Elliptical Rotation Research Articles

Critical behavior in ultrastrong-coupled oscillators

We investigate the strong coupling regime of a linear $x$-$x$ coupled harmonic oscillator system, by performing a direct diagonalization of the hamiltonian. It is shown that the $x$-$x$ coupled hamiltonian can be equivalently described by a Mach-Zehnder-type interferometer with a quadratic unitary operation in each of its arms. We show a sharp transition of the unitary operation from an elliptical phase rotator to an elliptical squeezer as the coupling gets stronger, which leads to the continuous generation of entanglement, even for a significantly thermal state, in the ultra-strong coupled regime. It is also shown that this critical regime cannot be achieved by a classical Hookian coupling. Finally, the effect of a finite-temperature environment is analyzed, showing that entanglement can still be generated from a thermal state in the ultra-strong coupled regime, but is destroyed rapidly.

The active and passive ciliary motion in the embryo node: A computational fluid dynamics model

The breaking of left–right symmetry in the mammalian embryo is believed to occur in a transient embryonic structure, the node, when cilia create a leftward flow of liquid. The two-cilia hypothesis proposes that the node contains two kinds of primary cilia: motile cilia that rotate autonomously to generate the leftward fluid flow and passive cilia that act as mechano-sensors, responding to flow. While studies support this hypothesis, the mechanism by which the sensory cilia respond to the fluid flow is still unclear. In this paper, we present a computational model of two cilia, one active and one passive. By employing computational fluid dynamics, deformable mesh computational techniques and fluid–structure interaction analysis, and solving the three-dimensional unsteady transport equations, we study the flow pattern produced by the movement of the active cilium and the response of the passive cilium to this flow. Our results reveal that clockwise rotation of the active cilium can generate a counter-clockwise elliptical rotation and overall lateral displacement for its neighboring passive one, of measurable magnitude and consistent pattern. This supports the plausibility of the two-cilia hypothesis and helps quantify the motion pattern for the passive cilium induced by this regional flow.

Wind Spatial Variability and Topographic Wave Frequency

Abstract The association of topographic waves with wind action has been documented in several natural lakes throughout the world. However, the influence of the wind’s spatial variability (wind stress curl) on the frequency of topographic waves has only been partially investigated. Here the role of wind stress curl on the frequency of topographic waves in an idealized elliptic paraboloid basin has been studied both analytically and numerically. It is shown that the analytical solution is the sum of an elliptic rotation determined by the wind stress curl and two counterrotating circulation cells, which propagate cyclonically after the wind ceases. Furthermore, it is shown that cyclonic elliptical rotation (associated with positive wind stress curl) increases the rotation frequency of the double-gyre pattern while anticyclonic elliptical rotation (associated with negative wind stress curl) decreases the oscillatory mode frequency. It is also shown that bottom friction has some effect on the structure of the double-gyre pattern but hardly affects the oscillatory frequency. Numerical solutions of the depth-integrated nonlinear shallow-water equations confirmed that the frequency of the topographic wave increases (decreases) when forcing the model with cyclonic (anticyclonic) wind curl.

A simple rotation flap for closure of simple and complex pilonidal sinus

Surgical treatment of pilonidal sinus disease has a significant morbidity and recurrence rate. Controversy still exists regarding the best surgical technique for the treatment of the disease. An elliptical rotation flap has been previously used for pilonidal sinus treatment with no recurrence rate. In a two-year period, we used this technique to treat 19 patients (17 men and 2women) with chronic pilonidal sinus with a mean follow-up of 9 months. All patients were discharged on the second postoperative day. Primary healing was achieved in 18 (94.7%) of the patients in 2 weeks with no long-term recurrences. We conclude that this method, in addition to its use in primary sinuses, is particularly useful for recurrent and complex ones with extended tracts where radical excision leaves a large defect.

Harmonic oscillator model for current- and field-driven magnetic vortices

In experiments, the distinction between spin-torque and Oersted-field-driven magnetization dynamics is still an open problem. Here, the gyroscopic motion of current- and field-driven magnetic vortices in small thin-film elements is investigated by analytical calculations and by numerical simulations. It is found that for small harmonic excitations, the vortex core performs an elliptical rotation around its equilibrium position. The global phase of the rotation and the ratio between the semiaxes are determined by the frequency and the amplitude of the Oersted field and the spin torque.

