Dynamic Twist Research Articles

Dynamical quantum groups at roots of 1

Given a dynamical twist for a finite-dimensional Hopf algebra, we construct two weak Hopf algebras, using methods of P. Xu and of P. Etingof and A. Varchenko, and we show that they are dual to each other. We generalize the theory of dynamical quantum groups to the case when the quantum parameter q is a root of unity. These objects turn out to be self-dual—which is a fundamentally new property, not satisfied by the usual Drinfeld-Jimbo quantum groups.

Parton distribution functions from nonlocal light-cone operators with definite twist

We introduce the chiral-even and chiral-odd quark distributions as forward matrix elements of related bilocal quark operators with well-defined (geometric) twist. Thereby, we achieve a Lorentz invariant classification of these distributions which differ from the conventional ones by explicitly taking into account the necessary trace terms. The relations between both kinds of distribution functions are given and the mismatch between their different definition of twist is discussed. Wandzura-Wilczek--like relations between the conventional distributions (based on dynamical twist) are derived by means of geometric twist distribution functions.

Dynamical twists in group algebras

We classify twists in group algebras of finite groups. Namely, we set up a bijective correspondence between gauge equivalence classes of twists (which are solutions of a certain non-linear functional equation) and isomorphism classes of dynamical data described in purely group theoretical terms. This generalizes the classification of usual twists obtained by Movshev and Etingof-Gelaki.

Vertex-IRF transformations and quantization of dynamical $r$-matrices

Motivated by the correspondence between the vertex and IRF models in statistical mechanics, we define and study a notion of vertex-IRF transformation for dynamical twists that generalizes a usual gauge transforma- tion. We use vertex-IRF transformations to quantize all completely degenerate dynamical r-matrices on finite-dimensional Lie algebras.

The chiral WZNW phase space as a quasi-Poisson space

It is explained that the chiral WZNW phase space is a quasi-Poisson space with respect to the ‘canonical’ Lie quasi-bialgebra which is the classical limit of Drinfeld's quasi-Hopf deformation of the universal enveloping algebra. This exemplifies the notion of quasi-Poisson–Lie symmetry introduced recently by Alekseev and Kosmann–Schwarzbach, and also permits us to generalize certain dynamical twists considered previously in this example.

Explicit quantization of dynamical r-matrices for finite dimensional semisimple Lie algebras

We provide an explicit quantization of dynamical r-matrices for semisimple Lie algebras, classified earlier by the third author, which includes the Belavin-Drinfeld r-matrices. We do so by constructing an appropriate (dynamical) twist in the tensor square of the Drinfeld-Jimbo quantum group $U_q(\mathfrak g)$, which twists the R-matrix of $U_q(\mathfrak g)$ into the desired quantization. The construction of this twist is based on the method stemming from the work of Jimbo-Konno-Odake-Shiraishi and Arnaudon-Buffenoir-Ragoucy-Roche, i.e. on defining the twist as a unique solution of a suitable difference equation. This yields a simple closed formula for the twist. This construction allows one to confirm the alternate version of the Gerstenhaber-Giaquinto-Schack conjecture (about quantization of Belavin-Drinfeld r-matrices for $\mathfrak {sl}(n)$ in the vector representation), which was stated earlier by the second author on the basis of computer evidence. It also allows one to define new quantum groups associated to semisimple Lie algebras. We expect them to have a rich structure and interesting representation theory.

The dynamical twisting and nondynamical r-matrix structure of the elliptic Ruijsenaars–Schneider model

From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars–Schneider model (cf. Ruijsenaars). The corresponding r-matrix is shown to be the classical Zn-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version—the An−1 Calogero–Moser model.

The non-dynamicalr-matrix structure for the elliptic Calogero-Moser model

In this paper we construct a new Lax operator for the elliptic Calogero-Moser model with general from the classical dynamical twisting, in which the corresponding r-matrix is purely numerical (non-dynamic). The non-dynamical r-matrix structure of this Lax operator is obtained, which is the elliptic -symmetric r-matrix.

