Torsion Field Research Articles

Cosmological solutions in polynomial affine gravity with torsion

The Polynomial Affine Gravity is an alternative gravitational model, where the interactions are mediated solely by the affine connection, instead of the metric tensor. In this paper, we explore the space of solutions to the field equations when the torsion fields are turned on, in a homogeneous and isotropic (cosmological) scenario. We explore various metric structures that emerge in the space of solutions.

Phase space analysis of torsion cosmology

In this paper, we study the dynamical stability analysis by considering the torsion field [Formula: see text] which is proportional to the Hubble parameter and barotropic equation-of-state parameter in the framework of the homogenous and isotropic FLRW metric with non-zero torsion in the scenario of dark matter and dark energy interacting terms. We discuss the stability of the critical points corresponding to the eigenvalues in the presence of dust and radiation at quintessence, [Formula: see text]CDM and phantom regimes by utilizing the different linear and nonlinear interaction models which depend on the energy density. As a result, we observe that the first linear model shows the stable behavior throughout the universe for dust and radiation phase. The other linear and nonlinear models show the stable critical points, computing with the eigenvalues at phantom and [Formula: see text]CDM era with the best fit value of interaction strength and coupling constant for dust and radiation.

Accelerating universe in f(T) teleparallel gravity

In recent decades, there has been significant research on the role of torsion in gravity, with a focus on aligning gravity with its gauge formulation and including spin into a geometric description. In order to account for the present phenomenon of the universe’s accelerated expansion, recent developments have introduced [Formula: see text] theories that rely on the disparities found in teleparallel gravity. Torsion, rather than curvature, is the fundamental geometric property that describes gravity in these theories. When compared to theories involving [Formula: see text] functions, the field equations are consistently of second order and surprisingly simple. We consider a specific type of function called torsion, which is defined as [Formula: see text]. The expression consists of two free parameters, [Formula: see text] and [Formula: see text], and the current value of the torsion scalar, [Formula: see text]. In order to solve the modified torsion field equations (MTFEs), we can utilize the parametrization of the deceleration parameter (DP) in terms of redshift, denoted as [Formula: see text]. Here, [Formula: see text] and [Formula: see text] represent the model parameters. The model parameters are determined by utilizing observable constraints, including as 57 Hubble data points, 1048 Pantheon supernovae type Ia data, and Baryon Acoustic Oscillations (BAO) datasets. In addition, we utilize Markov Chain Monte Carlo (MCMC) methods for statistical analysis.

Torsion Fields as a Reality

Torsion Fields as a Reality

Trajectories of Solitons Movement in the Potential Field of pPF1 Plasmid with Non-Zero Initial Velocity

Nonlinear conformational distortions, such as, for example, locally unwound regions of the DNA double helix, named open states, are considered in this work as solitons moving in the potential field of this molecule. It is believed that open states play an important role in the processes of transcription, replication, denaturation, as well as in the transmission of structural changes and information along the DNA molecule. This work examines the problem of the movement of kink-like solitons (kinks) in the potential field of the pPF1 plasmid, the sequence of which includes the genes of the fluorescent proteins Egfp and mCherry, separated by a small intermediate region. The results of calculations of energy profiles of the main and complementary sequences of the plasmid, as well as 2D and 3D trajectories of kinks with a non-zero initial velocity are presented. It has been shown that two types of kinks can be activated in the pPF1 plasmid, which can be considered as two types of quasiparticles that have their own energy, mass, velocity and move in the potential field of the plasmid. It was found that the lowest energy required to form these kinks is observed in the intermediate region located between the fluorescent protein genes. It was shown that the nature of the motion of kinks does not depend on the value of their initial velocity. It was shown that there are threshold values of the torsion field, upon reaching which the behavior of kinks changes sharply: from damped oscillations within the intermediate region to forward motion and penetration into neighboring regions. These values have been calculated. It turned out that for the first kink moving in the main sequence potential field, the threshold value is 4.95×10–22 J, and for the second kink – 4.20 × 10–22 J.

Massive propagating modes of torsion

The dynamics of the torsion field is analyzed in the framework of the Covariant Canonical Gauge Theory of Gravity (CCGG), a De Donder–Weyl Hamiltonian formulation of gauge gravity. The action is quadratic in both, the torsion and the Riemann–Cartan tensor. Since the latter adds the derivative of torsion to the equations of motion, torsion is no longer identical to spin density, as in the Einstein–Cartan theory, but an additional propagating degree of freedom. As torsion turns out to be totally anti-symmetric, it can be parametrised via a single axial vector. It is shown in this paper that, in the weak torsion limit, the axial vector obeys a wave equation with an effective mass term which is partially dependent on the scalar curvature. The source of torsion is thereby given by the fermion axial current which is the net fermionic spin density of the system. Possible measurable effects and approaches to experimental analysis are addressed. For example, neutron star mergers could act as a dipoles or quadrupoles for torsional radiation, and an analysis of radiation of pulsars could lead to a detection of torsion wave background radiation.