Observation of elliptical polarization rotation in a long twisted fiber

The intensity-dependent polarization rotation caused by the self-induced nonlinear birefringence in a long twisted fiber is studied numerically and experimentally. By using a 1 km length of twisted fiber, we show that the effect of ellipse rotation accumulates monotonically as if the fiber were perfectly isotropic. Such behavior cannot be observed in a typical nontwisted fiber with randomly varying birefringence and is a unique feature of the twisted fiber, in which the large circular birefringence plays an essential role of preserving the handedness of elliptical polarization. We demonstrate a novel Faraday-mirror configuration to ensure automatic polarization alignment, which is directly applicable to achieving a simple and stable intensity discriminator.

Coupled tangential-axial resonant modes of piezoelectric hollow cylinders and their application in ultrasonic motors

This paper describes a tangential-axial eigen-mode of a piezoelectric hollow cylinder. A new type of piezoelectric ultrasonic motor using this oscillation mode has been developed. The motor is a traveling-wave-type motor. The stator of such a motor consists of a solid piezoelectric hollow cylinder, which, excited in the tangential-axial resonant mode by a three-phase electrical signal, will exhibit elliptical displacement and transfer rotation to the rotor. The behavior of the stator has been simulated with finite element method (FEM) software. The simulation results have been checked with single-point contact measurements on the surface of the ultrasonic motors. The paper closes with the introduction of new ultrasonic motors based on this oscillation mode.

High-efficiency, simple setup for pulse cleaning at the millijoule level by nonlinear induced birefringence.

Nonlinear elliptical polarization rotation is used to improve the contrast of femtosecond pulses by several orders of magnitude. Using nonlinear induced birefringence in air, we produced cleaned pulses with an energy of a few hundreds of microjoules. This technique presents several major advantages, such as convenience and stability of the setup. We investigated the phase profile required for obtaining high-energy pulses. No phase distortion is observed, and the spatial quality of the beam is preserved.

Elliptical rotation flap for pilonidal sinus

Background The treatment of the symptomatic pilonidal sinus is surgical with one of the most extensive being excision of the diseased tissue down to the sacral fascia. The closure of the defect is the matter of debate. An elliptical rotation flap has been used for pilonidal sinus treatment with no recurrence rate. Methods From April 1996 to June 2001, 20 patients were treated with this technique. The surgical procedure is a vertical elliptical excision of the diseased tissue and an elliptical cutaneous rotation flap to close the defect. Results Twenty patients underwent with this technique, mean age 23.4 years (range 18 to 34). Mean follow-up was 42 months. All patients were discharged on the first postoperative day. Primary healing was achieved in all of the patients in 2 weeks. No recurrence was observed. Conclusions Elliptical rotation flap is recommended for patients selected for defect closure. It offers improved patient comfort, shorter hospital stay, and no recurrence rate.

Dynamics of kaleidoscopic maps

First, we introduce a certain class of piecewise affine elliptic rotation maps on T 2 , called the kaleidoscopic maps, and describe its importance. And then, we concentrate our efforts on a special case, when the rotation angle θ of a kaleidoscopic map is θ= π n , n∈ Z + . For the special case, we answer the conjectures regarding the periodicity and the singularity structure of such (kaleidoscopic) dynamics. In the process, we prove the partial riddling of the regular orbits that gives rise to the classification of periodic sets, and estimate the Hausdorff dimension of the singular set. Finally, we study the dynamics of such kaleidoscopic maps restricted within the singular set, and answer conjectures concerning the chaos, the local chaos, and the ergodicity with respect to the normalized Hausdorff measure of the singular set.