A Transverse Contour Model of Distributed Muscle Forces and Spinal Loads during Lifting and Twisting

This study has developed a realistic three-dimensional transverse contour model of distributed muscle forces and spinal consequences (compression, torsion, and shear) that occur during dynamic lifting, static holding, and dynamic twisting. The model utilizes multiple force vectors to represent broad flat muscles along with traditional single vector modeling of other trunk muscles. Instead of a two-dimensional transverse cutting plane, this model introduces a system analysis boundary in the form of a three-dimensional transverse cutting contour that was created by in vivo digitization of human subjects in symmetric and asymmetric postures. This transverse contour more realistically illustrates the complex nature of the human biomechanical system during the performance of industrial work in three-dimensional space. To investigate this model, surface electromyography data were collected from seven subjects. Also, to confirm the findings from surface data and to alleviate muscle signal crosstalk concerns, fine-wire electromyography data were collected from one additional subject. Both the surface and fine-wire data showed that differential muscle forces existed within each of the external obliques, internal obliques, and latissimus dorsi. Moreover, the data were used for validation which confirmed the viability of the model. This multi-vector distributed-force transverse contour model was found to be particularly useful for describing shear and compression during three-dimensional twisting.

Exact effective action for fermions in one dimension with backscattering at a boundary.

We report exact results for the partition function for free Dirac fermions on a half line with physically sensible boundary conditions. An exact effective action for general backscattering amplitudes is derived. The action also includes the effects of both a (time-dependent) forward scattering amplitude and a dynamical chiral twist of the fermion boundary conditions. For a small backscattering amplitude, the effective action has the expected boundary sine-Gordon form. We discuss applications of our results to one-dimensional Fermi systems with local backscattering. \textcopyright{} 1996 The American Physical Society.

Dynamic extension and twist of a non-linear elastic tube

The propagation of waves in a non-linear cylindrical elastic membrane is considered when one end is fixed and the other is subjected to a dynamic extension and twist. The governing equations are derived for a hyperelastic material with a general strain energy function. In order to obtain specific results the equations are specialised to deal with neo-Hookian materials and in this case we show that there are three real wave speeds in each direction along the cylinder. Numerical results are given and a limiting case considered which provides a check on these results.

A Biomechanical Assessment of Axial Twisting Exertions

Axial twisting of the torso has been identified as a significant risk factor for occupationally related low-back disorders. The purpose of this investigation was to examine the influence of dynamic twisting parameters upon spinal load. Measured trunk moments and muscle activities were employed in a biomechanical model to determine loads on the lumbar spine. Spinal loads were examined as a function of dynamic torsional exertions under various conditions of force, velocity, position, and direction. Results demonstrate significant flexion-extension and lateral moments were generated during the twisting exertions. Muscle coactivity was significantly greater than equivalent levels measured during sagittal lifting exertions. Relative spinal compression during dynamic twisting exertions was twice that of static exertions. Spine loading also varied as a function of whether the trunk was twisted to the left or right, and the direction of applied torsion, i.e. clockwise versus counter-clockwise. The results may help explain, biomechanically, why epidemiological findings have repeatedly identified twisting as a risk factor for low-back disorder

A Biomechanical Assessment and Model of Axial Twisting in the Thoracolumbar Spine

Measured trunk kinematics, applied moments, and trunk muscle activities were employed in a biomechanical model to determine load experiences by the spine during dynamic torsional exertions. The purpose of this investigation was to examine the influence of dynamic twisting parameters on spinal load. Axial twisting of the torso has been identified as a significant risk factor for occupationally related low back disorders. However, previous studies have had difficulty describing how twisting is accomplished biomechanically, or how the spine is loaded during twisting motions. Electromyograph activity of 10 trunk muscles was monitored while 12 subjects performed twisting exertions under various conditions of force, velocity, position, and direction. An electromyograph-assisted biomechanical model was developed to interpret the effects of those twisting parameters on spine loading. Significant flexion-extension and lateral moments were generated during the twisting exertions. Muscle co-activity associated with twisting exertions was significantly greater than that associated with lifting exertions. Employing electromyograph data to represent muscle co-activity, the model accurately predicted trunk moments and hence was assumed to reasonably reflect spine loading. Under the conditions tested, the results indicated that relative spinal compression during dynamic twisting exertions was twice that of static exertions. Spine loading also varied as a function of whether the trunk was twisted to the left or right and according to the direction of applied torsion--i.e., clockwise or counterclockwise. The results may help explain, biomechanically, why epidemiologic findings have repeatedly identified twisting as a risk factor for low back disorder.