Enhancing dynamic mixing and heat transfer of polymer by inducing ductile flow applying field synergy principle

An innovative and effective approach for screw design and optimization has been proposed, derived from multi-field synergy to address a growing challenge affected by the inadequate mixing and thermal management in plasticizing process of extrusion or injection. Dimensionless field synergy equations for incompressible non-Newtonian viscous polymers were established, and subsequently, two new types of screw structures—field synergy torsion element (FST) and field synergy elongation element (FSE)—were designed, fabricated, and validated through both simulation and experiment. Spiral and elongational flows were established in the newly designed screws owing to their unique structures of torsion channel and convergent channel, promoting the shear and stretch ductile deformations of polymer melt, documented to be a meaningful progress on flow patterns generated by conventional screw. A comparative investigation in this work of the newly designed screw with a conventional one showed that the newly proposed screws equipped with FSTs or FSEs performed better mixing and improved heat transfer and thermal uniformity. Multi-field synergy analysis revealed that the spiral and elongational flow enhanced the radial convection, improved the dependence of velocity and velocity gradient fields to facilitate melt stretching deformation as well as the dependence of velocity and temperature gradient fields to achieve heat transfer enhancement.

On torsion of FG elastic nanobeams on nonlocal foundations

A plethora of challenging nanomechanical applications deals with ultrasmall composite structures interacting with nonlocal media. To capture size dependent behaviors, effective tools of Nonlocal Continuum Mechanics can be conveniently adopted, provided that the relevant structural problem is well-posed. A crucial improvement in modeling of nanobeams on nanofoundations is provided in the present work with respect to the formulation based on the Eringen–Wieghardt nonlocal approach. Scale effects on FG nanobeams under torsion are effectively captured by exploiting the consistent stress-driven integral theory of elasticity. A novel formulation of size dependent elastic foundations is here introduced. Notably, the constitutive behavior describing interaction between twisted nanobeams and surrounding media is modeled by spatial convolution driven by the torsional rotation field. It is shown that the governing structural problem is mathematically represented by an integro-differential formulation. An equivalent simpler differential problem is then proven to reduce computational burdens. Exemplar case-studies are finally examined to show efficacy of the developed nonlocal methodology.

Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and F(R,T,Q,Tm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(R,T,Q,T_{m})$$\\end{document} gravity

We extend the anholonomic frame and connection deformation method, AFCDM, for constructing exact and parametric solutions in general relativity, GR, to geometric flow models and modified gravity theories, MGTs, with nontrivial torsion and nonmetricity fields. Following abstract geometric or variational methods, we can derive corresponding systems of nonmetric gravitational and matter field equations which consist of very sophisticate systems of coupled nonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and applying the AFCDM, we prove that such systems of PDEs can be decoupled and integrated in general forms for generic off-diagonal metric structures and generalized affine connections. We generate new classes of quasi-stationary solutions (which do not depend on time like coordinates) and study the physical properties of some physically important examples. Such exact or parametric solutions are determined by nonmetric solitonic distributions and/or ellipsoidal deformations of wormhole hole configurations. It is not possible to describe the thermodynamic properties of such solutions in the framework of the Bekenstein–Hawking paradigm because such metrics do not involve, in general, certain horizons, duality, or holographic configurations. Nevertheless, we can always elaborate on associated Grigori Perelman thermodynamic models elaborated for nonmetric geometric flows. In explicit form, applying the AFCDM, we construct and study the physical implications of new classes of traversable wormhole solutions describing solitonic deformation and dissipation of non-Riemannian geometric objects. Such models with nontrivial gravitational off-diagonal vacuum are important for elaborating models of dark energy and dark matter involving wormhole configurations and solitonic-type structure formation.

Shape Sensing in Plate Structures through Inverse Finite Element Method Enhanced by Multi-Objective Genetic Optimization of Sensor Placement and Strain Pre-Extrapolation.