Dynamics of symplectic piecewise affine elliptic rotation maps on tori

Dynamics of symplectic piecewise affine elliptic rotation maps on tori

Moduli of Elliptic Curves and Rotation Numbers of Circle Diffeomorphisms

Moduli of Elliptic Curves and Rotation Numbers of Circle Diffeomorphisms

Wear-based aspherics generator based on a novel elliptical rotator

Derived from an earlier development (fabrication of ultrapre- cise surfaces using a tube; patent pending (FAUST)), a new fabrication technique to produce on- and off-axis optical surfaces of revolution is presented. Although based on a shape-copying method, it is possible to generate different types of surfaces with the same machining tool. Load- controlled point-contact machining is applied using a small tool that is guided along a predetermined tool path, not requiring an in-process tool- path control. This fabrication technique constitutes a self-correcting pro- cess and is characterized by an advantageous error propagation be- tween tool path and workpiece shape. The characteristics of this fabrication technique are discussed together with its application for the generation of on- and off-axis surfaces with conic sections as generators (''conic surfaces''). We present the design of a first setup for production of conic surfaces that facilitates the generation of all kinds of conic sur- faces on the same machine, featuring a pantograph enabling the produc- tion of different scales of the surfaces. A discussion of first experimental data is also presented. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)03408-4)

Myocardial sestamibi single-photon emission tomography: Variations in reference values with gender, age and rest versus stress?

Reference data files support the evaluation of myocardial perfusion single-photon emission tomography (SPET). The aim of this study was to create a large reference data base for technetium-99m sestamibi SPET, age and gender matched to the general patient population. One hundred and twenty-eight healthy volunteers (76 males and 52 females) with a likelihood of coronary artery disease of less than 5% underwent rest and maximal exercise 99mTc-sestamibi SPET with a 2-day protocol and 180 degrees elliptical rotation. The normalized activity values of 99mTc-sestamibi in the inferior wall differed significantly between men and women. Age variations were found for men in the anterior wall. Normalized activity values in all four walls were strikingly similar during rest and stress. Our results suggest that the use of reference files in 99mTc-sestamibi SPET requires a gender- and, for males, possibly an age-matched reference population. Different reference files at rest and during stress might not be necessary.

Hodographic analysis of gravity waves: Relationships among Stokes parameters, rotary spectra and cross‐spectral methods

The elliptical rotation with height of horizontal velocities produced by gravity waves provides considerable information about the wave field. Methods of statistically characterizing velocity ellipses from data currently fall into three main categories: (1) hodographic analyses, (2) cross‐spectral analyses, and (3) rotary spectral analyses. The three methods have some intuitive similarities, yet precise interrelationships among them are presently unclear. The three techniques are interrelated here using the so‐called “Stokes parameters” of the wave field, which initially provide a concise description of the hodographic analysis method (1). On Fourier transforming the Stokes parameters, standard formulae employed in rotary‐spectral and cross‐spectral analysis methods can then be expressed in terms of the resulting “Stokes‐parameter spectra.” The results highlight some drawbacks in the use of cross‐coherence spectra between velocity components to verify the existence of a coherent wave motion. A more robust measure is suggested, based on the “degree of polarization” of classical hodograph‐based Stokes‐parameter analysis, which can be generalized to provide an analogous spectral measure for evaluation in rotary‐spectral and cross‐spectral analyses.

Measurement of magnetic fields in the direct proximity of power line conductors

Modeling and managing of power frequency magnetic fields requires verification of theory with actual measurements. Measurements only at ground level are not always sufficient for comprehensive studies. The technique and the results of three-dimensional mapping of the power frequency magnetic fields high above ground level are presented in this paper. Comparative calculations illustrate relevance and approximations of the existing theoretical approach to field modeling. The influence of harmonics on the elliptical rotation of the magnetic field vector is illustrated. The possibility of use of the magnetic fields for the power line proximity detection is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Anisotropy of grain-oriented steel sheet under various elliptical field conditions

We investigated the magnetic behavior of grain-oriented steel sheet under various elliptical field conditions. The measurements show an additional anisotropy of the material properties depending on the direction of the elliptic rotation. We ascribe these phenomena to the different symmetries of the crystal anisotropy energy and of the ellipsoidal fields.

Platelet membrane glycoprotein changes during the preparation and storage of platelet concentrates.

