Torsion Components Research Articles

A NOTE ON CLASSIFICATION OF BIANCHI TYPE I SPACETIMES ACCORDING TO THEIR TELEPARALLEL KILLING VECTOR FIELDS

In this paper we classify Bianchi type I spacetimes according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 3, 4, 6 or 10 which are the same in numbers as in general relativity. In case of 3, 4 or 6 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 10 Killing vector fields, the spacetime becomes Minkowski and all the torsion components are zero. The Killing vector fields in this case are exactly the same as in the general relativity.

EXTRA DIMENSIONS WITH NONTRIVIAL TORSION AND SPINS OF COSMIC STRINGS

As two generalizations of Einstein's general relativity, the nontrivial spacetime torsion and the compact extra dimensions have been largely studied in the literature. In this paper, by combining a torsioned Kaluza–Klein scheme and the field-theory cosmic string theory, we discuss that a higher-dimensional torsion component can be expressed in terms of the usual four-dimensional field strength two-form, and this torsion form can then get trapped into the cores of the cosmic strings and further relate to the intrinsic spins of the strings.

Reliability and Validity of Goniometric Turnout Measurements Compared with MRI and Retro-Reflective Markers

There is no consensus on a valid and reliable method of measuring turnout. However, there is a building awareness that such measures need to exist. Total turnout is the sum of hip rotation, tibial torsion, and contributions from the foot. To our knowledge, there has been no research that directly measures and then sums each individual component of turnout to verify a total turnout value. Furthermore, the tibial torsion component has not previously been confirmed by an imaging study. The purpose of this study was to test the validity and reliability of a single total passive turnout (TPT) test taken with a goniometer by comparing it with the sum of the individual components. Fourteen female dancers were recruited as participants. Measurements of the subjects’ right and left legs were gathered for the components of turn-out. Tibial torsion was measured using Magnetic Resonance Imaging (MRI). Retro-reflective marker assisted measurements were used to calculate the static components of TPT. Hip external rotation, TPT, and total active turnout (TAT) were measured by goniometer. Additional standing turnout values were collected on rotational disks. Tibial torsion and hip rotation were summed and compared with three whole-leg turnout values using Two-Tailed T-Tests and Pearson product-moment correlation coefficients. Tibial torsion measurements in dancers were found to demonstrate substantial variation between subjects and between legs in the same subject. The range on the right leg was 16° to 60°, and the range on the left leg was 16° to 52°. Retro-reflective markers and biomechanical theory demonstrated that when the knee is extended and locked, “screwed home,” it will not factor into a whole-leg turnout value. TAT and turnout on the disks were not statistically significant when compared with the summed total. Statistical significance was achieved in four of the eight measurement series comparing TPT with the summed value of tibial torsion and hip rotation. The advantages of a standard, valid, and reliable method of measuring turnout are many, and the risks are few. Some advantages include improved training techniques, mastery of the use of turnout at an earlier age, better dancer and teacher compliance with suggested turnout rates, understanding the use of parallel position, understanding the etiology of many dance-related injuries, and possible development of preventative measures.

Constraints on Torsion from Bounds on Lorentz Violation

Exceptional sensitivity to space-time torsion can be achieved by searching for its couplings to fermions. Recent experimental searches for Lorentz violation are exploited to extract new constraints involving 19 of the 24 independent torsion components down to levels of order 10(-31) GeV.

Geometrical Nonlinear Aeroelastic Stability Analysis of a Composite High-Aspect-Ratio Wing

A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE) aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN), and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.

