Torsion Terms Research Articles

Gravity with torsion as deformed BF theory *

We study a family of (possibly non topological) deformations of BF theory for the Lie algebra obtained by quadratic extension of so(3,1) by an orthogonal module. The resulting theory, called quadratically extended General Relativity (qeGR), is shown to be classically equivalent to certain models of gravity with dynamical torsion. The classical equivalence is shown to promote to a stronger notion of equivalence within the Batalin–Vilkovisky formalism. In particular, both Palatini–Cartan gravity and a deformation thereof by a dynamical torsion term, called (quadratic) generalised Holst theory, are recovered from the standard Batalin–Vilkovisky formulation of qeGR by elimination of generalised auxiliary fields.

Quantum cosmology in teleparallel gravity with a boundary term

We quantize a homogeneous and isotropic universe for two models of modified teleparallel gravity: one wherein an arbitrary function of the boundary term, namely B, is present in the action, and in the other model, a scalar field that is non-minimally coupled to both the torsion and boundary term. In this regard, we study exact solutions of both the classical and quantum frameworks by utilizing the corresponding Wheeler–DeWitt (WDW) equations of the models. To correspond to the comprehensive classical and quantum levels, in the second model, we propose an appropriate initial condition for the wave packets and observe that they closely adhere to the classical trajectories and reach their peak. We quantify this correspondence using the de Broglie–Bohm interpretation of quantum mechanics. According to this proposal, the classical and Bohmian trajectories coincide when the quantum potential vanishes along the Bohmian paths. Furthermore, we apply the de-parameterization technique to our model in the realm of the problem of time in quantum cosmological models based on the WDW equation, utilizing the global internal time denoted as χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}, which represents a scalar field.

Quantum Field Theory of Neutrino Mixing in Spacetimes with Torsion

In the framework of quantum field theory, we analyze the neutrino oscillations in the presence of a torsion background. We consider the Einstein–Cartan theory and we study the cases of constant torsion and of linearly time-dependent torsion. We derive new neutrino oscillation formulae which depend on the spin orientation. Indeed, the energy splitting induced by the torsion influences oscillation amplitudes and frequencies. This effect is maximal for values of torsion of the same order of the neutrino masses and for very low momenta, and disappears for large values of torsion. Moreover, neutrino oscillation is inhibited for intensities of torsion term much larger than neutrino masses and momentum. The modifications induced by torsion on the CP-asymmetry are also presented. Future experiments, such as PTOLEMY, which have as a goal the analysis of the cosmological background of neutrino (which have very low momenta), can provide insights into the effect shown here.

Reference frames and black hole thermodynamics

In the context of the absolute parallelism formulation of General Relativity, and because of the fact that the scalar curvature can be written in purely torsional terms, it was known for a long time that a surface term based solely on the torsion tensor appears in the action. It was subsequently suggested that this term might play the role of the Gibbons-Hawking-York boundary term which, in turn, is associated to the free energy in the path integral approach, and then, to the black hole entropy by standard thermodynamic arguments. We show that the identification of the two boundary terms is rather incomplete, and that it strongly depends on the choice of the tetrad (frame) field used to reproduce a given metric. By considering variations of the tetrad field not necessarily subjected to Dirichlet-like conditions on the boundary surface, we find a class of frames adapted to the Schwarzschild spacetime in which the Gibbons-Hawking-York/torsion link is actually established, and conducing to the right black hole entropy without the need of any background subtraction. Remarkably, these frames are also responsible for the correct value of the gravitational energy as computed from the teleparallel energy-momentum pseudo-current.

Generalized strain-based finite element for non-linear stability analysis of beams with thin-walled open cross-section

Based on the generalized strain theory a shear-deformable finite element is developed for nonlinear stability analysis of thin-walled open-section beams in multibody systems. In this formulation a finite number of deformations, characterized as generalized strains, is defined which are related to dual stress resultants in a co-rotational frame. The stiffness formulation is based on a second-order approximation of the local elastic displacement field. Timoshenko’s beam theory and Vlasov’s modified thin-walled beam theory are used to include the shear strain effects due to non-uniform bending and restrained warping torsion and their mutual coupling effects. Axial shortening associated with the Wagner Hypothesis is taken into account such that the nonlinear behaviour of the beam is predicted accurately, especially under large torsion. Coupling between bending and torsional deformation due to non-coincident centroid and shear centre is modelled using a second-order cross-section transformation matrix. Cubic Hermitian polynomials are used as shape functions for the lateral displacements and twist rotation to derive the elastic and geometric stiffness matrices. Geometric nonlinearities associated with axial elongation and bending curvatures are described by additional torsion, bending and warping-related quadratic deformation terms yielding a set of modified deformations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. The accuracy and the computational efficiency of the new beam element is demonstrated in several static and dynamic examples.