The dynamic problem of electroelasticity for a non-homogeneous cylinder

The non-stationary coupled problem of electroelasticity in connection with the dynamic twisting of a finite hollow cylinder of non-homogeneous piezoelectric material is considered in the case when the electric potential or shear stresses, which depend arbitrarily on time, are specified on its curvilinear surfaces. The method of expansion in eigen vector-valued functions in the form of a structural algorithm of finite integral transformations is used. It is shown that a closed solution can be obtained for a power law of the non-homogeneity of the electric, elastic and inertial characteristics of the material. The results obtained hold for crystals of tetragonal symmetry of class 422 and the hexagonal system of class 622.

Electromyographic activity of the abdominal and low back musculature during the generation of isometric and dynamic axial trunk torque: Implications for lumbar mechanics

This study focused on the electromyographic activity of the trunk musculature, given the well-documented link between occupational twisting and the increased incidence of low back pain. Ten men and 15 women volunteered for this study, in which several aspects of muscle activity were examined. The first aspect assessed the myoelectric relationships during isometric exertions. There was great variability in this relationship between muscles and between subjects. Further, the myoelectric activity levels (normalized to maximal electrical activity) obtained from nontwist activities were not maximal despite maximal efforts to generate axial torque (e.g., rectus abdominis, maximum voluntary contraction; 22% external oblique, 52%; internal oblique, 55%; latissimus dorsi, 74%; upper erector spinae [T9], 61%; lower erector spinae [L3], 33%). In the second aspect of the study, muscle activity was examined during dynamic axial twist trials conducted at a velocity of 30 and 60 degrees/s. The latissimus dorsi and external oblique appeared to be strongly involved in the generation of axial torque throughout the twist range and activity in the upper erector spinae displayed a strong link with axial torque and direction of twist, even though they have no mechanical potential to contribute axial torque, suggesting a stabilization role. The third aspect of the study was comprised of the formulation of a model consisting of a three-dimensional pelvis, rib cage, and lumbar vertebrae and driven from kinematic measures of axial twist and muscle electromyograms. The relatively low levels of normalized myoelectric activity during maximal twisting efforts coupled with large levels of agonist-antagonist cocontraction caused the model to severely underpredict measured torques (e.g., 14 Nm predicted for 91 Nm measured). Such dominant coactivity suggests that stabilization of the joints during twisting is far more important to the lumbar spine than production of large levels of axial torque.

A precise extraction of R= σL/ σT from a global analysis of the SLAC deep inelastic e-p and e-d scattering cross sections

We report the extraction of R= σ L/ σ T from a global analysis of eight SLAC deep inelastic experiments on e-p and e-d scattering performed between 1970 and 1985. Values of R p, R d, and R d − R p are determined over the entire SLAC kinematic range: 0.1⩽ x⩽0.9 and 0.6⩽ Q 2⩽20.0 (GeV/ c) 2. We find that R p= R d. Measured values of R( x, Q 2) are larger than predictions based on perturbative QCD and on QCD with the inclusion of kinematic target mass terms, indicating that dynamical higher twist effects may be important in the SLAC kinematic range.