Decreased Left Ventricular Torsion and Untwisting in Children with Dilated Cardiomyopathy

The purpose of this study was to analyze left ventricular (LV) torsion and untwisting, and to evaluate the correlation between torsion and other components of LV contraction in children with dilated cardiomyopathy (DCM). Segmental and global rotation, rotational rate (Vrot) were measured at three levels of LV using the two-dimensional (2D) speckle tracking imaging (STI) method in 10 DCM patients (range 0.6-15 yr, median 6.5 yr, 3 females) and 17 age- and sex-matched normal controls. Global torsion was decreased in DCM (peak global torsion; 10.9±4.6° vs. 0.3±2.1°, p<0.001). Loss of LV torsion occurred mainly by the diminution of counterclockwise apical rotation and was augmented by somewhat less reduction in clockwise basal rotation. In DCM, the normal counterclockwise apical rotation was not observed, and the apical rotation about the central axis was clockwise or slightly counterclockwise (peak apical rotation; 5.9±4.1° vs. -0.9±3.1°, p<0.001). Systolic counterclockwise Vrot and early diastolic clockwise Vrot at the apical level were decreased or abolished. In DCM, decreased systolic torsion and loss of early diastolic recoil contribute to LV systolic and diastolic dysfunction. The STI method may facilitate the serial evaluation of the LV torsional behavior in clinical settings and give new biomechanical concepts for better management of patients with DCM.

The Einstein–Cartan–Elko system

AbstractThe present paper analyses the Einstein‐Cartan theory of gravitation with Elko spinors as sources of curvature and torsion. After minimally coupling the Elko spinors to torsion, the spin angular momentum tensor is derived and its structure is discussed. It shows a much richer structure than the Dirac analogue and hence it is demonstrated that spin one half particles do not necessarily yield only an axial vector torsion component. Moreover, it is argued that the presence of Elko spinors partially solves the problem of minimally coupling Maxwell fields to Einstein‐Cartan theory.

The Einstein–Cartan–Elko system

The present paper analyses the Einstein-Cartan theory of gravitation with Elko spinors as sources of curvature and torsion. After minimally coupling the Elko spinors to torsion, the spin angular momentum tensor is derived and its structure is discussed. It shows a much richer structure than the Dirac analogue and hence it is demonstrated that spin one half particles do not necessarily yield only an axial vector torsion component. Moreover, it is argued that the presence of Elko spinors partially solves the problem of minimally coupling Maxwell fields to Einstein-Cartan theory.

Texture Development in Interstitial Free (IF) Steel Subjected to Two Cycles of Equal Channel Angular Extrusion

Texture development and grain refinement of interstitial-free (IF) steel as a function of ideal simple shear or torsion was undertaken for up to 8 pressings, Route BC. Dominant texture components evolved after a single pass and remained correspondent for all subsequent passes. End-cycle (4 and 8 pass) orientation distribution functions (ODFs) showed an increased spread of contour levels and the re-appearance of texture components similar to the 0-pass condition. Rotation of torsion components away from their ideal pole figure (PF) orientations increased at mid-cycle and decreased to almost equivalent levels after end-cycle passes. This is attributed to the principle slip directions of BCC structures aligning with the shear direction.

Spontaneous Lorentz violation, Nambu-Goldstone modes, and gravity

The fate of the Nambu-Goldstone modes arising from spontaneous Lorentz violation is investigated. Using the vierbein formalism, it is shown that up to 10 Lorentz and diffeomorphism Nambu-Goldstone modes can appear and that they are contained within the 10 modes of the vierbein associated with gauge degrees of freedom in a Lorentz-invariant theory. A general treatment of spontaneous local Lorentz and diffeomorphism violation is given for various spacetimes, and the fate of the Nambu-Goldstone modes is shown to depend on both the spacetime geometry and the dynamics of the tensor field triggering the spontaneous Lorentz violation. The results are illustrated within the general class of bumblebee models involving vacuum values for a vector field. In Minkowski and Riemann spacetimes, the bumblebee model provides a dynamical theory generating a photon as a Nambu-Goldstone boson for spontaneous Lorentz violation. The Maxwell and Einstein-Maxwell actions are automatically recovered in axial gauge. Associated effects of potential experimental relevance include Lorentz-violating couplings in the matter and gravitational sectors of the Standard-Model Extension and unconventional Lorentz-invariant couplings. In Riemann-Cartan spacetime, the possibility also exists of a Higgs mechanism for the spin connection, leading to the absorption of the propagating Nambu-Goldstone modes into the torsion component of the gravitational field.

