Linear Twist Research Articles

Comments on superconformal algebras

We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SL(2) \otimes U(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. In the context of string theory, the asymmetric N=4 superconformal algebra is provided with an explicit construction on the boundary of AdS_3, and is induced by an affine SL(2|2) current superalgebra residing on the world sheet. Substituting the world sheet SL(2|2) by the coset SL(2|2)/U(1) results in the small N=4 superconformal algebra on the boundary of AdS_3.

Automatic matrix-based analysis method for extraction of optical fiber parameters from polarimetric optical time domain reflectometry data

Interpretation of polarimetric optical time domain reflectometry (POTDR) data can be time consuming due to the complicated dependence of the state of polarization evolution on the optical fiber parameters. In this paper, a fully automatic matrix-based analysis method is presented which can extract the linear birefringence and external twist rate from relative backscattered state of polarization data, without error propagation. Practical measurements on fiber samples demonstrate the capability of the technique.

A non-discretized global method for free vibration of generally laminated fibre-reinforced pre-twisted cantilever plates

The paper presents a computational method for characterizing the resonant frequency properties of cantilever pre-twisted plates composed of fibre-reinforced laminated composites. It aims to simulate a laminated turbomachinery blade or a fan blade with a relatively small aspect ratio for which the conventional beam model fails to provide accurate solutions. The strain and kinetic energy components are expressed in area integration equations with respect to the plate mid-surface. An energy functional is defined and a governing eigenvalue equation is derived. There is no domain mesh generation in the numerical analysis thus reducing accuracy loss due to discretization. New numerical solutions are presented and the effects of angle of pre-twist, aspect ratio, and symmetric and antisymmetric lamination for two different composite laminates are analyzed in detail. The limit of linear twisting curvature omitted in previous analysis is strictly adopted here and the consequences of exceeding the limit are discussed.

Structures of Fibrous Supramolecular Assemblies Constructed by Amino Acid Surfactants: Investigation by AFM, SANS, and SAXS

Aqueous gel-like solutions of N-acyl-L-aspartic acids (C(n)Asp, n=14, 16, 18) and N-dodecanoyl-beta-alanine (C(12)Ala) were prepared at pH 5-6 at room temperature. Structures of supramolecular assemblies in the solutions were investigated by atomic force microscopy (AFM), small-angle neutron scattering (SANS), and small-angle X-ray scattering (SAXS). The cross-sectional radii, 22-30 Å, of helical, fibrous assemblies were obtained from analysis of SANS for 1% gel-like C(n)Asp solutions. Three Bragg spacings were observed in a SANS spectrum for a 6% C(16)Asp solution. C(n)Asp molecules are associated into the unit chain of a helical bilayer strand with a diameter of 50-60 Å. Unit chains where linear bilayers twist form a double strand with helical sense of approximately 650-Å pitch. It was confirmed from AFM images that cylindrical fibers in a gel-like C(12)Ala solution had a circular cross-section. The SAXS spectrum showed characteristic Bragg spacings. Cylindrical C(12)Ala fibers consist of multilamellar layers of period approximately 34-Å. The fibers are laterally organized with period 365-380 Å. Copyright 2000 Academic Press.

Coupling between elliptic screw polarization modes in single-mode optical waveguides with linear birefringence and regular twist of anisotropy axes in the presence of random axis twist

An analysis is made of single-mode fiber optical waveguides with linear birefringence and regular twist of anisotropy axes in the presence of random twist, which shows that, in this case, the coupling of orthogonal polarization modes having elliptic polarization in the screw coordinate system comoving with twist cannot be characterized by one coupling parameter, as differentiated from the case where constant twist is absent. In this case, the coupling between polarization modes is characterized by three independent parameters, which are different in nature and have different effects on the coupling of polarization modes. An estimate is made of the domain of applicability of the classical formula for the h parameter in single-mode fiber optical waveguides without regular twist of anisotropy axes.

Structure and Properties of Cotton Sirospun® Yarn

Cotton Sirospun® yarn has a circular cross-sectional shape, with the two strands segregated and consolidated into an adjacent array. When it is untwisted, the strand twists in an alternate direction. When compared to single yam with the same linear density and twist multiplier, cotton Sirospun yam is superior in tenacity, evenness, hairiness, and abrasion resistance. Although cotton Sirospun yam is less hairy and more extensible than two-plied yarn, it is inferior to two-plied yam in evenness and imperfections.

Single channel polarimetric OTDR for measurementof backscattered SOP evolution along a fibre with twist

The authors show how the state of polarisation (SOP) evolution along an optical fibre can be measured non-destructively by using a commercial OTDR modified to act as a single channel polarimetric OTDR (POTDR). From the SOP evolution, the linear birefringence and twist can be calculated along the fibre, thus identifying fibre sections with relatively high and low polarisation mode dispersion (PMD).

