous symmetric splitting in the transverse plane, while the latter displays periodic expand-merge cycles in the longitudinal direction.

The ring lemma in three dimensions

Suppose that n cyclically tangent discs with pairwise disjoint interiors are externally tangent to and surround the unit disc. The sharp ring lemma in two dimensions states that no disc has a radius below cn(R2) = (F2n−3−1)−1—where Fk denotes the kth Fibonacci number—and that the lower bound is attained in essentially unique Apollonian configurations. In this article, generalizations of the ring lemma to three dimensions are discussed, a version of the ring lemma in three dimensions is proved, and a natural generalization of the extremal two-dimensional configuration—thought to be extremal in three dimensions—is given. The sharp three-dimensional ring lemma constant of order n is shown to be bounded from below by the two-dimensional constant of order n − 1.

Fine-scale density wave structure of Saturn's rings: A hydrodynamic theory

Aims. We examine the linear stability of the Saturnian ring disk of mutually gravitating and physically colliding particles with special emphasis on its fine-scale ∼100 m density wave structure, that is, almost regularly spaced, aligned cylindric density enhancements and optically-thin zones with the width and the spacing between them of roughly several tens particle diameters. Methods. We analyze the Jeans’ instabilities of gravity perturbations (e.g., those produced by a spontaneous disturbance) analytically by using the Navier-Stokes dynamical equations of a compressible fluid. The theory is not restricted by any assumptions about the thickness of the system. We consider a simple model of the system consisting of a three-dimensional ring disk that is weakly inhomogeneous and whose structure is analyzed by making a horizontally local short-wave approximation. Results. We demonstrate that the disk is probably unstable and that gravity perturbations grow effectively within a few orbital periods. We find that self-gravitation plays a key role in the formation of the fine structure. The predictions of the theory are compared with observations of Saturn’s rings by the Cassinispacecraft and are found to be in good agreement. In particular, it appears very likely that some of the quasi-periodic microstructures observed in Saturn’s A and B rings ‐ both axisymmetric and nonaxisymmetric ones ‐ are manifestations of these effects. We argue that the quasi-periodic density enhancements revealed in Cassini data are flattened structures, with a height to width ratio of about 0.3. One should analyze high-resolution of the order of 10 m data acquired for the A and B rings (and probably C ring as well) to confirm this prediction. We also show that the gravitational instability is a potential cluster-forming mechanism leading to the formation of porous 100-m-diameter moonlets of preferred mass ∼10 7 g each embedded in the outer A ring, although this has yet to be directly measured.

A single-mode single-polarization monolithically silica waveguide ring resonator used in microoptic gyro

A single-mode single-polarization waveguide (SMSPW) ring resonator for the microoptic gyro (MOG) was proposed, and it could be monolithically integrated onto a silica planar lightwave circuit. We have presented the design of a three-dimensional SMSPW ring resonator in which the TM mode cuts off and the TE mode transmits by taking into consideration the stress-induced birefringence effect of the Si-based silica waveguide using the effective-index method. The characteristics of the light propagation across the SMSPW resonator were studied by a three-dimensional finite difference beam propagation method. Numerical simulation results showed the SMSPW ring resonator has a high extinction ratio over 50 dB cm−1 for the TM mode, low propagation loss of 0.055 dB cm−1 for the TE mode, and a high finesse of 36. A rate detection limit of 0.8° h−1 can be achieved. Without increasing the complexity of the waveguide fabrication process, this structure can solve the MOGs output bias instabilities induced by polarization fluctuations and provide a new solution for MOGs.

Self-Assembled Three-Dimensional Non-Volatile Memories

The continuous increase in capacity of non-volatile data storage systems will lead to bit densities of one bit per atom in 2020. Beyond this point, capacity can be increased by moving into the third dimension. We propose to use self-assembly of nanosized elements, either as a loosely organised associative network or into a cross-point architecture. When using principles requiring electrical connection, we show the need for transistor-based cross-talk isolation. Cross-talk can be avoided by reusing the coincident current magnetic ring core memory architecture invented in 1953. We demonstrate that self-assembly of three-dimensional ring core memories is in principle possible by combining corner lithography and anisotropic etching into single crystal silicon.