Previous studies of platelet membrane glycoproteins during blood bank storage have reported conflicting results. This study assessed two major plasma membrane glycoproteins (GP Ib and GP IIb), an alpha-granule membrane protein (GMP-140), and the concentration of platelet membrane microparticles in cell-free plasma during routine hospital blood bank platelet storage. 125I-monoclonal antibody binding was used to measure membrane glycoproteins on the surface of intact platelets and to measure the concentration of membrane microparticles in cell-free plasma. Platelet concentrates were stored at room temperature in polyolefin bags for 7 days. In this blood bank, two types of rotators are routinely used for platelet concentrate storage: a 2-rpm circular tumbler rotator and a 6-rpm elliptical rotator. Different results were obtained with the rotators. With the tumbler rotator, there was no loss of platelets and antibody binding to GP Ib remained normal. With the elliptical rotator, one third of platelets were lost into clumps during storage, and a 50 percent decrease of antibody binding to GP Ib occurred in the remaining single platelets. There was no loss of antibody binding to GP IIb with either rotator. Antibody binding to GMP-140 increased equally in both rotators indicating that the remaining single platelets had secreted about 16 percent of their alpha-granule contents. The plasma concentration of platelet membrane microparticles was greater in the bags stored in the elliptical rotator. These results indicate that it is possible to maintain the normal concentration of platelet membrane glycoproteins Ib and IIb during 7 days of room-temperature blood bank storage.(ABSTRACT TRUNCATED AT 250 WORDS)

Exact analytical solutions for elliptical vortices of the shallow-water equations

It has long been known that the shallow-water equations in a rotating framework admit exact solutions for which the velocity components are linear and the height field is quadratic in the coordinate variables. The resulting 12 coefficients are, in general, functions of time and are governed by a set of nonlinear, coupled, ordinary differential equations. While previous analytical solutions have been plagued by a reduced number of degrees of freedom, the most general solution presented here contains 10 arbitrary constants of integration. These degrees of freedom can be sorted as follows: 4 are accounted for by inertial oscillations of the vortex' center of mass, 2 by an average circular structure (depth and radius), 2 by a circular pulsation mode (amplitude and phase), and 2 by 1 of 2 possible elliptical rotation modes (amplitude and phase). The complete solution with 12 degrees of freedom would be achieved if these 2 elliptical modes could be incorporated simultaneously. Unfortunately, the solution that includes the nonlinear interaction between the elliptical rotation modes has yet to be found. The present solution sheds some ***light on the behavior of time-dependent elliptical warm-core rings as observed in the ocean. It can be used as the basis for further theoretical investigations and testing of numerical models. DOI: 10.1111/j.1600-0870.1987.tb00304.x

The effect of mode of agitation and type of plastic bag on storage characteristics and in vivo kinetics of platelet concentrates.

We studied the characteristics of platelet concentrates stored for 5 days at 22 degrees C. Platelets were prepared in three plastic bags (PL 732, PL 1240, and CLX) and stored on one of four platelet agitators, 1- or 6-rpm elliptical and 2- or 6-rpm circular rotators. A total of 76 studies were divided among 12 groups, each group being composed of a different storage bag-rotator combination. In vivo recovery and survival were calculated using Indium-111 oxine-labeled platelets injected into autologous volunteers. Platelet recovery was assessed at 2 hours postinjection or as the y-intercept of the multiple-hit model survival curve. Survival was calculated using linear, exponential, and multiple-hit computer models. Linear T 1/2 also was calculated as an index of platelet survival. At 5 days, the pH of all concentrates was above pH 7.0 and platelet counts were above 5.5 X 10(10) per bag except for the PL 732 with the 6-rpm elliptical rotator, which was 4.6 X 10(10) per bag. This combination also showed a significantly higher poststorage lactic dehydrogenase (LDH) discharge compared to the mean of the other 11 groups (23.6 +/- 5.4% vs. 10.4 +/- 3.0%, p less than 0.05); however, the beta-thromboglobulin (beta-TG) release was not statistically different.(ABSTRACT TRUNCATED AT 250 WORDS)