Hover Testing of Smart Rotor with Induced-Strain Actuation of Blade Twist

The experimental results are presented of hover test with a one-eighth dynamically scaled (Froude scale) helicopter rotor model with embedded piezoceramic elements as actuators to suppress vibrations. A 6-ft-dlam two-bladed bearingless rotor model was built with banks of piezoelectric torsional actuators capable of manipulating blade twist at harmonics of the rotational speed. The twist performances of several rotor blade configurations were investigated using accelerometers embedded in the blade tip. The change in oscillatory rotor lift due to plezoactuation was measured by a hub balance. Experimental results show that linear twist distributions of up to 0.6 deg, resulting in increases of up to 10% of the nominal rotor lift, are possible with existing piezoceramic technology. Although the twist amplitudes attained in this experiment were less than the target value (1-2 deg), it is expected that partial reduction of hub vibration can be achieved with the current smart rotors.

Aerodynamic Damping of Blade Flap Motions at High Angles of Attack

The YawDyn computer code is used to calculate the aerodynamic damping for a typical teetering rotor configuration. The code has been modified to calculate the net work done by aerodynamic forces in one complete rotor revolution. All cases were run for a teetering rotor similar to the ESI-80 with a specified teeter angle motion in order to isolate the aerodynamic effects from the inertial and gravitational loads. Effects of nonlinear static stall, dynamic stall, dynamic inflow, and delayed static stall due to rotation are analyzed separately and in combinations to explain the stability of flap motions in high winds. Contributions of the various steady and unsteady aerodynamic effects are presented for two airfoils: the LS(1) and the NREL Thin Airfoil Family (S805A, S806, S807). Teeter stability is compared for a blade with 10 deg of linear twist and a blade with optimum aerodynamic twist.

Nonmonotonic twist maps

We investigate a family of nonmonotonic radial twist maps constructed by unfolding the linear twist function. We find several new modes of reconnection and derive conditions for them to occur. Reconnection and bifurcation of higher order resonances are studied in detail, including vortex pairs and triplets. The structural instability of some of these exotic figures is mitigated by the presence of chaotic separatrix layers. Invariant curves of involution pairs are utilized to locate and chart their often very complex metamorphoses.

Visual and Tactile Perceptions of Textile Quality

Quality, appearance, and tactile properties of textiles arise from the choices of fibre type, linear density, staple length and degree of crimp, yarn linear density, mass, and twist, and fabric mass, weave type, density, and type of finishing, and especially the types of fibre assembly chosen. Information on how these choices affect the ultimate appearance and skin-contact sensations is constantly being sought in a world in which fibre choices and blends may provide several routes to a high-quality product. This paper examines these issues for wool and cotton blends with man-made fibres and suggests techniques for achieving a better understanding of how the perceptions of quality can be assessed. The goal in this work is to achieve a reference framework through the language of quality issues voiced by users of these products. Examples from apparel-performance studies are presented to illustrate this process.

Analytical study of Cantori: Gap structure, initial conditions, and dimensions.

A complete exact analysis of invariant Cantor sets in a piecewise linear but nontrivial area-preserving twist map is given. The results are based on concise formulas for minimizing periodic orbits, which in turn are derived from rigorous work by Aubry and Percival using only fundamental relations of continued-fraction theory. The exponential law for the decay of Cantori gaps, however, is found from the mapping itself with the aid of an elementary argument. The general scheme determining the initial conditions is transformed in the case of noble Cantori to an equivalent dynamical system permitting superexponentially fast calculations. By constructing polygonal embeddings the fractal and Hausdorff dimension of the invariant sets considered is proved to be precisely zero under all circumstances. Thus most notions and generic properties of Cantori can be understood within the frame of an explicitly solved example.

Geometry and Dimensional Properties of Plain Loops Made of Rotor Spun Cotton Yarns

The data on loop length generated in the course of these experiments have been analyzed to establish the effect of yarn linear density and twist factor as well as machine gauge and cam setting on the dry relaxed loop length. The effects of cam setting and sinker spacing have been quantified by empirical relations.

Weft Insertion on Air-jet Looms: Velocity Measurement and Influence of Yarn Structure Part II: Effects of System Parameters and Yarn Structure

An investigation of the effects of different weft–insertion–system parameters on yarn velocity is reported. Increasing the air–supply pressure, initial loop length, and running speed decreases the total insertion time and hence increases the average yarn velocity. To examine the effects of yarn characteristics on yarn velocity, several yarns were tested under the same laboratory conditions. For every yarn, relations between total insertion time, yarn velocity, and air velocity and distance were obtained. It was found that open–end–spun (OE) yarns had a higher yarn velocity than ring–spun (R) yarns owing to the bulkier structure. However, R yarns had a higher initial acceleration than OE yarns. Murata air–jet–spun yarns had a higher velocity than R yarns. Increasing the yarn linear density and twist increased the insertion time. Texturing of continuous–filament yarns increased the yarn velocity by comparison with straight continuous–filament yarns.