Measurement of the structure functionsF 2 andxF 3 and comparison with QCD predictions including kinematical and dynamical higher twist effects

The isoscalar nucleon structure functionsF2(x, Q2) andxF3(x, Q2) are measured in the range 0<Q2<64 GeV2, 1.7<W2<250 GeV2,x<0.7 using ν and\(\bar v\) interactions on neon in BEBC. The data are used to evaluate possible higher twist contributions and to determine their impact on the evaluation of the QCD parameter Λ. In contrast to previous analyses reaching to such lowW2 values, it is found that a low\(\Lambda _{\overline {MS} } \) value in the neighbourhood of 100 MeV describes the data adequately and that the contribution of dynamical higher twist effects is small and negative.

The dynamic twisting of the left ventricle: a computer study.

A mathematical analysis which relates the dynamic twisting motion of the heart around its longitudinal axis to the mechanical function of the left ventricle (LV) is presented. The study thus extends our earlier model which relates the micro-scale sarcomere dynamics, the fibrous structure of the myocardium, and the electrical transmural activation wave to the global LV function. The analysis demonstrates that although the angular twisting motion of the heart moderates the sarcomere length (SL) and the strain rate distributions throughout the myocardium, the global characteristics of the LV function are almost independent of the twisting phenomenon. The endocardial sarcomeres are nevertheless subjected to higher strains and higher (negative) strain rates than the corresponding (positive) epicardial sarcomeres. Utilizing the sarcomere stress length area to predict oxygen demand, it is shown that the twisting motion of the heart produces the metabolic gradient across the LV wall. In spite of the moderating effect of the twist, a larger than normal gradient in oxygen demand is predicted for cases of concentric hypertrophy.

Fluid dynamical twisting of the radio jets in 3C 449

view Abstract Citations (30) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Fluid dynamical twisting of the radio jets in 3C 449 Hardee, P. E. Abstract The jet structure of the double jets in the radio galaxy 3C 449 can be understood as resulting from helical instability of an initially cylindrically symmetric straight jet. A growing helical wave is convected out along the jets and reaches a large amplitude at the position of the radio lobes, disrupting well-directed flow. Adiabatic expansion of the thermalized jet material produces the radio lobes. The extended diffuse emission outside the present radio lobes is the remnant of earlier, more luminous jets. Conditions in the expanding inner jets required for this mechanism to operate are almost the same as those inferred by Perley et al. (1979) from their VLA observations. The jets are supersonic, with Mach number on the order of 10, and the flow velocity is about 1500 km/sec. The density of the interstellar medium in the galaxy is inferred to be about the same as the jets' density. The age of the radio source is probably less than several times 100 million years. Publication: The Astrophysical Journal Pub Date: November 1981 DOI: 10.1086/183664 Bibcode: 1981ApJ...250L...9H Keywords: Fluid Dynamics; Galactic Structure; Interstellar Matter; Jet Flow; Radio Galaxies; Radio Jets (Astronomy); Adiabatic Conditions; Flow Stability; Flow Velocity; Kelvin-Helmholtz Instability; Mach Number; Supersonic Jet Flow; Astrophysics full text sources ADS | data products NED (2)

Wind Tunnel Evaluation of Aeroelastically Conformable Rotors

Abstract : The concept of controlling blade dynamic twist to reduce rotor system loads and to improve aerodynamic efficiency was investigated through wind tunnel testing and analysis. Blade design features which promote favorable dynamic twist were selected based on aeroelastic analysis. Two four-bladed 9-ft diameter 1/6 scale model rotors which permitted parametric investigation of blade torsional stiffness, tip sweep, and camber were fabricated and subjected to forward flight testing in the Langley Research Center Transonic Dynamics Wind Tunnel. The azimuthal variation of dynamic twist was determined based on measured twisting moments. Results showed that relative to a conventional stiffness blade, 20 to 40 percent reductions in vibratory flatwise and torsional moments and 10-percent reductions in power were achieved at an advance ratio of 0.3 by configurations which produced noseup elastic twist on the advancing blade. Four/rev hub vibration was also reduced by blades which reduced advancing blade total twist. The important trends shown by the test results were adequately predicted by a blade aeroelastic response analysis although magnitudes of blade loads were generally unpredicted.