The real-time reconstruction of the displacement field of a structure from a network of in situ strain sensors is commonly referred to as "shape sensing". The inverse finite element method (iFEM) stands out as a highly effective and promising approach to perform this task. In the current investigation, this technique is employed to monitor different plate structures experiencing flexural and torsional deformation fields. In order to reduce the number of installed sensors and obtain more accurate results, the iFEM is applied in synergy with smoothing element analysis (SEA), which allows the pre-extrapolation of the strain field over the entire structure from a limited number of measurement points. For the SEA extrapolation to be effective for a multitude of load cases, it is necessary to position the strain sensors appropriately. In this study, an innovative sensor placement strategy that relies on a multi-objective genetic algorithm (NSGA-II) is proposed. This approach aims to minimize the root mean square error of the pre-extrapolated strain field across a set of mode shapes for the examined plate structures. The optimized strain reconstruction is subsequently utilized as input for the iFEM technique. Comparisons are drawn between the displacement field reconstructions obtained using the proposed methodology and the conventional iFEM. In order to validate such methodology, two different numerical case studies, one involving a rectangular cantilevered plate and the other encompassing a square plate clamped at the edges, are investigated. For the considered case studies, the results obtained by the proposed approach reveal a significant improvement in the monitoring capabilities over the basic iFEM algorithm with the same number of sensors.

Piezoelectric PZT film-driven resonant torsional MEMS electric field sensor

Piezoelectric PZT film-driven resonant torsional MEMS electric field sensor

Ramified covers of abelian varieties over torsion fields

Abstract We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of ℚ {\mathbb{Q}} . In particular, we prove that every elliptic curve E over ℚ {\mathbb{Q}} has the weak Hilbert property of Corvaja and Zannier both over the maximal abelian extension ℚ ab {\mathbb{Q}^{\rm ab}} of ℚ {\mathbb{Q}} , and over the field ℚ ⁢ ( A tor ) {\mathbb{Q}(A_{\rm tor})} obtained by adjoining to ℚ {\mathbb{Q}} all torsion points of some abelian variety A over ℚ {\mathbb{Q}} .

Axial-lateral-torsional coupling nonlinear vibration of riserless drill-string considering both seawater and stratum parts

Riserless drilling has the obvious advantages of small platform load bearing and short well construction period because it discards the bulky conventional riser. However, because the drill-string is directly exposed to seawater, its dynamic behavior is extremely complex, which has an important impact on the safety and efficiency of drilling operations. Using the energy method and microelement method, an axial-lateral-torsional (ALT) coupling nonlinear vibration model of deepwater riserless drill-string considering both seawater and stratum sections is established. The model takes into account the platform heaving and slow drift motion, wind and ocean current, tidal current, wave load, wellbore contact, bit-rock interaction and seawater formation interaction. A bi-directional coupling scheme is proposed to obtain a good model solving efficiency. Using torsional vibration model results and field test data, the effectiveness of the model is presented in detail from the qualitative and quantitative aspects. The developed model and calculation program are used to analyze the dynamic behavior of a typical deep-water riserless drillings. The work in this paper can provide an effective analysis method and theoretical guidance for riserless drill-string design.

Sources of torsion in Poincarè gauge gravity

We study sources for torsion in Poincarè gauge theory in any dimension, signature, and spin. We find that symmetric kinetic terms for non-Yang–Mills bosonic fields of arbitrary rank drive torsion. Our detailed discussion of spin-3/2 Rarita–Schwinger fields shows that they source all independent parts of the torsion. We develop systematic notation for spin-(2k+1)/2 fields and find the spin tensor for arbitrary k in n ge 2k+1 dimensions. For k>0 there is a novel direct coupling between torsion and spinor fields. We also cast the well-known gauge relation between the canonical and Belinfante–Rosenfield energy tensors in terms of different choices of independent variables.

Reconstructing Torsion Cosmology from Interacting Holographic Dark Energy Model

We consider a cosmological model in the framework of Einstein–Cartan theory with a single scalar torsion ϕ=ϕ(t) and reconstruct the torsion model corresponding to the holographic dark energy (HDE) density. By studying the corresponding relation between the effective energy density of torsion field ρϕ and holographic dark energy density ρHDE, we naturally obtain a kind of torsion field from the interacting holographic dark energy with interaction term Q=−2ϕρm and ρm is the energy density of matter. We analyze the reconstructed torsion model and find that the torsion field behaves like the quintessence (w>−1) or quintom (exhibiting a transition from w>−1 to w<−1) dark energy, depending on the value of the model parameter c. We then perform a stability analysis according to the squared sound speed. It is shown that the model is classically stable in the current epoch for the case of c<1. We also investigate the model from the viewpoint of statefinder parameters and it turns out that the statefinder trajectories in the r−s plane behave differently for the three cases of c and also quite distinct from those of other cosmological models. From the trajectories of the statefinder pair {q,r}, we find that, for all the three cases of c, the universe has a phase transition from deceleration to acceleration, consistently with cosmological observations. In addition, we fit the reconstructed torsion model with the recent Type Ia supernovae (SNe Ia) samples, i.e., the Pantheon sample containing 1048 SNe Ia with the redshift in the range 0.01<z<2.3 and the Pantheon+ sample with 1701 light curves of 1550 distinct SNe Ia in the range 0.001<z<2.26. The analysis results show that the limits on the present fractional energy density of matter Ωm0 are completely compatible with those of the ΛCDM model obtained from the latest Planck mission observations at 68% confidence level. The mean value of c constrained from the Pantheon sample corresponds to the quintom-like scenario (i.e., c<1) and its mean value from the Pantheon+ sample corresponds to the quintessence-like scenario (i.e., c≥1). However, both of the Pantheon and Pantheon+ samples cannot distinguish the quintom-like and quintessence-like scenarios at 68% confidence level.