Positional Isotope Effect for the Water Tetramer

Ab initio studies are carried out for the water tetramer with a single H replaced by D, (H2O)3(HDO). The isomer with D in a free position, H7DfO4, has ZPE 0.17 kcal/mol higher than the isomer with D in an H-bond, H7DbO4. The same ZPE difference is found for HbD7O4 vs HfD7O4. The difference may be large enough for a preference for H rather than D in a free position to be experimentally measurable. Exploration of the components of ZPE shows that the stretch component alone favors H7DfO4, but this is more than compensated by the bend and torsion components.

Mirror Symmetric SU(3)-Structure Manifolds with NS Fluxes

When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex structure on the mirror side. Considering a general class of T3-fibered geometries admitting SU(3) structure, we find an exchange of pure spinors (e iJ and Ω) in dual geometries under fiberwise T–duality, and study the transformations of the NS flux and the components of intrinsic torsion. A complementary study of action of twisted covariant derivatives on invariant spinors allows to extend our results to generic geometries and formulate a proposal for mirror symmetry in compactifications with NS flux.

Possible effects of space-time nonmetricity on neutrino oscillations

The contribution of gravitational neutrino oscillations to the solar neutrino problem is studied by constructing the Dirac Hamiltonian and calculating the corresponding dynamical phase in the vicinity of the Sun in a non-Riemann background Kerr space-time with torsion and non-metricity. We show that certain components of non-metricity and the axial as well as non-axial components of torsion may contribute to neutrino oscillations. We also note that the rotation of the Sun may cause a suppression of transitions among neutrinos. However, the observed solar neutrino deficit could not be explained by any of these effects because they are of the order of Planck scales.

A Bochner formula for almost-quaternionic-Hermitian structures

An integral formula is derived, relating the six irreducible components of the intrinsic torsion of an Sp n Sp 1 structure on a compact 4 n-dimensional manifold with the Riemann curvature tensor. Some consequences of the formula are studied.

Supersymmetric M-theory compactifications with fluxes on seven-manifolds andG-structures

We consider Minkowski compactifications of M-theory on generic seven-dimensional manifolds. After analyzing the conditions on the four-form flux, we establish a set of relations between the components of the intrinsic torsion of the internal manifold and the components of the four-form flux needed for preserving supersymmetry. The existence of two nowhere vanishing vectors on any seven-manifold with G_2 structure plays a crucial role in our analysis, leading to the possibility of four-dimensional compactifications with N=1 and N=2 supersymmetry.

Nonlinear charge transport mechanism in periodic and disordered DNA

We study a model for polaron-like charge transport mechanism along DNA molecules with emphasis on the impact of parametrical and structural disorder. Our model Hamiltonian takes into account the coupling of the charge carrier to two different kinds of modes representing fluctuating twist motions of the base pairs and H-bond distortions within the double helix structure of λ-DNA. Localized stationary states are constructed with the help of a nonlinear map approach for a periodic double helix and in the presence of intrinsic static parametrical and/or structural disorder reflecting the impact of ambient solvent coordinates. It is demonstrated that charge transport is mediated by moving polarons and breather compounds carrying not only the charge but also causing local temporal deformations of the helix structure through the traveling torsion and bond breather components illustrating the interplay of structure and function in biomolecules.

Massive torsion modes, chiral gravity and the Adler–Bell–Jackiw anomaly

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler–Bell–Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin-½ particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to explain why torsion and its associated effects, including CPT violation in chiral gravity, have so far escaped detection. As a simpler manifestation of the reasons underpinning the ABJ anomaly than triangle diagrams, the vacuum polarization demonstration is also pedagogically useful. In addition, it is shown that the teleparallel limit of a Weyl fermion theory coupled only to the left-handed spin connection leads to a counter term which is the Samuel–Jacobson–Smolin action of chiral gravity in four dimensions.