Asymptotic behavior of the linear elasticity system with varying and unbounded coefficients in a thin beam

We study the asymptotic behavior of the solutions of the linear elasticity system in a thin beam of small thickness ε>0. The elasticity tensor also varies with ε, and it is assumed to be uniformly elliptic but non-uniformly bounded. Namely, we just impose that its norm in L∞ is an infinitesimal of 1/ε and its norm in L1 is bounded. We obtain an homogenized problem corresponding to a linear system in one dimension. It gives an approximation of the solution of the problem in the thin beam which consists in the sum of a Bernouilli-Navier's deformation plus a torsion term. This limit system provides a general asymptotic model for the behavior of an elastic beam composed by the mixture, at a mesoscopic level, of several materials, and therefore, which does not satisfy any homogeneity and/or isotropy conditions.

Towards a free energy-based elastic network model and its application to the SARS-COV2 binding to ACE2

Classical normal mode analysis (cNMA) is a standard method for studying the equilibrium vibrations of macromolecules. A major limitation of cNMA is that it requires a cumbersome step of energy minimization that also alters the input structure significantly. Variants of normal mode analysis (NMA) exist that perform NMA directly on PDB structures without energy minimization, while maintaining most of the accuracy of cNMA. Spring-based NMA (sbNMA) is such a model. sbNMA uses an all-atom force field as cNMA does, which includes bonded terms such as bond stretching, bond angle bending, torsional, improper, and non-bonded terms such as van der Waals interactions. Electrostatics was not included in sbNMA because it introduced negative spring constants. In this work, we present a way to incorporate most of the electrostatic contributions in normal mode computations, which marks another significant step toward a free-energy-based elastic network model (ENM) for NMA. The vast majority of ENMs are entropy models. One significance of having a free energy-based model for NMA is that it allows one to study the contributions of both entropy and enthalpy. As an application, we apply this model to study the binding stability between SARS-COV2 and angiotensin converting enzyme 2 (or ACE2). Our results show that the stability at the binding interface is contributed nearly equally by hydrophobic interactions and hydrogen bonds.

Parameterization of the miniPEG-Modified γPNA Backbone: Toward Induced γPNA Duplex Dissociation.

γ-Modified peptide nucleic acids (γPNAs) serve as potential therapeutic agents against genetic diseases. Miniature poly(ethylene glycol) (miniPEG) has been reported to increase solubility and binding affinity toward genetic targets, yet details of γPNA structure and dynamics are not understood. Within our work, we parameterized missing torsional and electrostatic terms for the miniPEG substituent on the γ-carbon atom of the γPNA backbone in the CHARMM force field. Microsecond timescale molecular dynamics simulations were carried out on six miniPEG-modified γPNA duplexes from NMR structures (PDB ID: 2KVJ). Three NMR models for the γPNA duplex (PDB ID: 2KVJ) were simulated as a reference for structural and dynamic changes captured for the miniPEG-modified γPNA duplex. Principal component analysis performed on the γPNA backbone atoms identified a single isotropic conformational substate (CS) for the NMR simulations, whereas four anisotropic CSs were identified for the ensemble of miniPEG-modified γPNA simulations. The NMR structures were found to have a 23° helical bend toward the major groove, consistent with our simulated CS structure of 19.0°. However, a significant difference between simulated methyl- and miniPEG-modified γPNAs involved the opportunistic invasion of miniPEG through the minor and major groves. Specifically, hydrogen bond fractional analysis showed that the invasion was particularly prone to affect the second G-C base pair, reducing the Watson-Crick base pair hydrogen bond by 60% over the six simulations, whereas the A-T base pairs decreased by only 20%. Ultimately, the invasion led to base stack reshuffling, where the well-ordered base stacking was reduced to segmented nucleobase stacking interactions. Our 6 μs timescale simulations indicate that duplex dissociation suggests the onset toward γPNA single strands, consistent with the experimental observation of decreased aggregation. To complement the insight of miniPEG-modified γPNA structure and dynamics, the new miniPEG force field parameters allow for further exploration of such modified γPNA single strands as potential therapeutic agents against genetic diseases.

Stability and singularity analysis of the cosmologies with different scenarios for deceleration parameter in the presence of torsion

In the current paper, path deviation equations in absolutely parametric parallel geometries are derived. It is considered as a geodesic deviation equation. Additionally, it is modified by a torsion term. It proposes the deviation path equation that describes the trajectory deviation of a particle under the influence of the gravitational field. To examine the singularity of the Cosmological models, the modified version of the Raychaudhuri equation is utilized. The generalized law of the variation of Hubble's parameter is utilized to achieve some Cosmological models.