Echocardiographic Follow-up of Tricuspid Annuloplasty with a New Three-Dimensional Ring in Patients with Functional Tricuspid Regurgitation

A new tricuspid valve (TV) annuloplasty system, the MC3 ring, includes a three-dimensional structure designed to remodel the TV annulus and preserve physiologic annular function. We investigated the early- and mid-term outcomes of TV annuloplasty with the MC3 ring. A total of 136 patients with functional tricuspid regurgitation (TR) had two-dimensional echocardiography before and 5 +/- 5 days after TV annuloplasty with the MC3 ring. Twenty-eight patients were followed for more than 1 year after surgery. Echocardiography was used to assess response to surgical therapy, including measures of cardiac function and geometry and identification of factors predisposing one to recurrent TR. TR severity was improved early after surgery (P < .001). At 5 days after surgery, 16% had TR graded greater than moderate; among patients followed more than 1 year, this figure was 14%. Postoperative TR severity was associated with preoperative TR severity and tethering height. TV annuloplasty with the new physiologic MC3 ring is effective for the management of TR and may be superior to conventional techniques. However, patients with extensive leaflet tethering (>1.0 cm) require additional maneuvers to ensure valve competence.

A Three-Dimensional Ring Annuloplasty for the Treatment of Tricuspid Regurgitation

Significant functional tricuspid regurgitation should be corrected in patients undergoing surgery for left-sided valvular diseases. Several clinical studies have shown the superiority of the remodeling annuloplasty over other repair techniques. Herein we report our early experience with a new three-dimensional remodeling prosthetic ring (Edwards MC3 annuloplasty system [Edwards LifeSciences, Irvine, CA]). From June 2002 to November 2004, 75 patients with functional tricuspid regurgitation (mean, 3.1 +/- 0.9) underwent tricuspid valve repair with this new prosthesis. Concomitant procedures were mitral valve repair (70%), replacement (26%), aortic valve replacement (10%), coronary artery bypass grafting (13%), and left atrial maze (34%). Median predicted EuroScore mortality was 21% (r = 3 to 62). Operative mortality was 5.3% (n = 4). Pre-discharge echocardiography showed significant decrease in tricuspid regurgitation to 0.3 +/- 0.4 (p < 0.001). Forty-five patients had follow-up transthoracic echocardiography after a median of 16 months (range, 4 to 34) demonstrating a stable result (mean tricuspid regurgitation, 0.3 +/- 0.5). There were no cases of ring dehiscence, prosthetic ring endocarditis, or thromboembolic events. This new three-dimensional ring is easy to implant, corrects tricuspid regurgitation effectively, and provides good short-term clinical and echocardiographic results. Long-term evaluation, however, is necessary to determine the stability of tricuspid valve repair using the MC3 annuloplasty system.

Numerical study of the parametric evolution of bifurcations in the three-dimensional ring problem of N bodies

We study the dynamics of a massless particle in an annular configuration of N bodies, N − 1 of which have equal masses m and are located in equal distances on a fictitious circle and one has mass βm and is located at the center of the circle. Our interest is focused on the bifurcation points from planar to three-dimensional families of symmetric periodic orbits in the above problem. We study numerically the evolution of these bifurcation points with respect to the variation of the mass parameter β. In particular we investigate the continuous evolution of bifurcation points for values of β from 2 up to 1000. The two distinct cases of the system’s behavior at β = 2 and 1000 are examined comparatively and various conclusions are drawn regarding the overall dynamical evolution of the three-dimensional system as the relative mass of the central body grows.

Numerical Calculation of Electronic Structure for Three-Dimensional Nanoscale Semiconductor Quantum Dots and Rings

In this paper the electronic structure of nanoscale ellipsoid-torus-shaped semiconductor quantum dot and quantum ring is investigated of utilizing a unified model. This three-dimensional model considers the effective one-band Hamiltonian, the position- and energy-dependent effective mass approximation and Lande factor, the finite hard wall confinement potential, and the Ben Daniel-Duke boundary conditions. It is solved numerically without any fitting parameters by using a computationally cost effective nonlinear iterative method. It is found that the penetration of magnetic fields into non-simply connected topology of structures leads to substantial difference in the transition energy between InAs/GaAs quantum dot and quantum ring. The quantum ring exhibits non-periodical electron-hole transition energies when the magnetic field increases. Contrary to the one-dimensional periodical argument on the ring's energy spectra, our examination into the nanoscale semiconductor quantum ring agrees with the experimental result. The energy band gap of quantum dot is an increasing function of the magnetic field. For quantum rings the energy band gap oscillates non-periodically and the oscillation period is strongly controlled by the inner radius of structures. The magnetization of quantum ring not only jumps non-periodically but also saturates eventually when the magnetic field increases.