New black hole solutions with a dynamical traceless nonmetricity tensor in Metric-Affine Gravity

In the framework of Metric-Affine Gravity, the existing correspondence between the Einstein tensor and the energy-momentum tensor of matter provided by General Relativity is extended towards a post-Riemannian description in terms of the torsion and nonmetricity fields, which are sourced by the spin, dilation and shear currents of matter. In this work, we focus on the dynamical role of the traceless part of the nonmetricity tensor and its intrinsic connection with shears, defining a model which encloses a new black hole solution endowed with shear charges. We show that the extension in the presence of dynamical torsion and Weyl vector leads to the broadest family of static and spherically symmetric black hole solutions with spin, dilation and shear charges in Metric-Affine Gravity so far.

Search for Manifestations of Spin–Torsion Coupling

We investigate the axial vector spin–torsion coupling effects in the framework of the Poincaré gauge theory of gravity with the general Yang–Mills type Lagrangian. The dynamical equations for the “electric” and “magnetic” components of the torsion field variable are obtained in the general form and it is shown that the helicity density and the spin density of the electromagnetic field appear as the physical sources. The modified Maxwell’s equations for the electromagnetic field are derived, and the electromagnetic wave propagation under the action of the uniform homogeneous torsion field is considered. We demonstrate the Faraday effect of rotation of the polarization for such a wave and establish the strong bound on the possible cosmic axial torsion field from the astrophysical data.

On affine geometrical structure, generalized of Born–Infeld models and Eddington’s world conjectures

In this work, we give a detailed description and discussion of the dynamic gravitational equations of the model with Lagrangian of the type [Formula: see text] as proposed by Eddington time ago but with [Formula: see text] being a non-Riemannian generalization of the Ricci tensor with the end to find the geometrical origin of the Eddington and Weyl conjectures concerning Lagrangian densities (generalized volume) and natural gauge. The Ricci tensor in our case is particularly based on an affine geometry with a generalized compatibility condition previously proposed in [B. McInnes, On the geometrical interpretation of ‘non-symmetric’ space-time field structures, Class. Quantum Grav. 1 (1984) 105–113; D. J. Cirilo-Lombardo, Non-Riemannian geometry, Born–Infeld models and trace-free gravitational equations, J. High Energy Astrophys. 16 (2017) 1–14]. Specifically, we show that: (i) the geometric action can be taken to a BI-type form considering a totally antisymmetric torsion field, (ii) Weyl’s proposal considering a universal gauge linked to a cosmological constant [Formula: see text] appears in the model naturally due to the proposed affine geometry, (iii) the Eddington conjecture that establishes a relationship between metric and curvature or fundamental tensor with constant of proportionality [Formula: see text] (natural gauge) is geometrically verified in the model with generalized affine geometry.

Torsional periodic lattice distortions and diffraction of twisted 2D materials

Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS2, CrI3, and WSe2/MoSe2.

Torsion Fields Generated by the Quantum Effects of Macro-bodies

We generalize Einstein’s General Relativity (GR) by assuming that all matter (including macro-objects) has quantum effects. An appropriate theory to fulfill this task is Gauge Theory Gravity (GTG) developed by the Cambridge group. GTG is a “spin-torsion” theory, according to which, gravitational effects are described by a pair of gauge fields defined over a flat Minkowski background spacetime. The matter content is completely described by the Dirac spinor field, and the quantum effects of matter are identified as the spin tensor derived from the spinor field. The existence of the spin of matter results in the torsion field defined over spacetime. Torsion field plays the role of Bohmian quantum potential which turns out to be a kind of repulsive force as opposed to the gravitational potential which is attractive. The equivalence principle remains and essential in this theory so that GR is relegated to a locally approximate theory wherein the quantum effects (torsion) are negligible. As a toy model, we assume that the macro matter content can be described by the covariant Dirac equation and apply this theory to the simplest radially symmetric and static gravitational systems. Consequently, by virtue of the cosmological principle, we are led to a static universe model in which the Hubble redshifts arise from the torsion fields.