Molecular Dynamics Simulation on Tensile Behavior of Cellulose at Different Strain Rates

At present, most high-performance cellulose matrix composites only use cellulose as reinforcement material, which is an obstacle to maximize the advantages of nanocellulose in structure and properties. The development of new functional nanocomposites with cellulose as the main component can better meet people’s needs for high-performance and degradable composites, which requires a comprehensive and thorough understanding of cellulose. Considering the limitations of physical experiments, we performed molecular dynamics simulation of the uniaxial tensile behavior of the cellulose system at three different strain rates (10−4/ps, 10−5/ps, and 10−6/ps), and the stress-strain responses of cellulose systems at different strain rates are obtained. The effect of the strain rate on the mechanical properties of amorphous cellulose system during the tensile processes is analyzed. The deformation mechanism of cellulose amorphous system during the tensile processes is characterized by the energy changes of the different terms including dihedral angle torsion term, bond tensile term, angle bending term, and nonbond term. Structural evolution of the cellulose crystal system during the tensile processes is used to explain the failure mechanism of cellulose. The kinetic simulation results show that the mechanical properties of the cellulose amorphous system increase with the increase of strain rate. Compared with the strain rate of 10−5/ps, the elastic modulus of the system increases by 6.73 GPa at the strain rate 10−4/ps. During the tensile processes, cellulose amorphous region adapts to the applied load mainly through the stretching of the cellulose macromolecular chains, i.e., the deformation of bond lengths and bond angles, without any breakage of the molecular chains. The main causes of chain lengthening at different strain rates are different. The failure of cellulose is caused by the slip and rearrangement of some molecular chains in the crystal structure.

Fermions on curved backgrounds of matrix models

We discuss the propagation of fermions on generic, curved branes in Ishibashi-Kawai-Kitazawa-Tsuchiya-type matrix models. The Dirac operator can be understood either in terms of a Weitzenb\"ock connection, or in terms of the Levi-Civita connection with an extra torsion term. We discuss in detail the coupling of spin to the background geometry using the Jeffreys-Wentzel-Kramers-Brillouin approximation. Despite the absence of local Lorentz invariance in the underlying Ishibashi-Kawai-Kitazawa-Tsuchiya framework, our results agree with the expectations of Einstein-Cartan theory, and differ from general relativity only by an extra coupling to the totally antisymmetric part of the torsion. The case of Friedmann–-Lema\^{\i}tre-–Robertson-–Walker cosmic background solutions is discussed as a special case.

Analysis of cosmic aspects through string-inspired teleparallel gravity models

We consider a generic string inspired gravitational theory in the framework of teleparallel gravity whose stringy action based on a particular function which depends on the scalar field, its kinetic energy, the boundary and torsion terms as well as the Gauss-Bonnet terms We examine some cosmographic parameters like the equation of state parameter (ω tot), plane behavior and their stability with the help of squared speed of sound parameter (v2 s ). Under the choice of some specific values of model parameters, the equation of state parameter ω tot indicates the range of cosmological constant and quintessence region of the evolving universe for the past, present and near future times while phantom phase in the far future times. The phase plane expresses the super accelerated phase (the freezing region) whereas gives the stability of each underlying model in the realm of accelerated universe.

Torsional dark energy

Dark energy from kinetic torsion is discussed. The torsion incorporated in the Einstein–Cartan (EC) Lagrangian is assumed to be totally anti-symmetric, represented by a timelike axial vector [Formula: see text]. The dynamics of torsion is invoked by a novel kinetic term that gives rise to dark energy, while the massive quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing term.

Big Bang Nucleosynthesis Constraints on f (T, TG) Gravity

We confront f(T,TG) gravity, with big bang nucleosynthesis (BBN) requirements. The former is obtained using both the torsion scalar, as well as the teleparallel equivalent of the Gauss–Bonnet term, in the Lagrangian, resulting to modified Friedmann equations in which the extra torsional terms constitute an effective dark energy sector. We calculate the deviations of the freeze-out temperature Tf, caused by the extra torsion terms in comparison to ΛCDM paradigm. Then, we impose five specific f(T,TG) models and extract the constraints on the model parameters in order for the ratio |ΔTf/Tf| to satisfy the observational BBN bound. As we find, in most of the models the involved parameters are bounded in a narrow window around their general relativity values as expected, asin the power-law model, where the exponent n needs to be n≲0.5. Nevertheless, the logarithmic model can easily satisfy the BBN constraints for large regions of the model parameters. This feature should be taken into account in future model building.