Ricci and Bianchi identities for h‐normal Γ‐linear connections on J1(T, M)

The aim of this paper is to describe the local Ricci and Bianchi identities of an h‐normal Γ‐linear connection on the first‐order jet fibre bundle J1(T, M). We present the physical and geometrical motives that determined our study and introduce the h‐normal Γ‐linear connections on J1(T, M), emphasizing their particular local features. We describe the expressions of the local components of torsion and curvature d‐tensors produced by an h‐normal Γ‐linear connection ∇Γ, and analyze the local Ricci identities induced by ∇Γ, together with their derived local deflection d‐tensors identities. Finally, we expose the local expressions of Bianchi identities which geometrically connect the local torsion and curvature d‐tensors of connection ∇Γ.

ICFF: a new method to incorporate implicit flexibility into an internal coordinate force field.

We introduce a new method to accurately "project" a Cartesian force field onto an internal coordinate molecular model with fixed-bond geometry. The algorithm automatically generates the Internal Coordinate Force Field (ICFF), which is a close approximation of the "source" Cartesian force field. The ICFF method reduces the number of free variables in a model by at least 10-fold and facilitates the fast convergence of geometry optimizations, an advantage that is critical for many applications such as the docking of flexible ligands or conformational modeling of macromolecules. Although covalent geometry is fixed in an ICFF model, implicit flexibility is incorporated into the force field parameters in the following two ways. First, we formulate an empirical torsion energy term in ICFF as a sixfold Fourier series and develop a procedure to calculate the Fourier coefficients from the conformational energy profiles of the fully flexible Cartesian model. The ICFF torsion parameters thus represent not only torsion component of the source force field, but also bond bending, bond stretching, and "1-4" van der Waals interactions. Second, we use a soft polynomial repulsion function for "1-5" and "1-6" interactions to mimic the flexibility of bonds, connecting these atoms. Also, we suggest a way to use a local part of the Cartesian force field to automatically generate fixed covalent geometries, compatible with the ICFF energy function. Here, we present an implementation of the ICFF algorithm, which employs the MMFF94s Cartesian force field as a "source." Extensive benchmarking of ICFF with a representative set of organic molecules demonstrates that the implicit flexibility model accurately reproduces MMFF94s equilibrium conformational energy differences (RMSD approximately 0.64 kcal) and, most importantly, detailed torsion energy profiles (RMSD approximately 0.37 kcal). This accuracy is characteristic of the method, because all the ICFF parameters (except one scaling factor in the "1-5,1-6" repulsion term) are derived directly from the source Cartesian force field and do not depend on any particular molecular set. In contrast, the rigid geometry model with the MMFF94s energy function yields highly biased estimations in this test with the RMSD exceeding 1.2 kcal for the equilibrium energy comparisons and approximately 3.4 kcal for the torsion energy profiles.

Adaptive control of vergence in humans.

Vergence eye alignment minimizes horizontal, vertical, and cyclodisparities to optimize stereo-depth perception. Only the horizontal component of vergence is under voluntary control. Couplings with voluntary version and horizontal vergence guide vertical vergence and cyclovergence. Can these couplings be modified in response to sensory demands on binocular vision? We have modified vertical vergence and cyclovergence in response to optical changes in disparity. Vertical vergence was stimulated with aniseikonic lenses that exaggerated vertical disparity in tertiary gaze. Vertical vergence adapted in an hour to produce nonconcomitant changes in vertical phoria that varied with vertical eye position in tertiary gaze. Cyclovergence was stimulated with cyclodisparities that varied with gaze elevation and convergence angle. Cyclovergence adapted within 2 hours to produce nonconcomitant changes in cyclophoria that varied with gaze elevation and convergence. The adaptive couplings for vertical vergence and cyclovergence are modeled as a combination of passive orbital mechanics and active gain control of the vertical recti and obliques. Vergence adaptation is a calibration process that adjusts the innervation for horizontal, vertical, and torsion components of vergence to the physical constraints set by the extraocular muscles and orbital connective tissues. Passive orbital mechanics simplify the neural control for precise vertical vergence and cyclovergence that are needed to achieve binocular alignment under open-loop conditions in response to perceived spatial location.