A Hasse principle for three-dimensional complete local rings of positive characteristic

A Hasse principle for three-dimensional complete local rings of positive characteristic

A Computational Technique for Electron Energy States Calculation in Nano-Scopic Three-Dimensional InAs/GaAs Semiconductor Quantum Rings Simulation

We study theoretically the electron energy states for three-dimensional (3D) nano-scopic semiconductor quantum rings. In this study, the model formulation includes: (i) the effective one-band Hamiltonian approximation, (ii) the position and energy dependent quasi-particle effective mass approximation, (iii) the finite hard wall confinement potential, and (iv) the Ben Daniel-Duke boundary conditions. To calculate the energy levels, the 3D model is solved by nonlinear iterative algorithm to obtain self-consistent solutions. The model and solution method provide a novel way to calculate the energy levels of nano-scopic semiconductor quantum ring and are useful to clarify the principal dependencies of quantum ring energy states on material band parameter, ring size and shape. We find the energy levels strongly depend on the radial cross section shapes of quantum rings. The dependence of energy states on shapes of 3D quantum ring reveals a significant difference from results derived on basis of 2D approaches.

Layer manufacture of jewel ring by volume efficient methodology

Rapid prototyping (RP) technology has been widely used in making prototypes for quite a long time. However, an in-depth study of methods used to fabricate jewellery products with RP is not available. In this paper, a new direct and adaptive slicing methodology is applied to three-dimensional solid jewel ring models to produce maximum inscribed three-dimensional stacked slab models. Jewel rings that are symmetrical in one or more principal planes XY, YZ and ZX are considered. The maximum inscribed slab model will minimize material wastage in post-treatment processes and preserve the symmetric property of the original jewel ring model. A solid torus is used as a simplified representation of the jewel ring in the description of the methodology. A case study based on the methodology is presented.

Zero-velocity surfaces in the three-dimensional ring problem of N + 1 bodies

The zero-velocity surfaces in the three-dimensional ring problem of N + 1 bodies and their parametric evolution is the subject of this paper. These surfaces, which are also known as Hill's or Jacobian surfaces, provide us with valuable information concerning the regions of the permissible particle motion and the existence of equilibrium positions.

Higher-dimensional orders, graph-orders, and derived equivalences

Green-orders (tree-orders) in the classical one-dimensional case are the setting, to understand p-adic blocks with cyclic defect of finite groups. Blocks with “cyclic defect” of Hecke orders however, are Green-orders over two-dimensional rings. Hecke orders of dihedral groups of order divisible by 4 are even defined over a three-dimensional ring. We extend the notion of Green-orders to orders associated to a locally embedded graph instead of a tree, and to general complete regular local noetherian ground rings of finite dimension. We extend the result, that classical tree-orders are derived equivalent to star-orders. We then use these results to clarify the derived equivalence classes of tame algebras of Dihedral type.

An Abelian Group Structure on Orbits of “Unimodular Squares” in Dimension 3

The subject of whether orbit sets of unimodular rows modulo the Ž . Ž . elementary subgroup Um A rE A have a group structure probably r r w x Ž . Ž . Ž . began first in 9 with the Vaserstein symbol V: Um A rE A a W A , 3 3 E which was shown to be bijective when the stable dimension of A was less Ž than or equal to 2. Here the stable dimension of the ring A is in the sense of Bass and equals the stable rank of A y 1. The reader could replace it by the more familiar Krull dimension for simplicity. The Vaserstein symbol Ž . V and the Grothendieck group W A of stably equivalent alternating E w x matrices of Pfaffian 1 is described in 9, p. 945 and briefly in the next . section. w x In 1, 2 van der Kallen has shown that if A is a commutative ring of Ž . Ž . stable dimension d then the coset space Um A rE A has the structure n n 1 4 of an abelian group provided n G max 3, d q 2 . For topological situa2 Ž . tions like A being the ring of continuous functions C X, R on a finite CW complex X of dimension d, he has given some nice models, namely the ny1Ž . higher cohomotopy groups p X , for this group. w x In 5 it was shown that the Vaserstein symbol was not injective for three-dimensional rings. So one could not expect to get a very nice group structure on the orbit set of unimodular 3-vectors over a three-dimensional ring. In this article we will prove that the orbit set of ‘‘squares’’ of