Invariant circles for the piecewise linear standard map

We investigate invariant circles for a one-parameter family of piecewise linear twist homeomorphisms of the annulus. We show that invariant circles of all types and rotation numbers occur and we classify them into families. We compute parameter ranges in which there are no invariant circles.

Influence of a Yarn Extractive Nozzle on the Apparent Loss of Twist in Rotor Open-End Acrylic Staple Spun Yarns

The influence of a yam extractive nozzle on the apparent loss of twist or "residual twist" has been studied for rotor open-end acrylic staple spun yarns. Four factors were studied: two quantitative factors - yam linear density at three levels and yarn twist multiplier at five levels, and two qualitative factors - three nozzle types and four rotor types. The analysis of results showed that both rotor type and extractive nozzle type exert a significant influence on residual twist, which tends to increase when the nozzle produces an increasing false twist effect on the yam and to decrease when yarn friction against the rotor increases. Residual twist increases significantly in a linear manner with both yarn linear density and twist multiplier. The nozzle type interacts significantly with all other factors (rotor type, yam linear density, and twist multiplier). An inter action between yarn linear density and twist multiplier has been also detected. Generally both nozzle type and twist multiplier exert a significant influence on the residual twist coefficient of variation.

An Evaluation of Vertical Drag and Ground Effect Using the RSRA Rotor Balance System

A flight test program utilizing the Rotor Systems Research Aircraft (RSRA) main rotor balance system was conducted to obtain data for the helicopter configuration. The test program is discussed along with the employed data reduction methods, and the results. NASA 740, the RSRA used for the vertical drag test, was in the standard helicopter configuration. The 31-foot radius blades have a linear twist of eight degrees and NACA 0012 airfoil sections. Aspects of instrumentation are considered, taking into account the data recording system, the static calibration facility, and aspects of data calibration and processing. Attention is given to the test procedure, data analysis methods, balance measurements, the ground effect, and vertical drag. It is found that the RSRA rotor balance system is capable of providing high quality performance data. The vertical drag of the RSRA is 4%, compared to 2.9% predicted.

A renormalization approach to invariant circles in area-preserving maps

Kadanoff and Shenker introduced a renormalisation approach to invariant circles in area-preserving maps. This paper makes more precise the connection between invariant circles and the renormalisation operator. Restricting attention to noble rotation numbers, the stability of a simple fixed point of the renormalisation is analysed, corresponding to a linear twist map. It is found to be essentially attracting, so that noble circles persist under perturbation, giving a new view on KAM theory. Shenker and Kadanoff found evidence for another fixed point, corresponding to a map with a non-smooth noble circle. Further evidence is given in this paper. It has essentially only one unstable direction, and its stable manifold is believed to give the boundary of the set of twist maps with a noble circle. Finally, noble circles are shown to be locally most robust, in an important sense.

Model helicopter rotor impulsive noise

An investigation of helicopter rotor blade slap was performed on a 1·27 m diameter model rotor. The rotor blades were a NACA 0012 section with a −8° linear twist. The experiments were conducted in the M.I.T. Anechoic Wind Tunnel. The effects of number of blades, blade pitch, advance ratio, and shaft angle on the generation and intensity of blade slap have been investigated. The effect of each parameter was determined by varying the parameter of interest while keeping the other constant. The rotor tip speeds of the tests performed in this study were limited to approximately Mach 0·4. The directivity associated with the blade slap signature was measured. The results of this investigation are based on a subjective definition of blade slap.

Supramolecular Structure of Polypeptides in Concentrated Solutions and Films. III. Inhomogeneous Twisting of Cholesteric Mesophase as Clarified from Multiple-Order Light-Scattering Maxima

We investigated the twisted structure in the cholesteric liquid crystals in which the directors n (parallel to axes of α-helical molecules of polypeptides) are helicoidally twisted about the helical axis. We propose here that this twisting occurs, in general, nonlinearly or inhomogeneously with displacement along the helical axis for the poly(γ-benzyl L-gultamate) systems studied in this work, in contrast to a picture of ‘linear twisting’ appearing in earlier literature on the cholesteric liquid crystals. The inhomogeneous twisting in the cholesterics is exhibited most spectacularly in the multiple-order scattering maxima of a laser-light. The deviation from the homogeneous twisting was studied as a function of cell thickness, solvent, polymer concentration, temperature, and aging; the results indicate that the inhomogeneous twisting of the directors is a general phenomenon in the lyotropic liquid crystal system studied in this work. We present a theory for elastic light scattering from the cholesteric mesophase having inhomogeneously twisted structure.