Dynamic stability of [formula omitted]-varying non-zero torsion cosmology

This paper aims to study the stability analysis of Friedmann-like spacetime in the presence of torsion through dynamical system techniques. For this purpose, we consider equations of motion which describe the evolution in an isotropic and homogeneous cosmological background with non-vanishing torsion and convert them into the first order autonomous system of differential equations. In order to identify system’s equilibrium points, we implement an ansatz for the torsion term ϕ(t)=λH. Furthermore, within this framework, the cosmological scenario of the varying vacuum is being considered where dark matter interacts with vacuum. We take into account various forms of interaction term to study the effects of linear and non-linear interaction and examine the stability in each case. It is found that these cosmological solutions can describe different evolutionary phases of the universe and behave as stable attractor for the specific values of the parameters. For each case of interaction model, the phase space portraits exhibit the attractive behavior of the universe.

Spherically symmetric vacuum solutions and horizons in covariant f(T) gravity theory

In this paper we study properties that the vacuum must possess in the minimal extension to the teleparallel equivalent of general relativity (TEGR) where the action is supplemented with a quadratic torsion term. No assumption is made about the weakness of the quadratic term although in the weak-field regime the validity of our previously derived perturbative solution is confirmed. Regarding the exact nature of the vacuum, it is found that if the center of symmetry is to be regular, the mathematical conditions on the tetrad at the isotropy point mimic those of general relativity. With respect to horizons it is found that, under very mild assumptions, a smooth horizon cannot exist unless the quadratic torsion coupling, $\alpha$, vanishes, which is the TEGR limit (with the Schwarzschild tetrad as its solution). This analysis is then supplemented with computational work utilizing asymptotically Schwarzschild boundary data. It is verified that in no case studied does a smooth horizon form. For $\alpha > 0$ naked singularities occur which break down the equations of motion before a horizon can form. For $\alpha < 0$ there is a limited range of $\alpha$ where a vacuum horizon might exist but, if present, the horizon is singular. Therefore physically acceptable black hole horizons are problematic in the studied theory at least within the realm of vacuum static spherical symmetry. These results also imply that static spherical matter distributions generally must have extra restrictions on their spatial extent and stress-energy bounds so as to render the vacuum solution invalid in the singular region and make the solutions finite.

Development and Validation of Fluorinated, Aromatic Amino Acid Parameters for Use with the AMBER ff15ipq Protein Force Field.

We developed force field parameters for fluorinated, aromatic amino acids enabling molecular dynamics (MD) simulations of fluorinated proteins. These parameters are tailored to the AMBER ff15ipq protein force field and enable the modeling of 4, 5, 6, and 7F-tryptophan, 3F- and 3,5F-tyrosine, and 4F- or 4-CF3-phenylalanine. The parameters include 181 unique atomic charges derived using the implicitly polarized charge (IPolQ) scheme in the presence of SPC/Eb explicit water molecules and 9 unique bond, angle, or torsion terms. Our simulations of benchmark peptides and proteins maintain expected conformational propensities on the μs time scale. In addition, we have developed an open-source Python program to calculate fluorine relaxation rates from MD simulations. The extracted relaxation rates from protein simulations are in good agreement with experimental values determined by 19F NMR. Collectively, our results illustrate the power and robustness of the IPolQ lineage of force fields for modeling the structure and dynamics of fluorine-containing proteins at the atomic level.

On Nieh-Yan transport

We study nondissipative transport induced by the Nieh-Yan anomaly. After computing the torsional terms in the equilibrium partition function using transgression, we find the constitutive relations for the covariant axial-vector, heat, stress, and spin currents. A number of new transport effects are found, driven by background torsion and the spin chemical potential. Torsional constitutive relations in two-dimensional systems are also analyzed.

The dark side of the torsion: dark energy from propagating torsion

An extension to the Einstein–Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, represented by a time-like axial vector S^mu . The dynamics of torsion is invoked by a novel kinetic term. Here we show that this kinetic term gives rise to dark energy, while the quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing cosmology solution. A constraint on the bouncing solution is calculated using cosmological data from different epochs.

Simultaneous parametrization of torsional and third-neighbor interaction terms in force-field development: The LLS-SC algorithm.

The calibration of torsional interaction terms by fitting relative gas-phase conformational energies against their quantum-mechanical values is a common procedure in force-field development. However, much less attention has been paid to the optimization of third-neighbor nonbonded interaction parameters, despite their strong coupling with the torsions. This article introduces an algorithm termed LLS-SC, aimed at simultaneously parametrizing torsional and third-neighbor interaction terms based on relative conformational energies. It relies on a self-consistent (SC) procedure where each iteration involves a linear least-squares (LLS) regression followed by a geometry optimization of the reference structures. As a proof-of-principle, this method is applied to obtain torsional and third-neighbor interaction parameters for aliphatic chains in the context of the GROMOS 53A6 united-atom force field. The optimized parameter set is compared to the original one, which has been fitted manually against thermodynamic properties for small linear alkanes. The LLS-SC implementation is freely available under http://github.com/mssm-labmmol/profiler.