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We develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver. [ABSTRACT FROM AUTHOR]

The pure rotational and rovibrational spectra of the ν27 –NH2 torsion of cyclopropylamine (CPA) in the far-infrared region were measured with a high-resolution Fourier transform infrared coupled to a synchrotron. The complex spectra reflect the presence of both trans and gauche conformers. Analysis of the pure rotational spectra (34–64 cm−1) yielded accurate rotational and centrifugal distortion constants of the ground and first two torsional excited states of trans-CPA. The fundamental, hot bands and weak overtones were identified and assigned in the 200–550 cm−1 range. Global analysis of over 19 000 transitions provides accurate energy levels of the torsional polyads up to vT = 3. The torsional levels and their rotational constants were in agreement with the theoretical results from quasiadiabatic channel reaction path Hamiltonian (RPH) calculations, emphasizing the need for molecular-specific theoretical treatments for large amplitude motions. Tunneling components of the torsional fundamental of gauche-CPA were assigned based on the RPH results and symmetry considerations, differing from previous experimental and theoretical work. This comprehensive spectroscopic characterization of CPA is crucial for its potential detection in the interstellar medium as a precursor to complex prebiotic molecules, providing essential data for future astronomical searches and advancing our understanding of nitrogen-containing organic molecules in space. [ABSTRACT FROM AUTHOR]

The lack of observational data for the AlO molecule in the mesosphere/lower thermosphere may be due to ablated aluminum reacting quickly to form other species. Previously proposed reaction pathways show that aluminum could be ablated in the atmosphere from meteoritic activity, but there currently exist very limited spectroscopic data on the intermediates in these reactions, limiting the possible detection of said molecules. As such, rovibrational spectroscopic data are computed herein using quartic force field methodology at four different levels of theory for the neutral intermediates AlCO3, OAlO2, and HOAlO2. Each molecule exhibits multiple vibrational modes with large vibrational transition intensities. For instance, the C–O stretch (ν1) in AlCO3 has a harmonic intensity of 536 km mol−1, the Al–O stretch (ν2) in OAlO2 has an intensity of 678 km mol−1, and the out-of-plane torsion (ν9) in HOAlO2 has an intensity of 158 km mol−1. All three molecules have exceptionally large dipole moments of 6.27, 4.21, and 5.04 D, respectively. These properties indicate that all three molecules are good candidates for potential atmospheric observation utilizing vibrational and/or rotational spectroscopic techniques. [ABSTRACT FROM AUTHOR]

A general formulation of the strong coupling between photons confined in a cavity and molecular electronic states is developed for the state-interaction state-average spin-restricted ensemble-referenced Kohn–Sham method. The light–matter interaction is included in the Jaynes–Cummings model, which requires the derivation and implementation of the analytical derivatives of the transition dipole moments between the molecular electronic states. The developed formalism is tested in the simulations of the nonadiabatic dynamics in the polaritonic states resulting from the strong coupling between the cavity photon mode and the ground and excited states of the penta-2,4-dieniminium cation, also known as PSB3. Comparison with the field-free simulations of the excited-state decay dynamics in PSB3 reveals that the light–matter coupling can considerably alter the decay dynamics by increasing the excited state lifetime and hindering photochemically induced torsion about the C=C double bonds of PSB3. The necessity of obtaining analytical transition dipole gradients for the accurate propagation of the dynamics is underlined. [ABSTRACT FROM AUTHOR]

We present a novel approach for systematically exploring the conformational space of small molecules with multiple internal torsions. Identifying unique conformers through a systematic conformational search is important for obtaining accurate thermodynamic functions (e.g., free energy), encompassing contributions from the ensemble of all local minima. Traditional geometry optimizers focus on one structure at a time, lacking transferability from the local potential-energy surface (PES) around a specific minimum to optimize other conformers. In this work, we introduce a physics-driven meta-Gaussian processes (meta-GPs) method that not only enables efficient exploration of target PES for locating local minima but, critically, incorporates physical surrogates that can be applied universally across the optimization of all conformers of the same molecule. Meta-GPs construct surrogate PESs based on the optimization history of prior conformers, dynamically selecting the most suitable prior mean function (representing prior knowledge in Bayesian learning) as a function of the optimization progress. We systematically benchmarked the performance of multiple GP variants for brute-force conformational search of amino acids. Our findings highlight the superior performance of meta-GPs in terms of efficiency, comprehensiveness of conformer discovery, and the distribution of conformers compared to conventional non-surrogate optimizers and other non-meta-GPs. Furthermore, we demonstrate that by concurrently optimizing, training GPs on the fly, and learning PESs, meta-GPs exhibit the capacity to generate high-quality PESs in the torsional space without extensive training data. This represents a promising avenue for physics-based transfer learning via meta-GPs with adaptive priors in exploring torsional conformer space. [ABSTRACT FROM AUTHOR]

The formulation of the hybrid‐Trefftz stress element for plate bending is extended to the modelling of concentrated forces and moments, either as prescribed loads or as reactions at point supports. As the bending, torsion and shear fields are hypersingular, the flexibility matrix of the element involves the use of the finite part integration concept. In addition, it requires the confirmation of the positive‐definiteness of the flexibility under gross shape distortion. The tests illustrate the modelling of applied concentrated forces and moments and also the combination of boundary layer and point reaction effects. The results obtained are validated using converged solutions obtained with a stress‐based hybrid‐mixed element (HMS) and a displacement‐based mixed element (MITC). [ABSTRACT FROM AUTHOR]

Taking two cacti species as source of bioinspiration and tubular metamaterials are developed and studied under torsion. A flower-like cross section and a void distribution are the two bioinspired characteristics used for the design of tubular metamaterials. The geometrical parameters that define the two bioinspired characteristics are identified. Changes in torsional stiffness due to varying these parameters are studied using finite element simulations. The shape of the tubular metamaterials cross section had a larger influence on their torsional stiffness compared to the void distribution. Results presented could serve as a guide for the design of tubular metamaterials with tuned torsional stiffness. [ABSTRACT FROM AUTHOR]

A new approach namely Plate-Beam theory was employed to perform the investigation into the lateral torsional buckling (LTB) performance of high strength steel (HSS) rectangular hollow section (RHS) beam-columns. Firstly, the total strain energy corresponding to the LTB failure mode of the beam-columns was established, and then the equilibrium differential equation was developed, through the variation of energy functional. Based on the Plate-Beam theory, the equivalent restrained torsional rigidity (warpage constant) that can simultaneously accounted for the secondary warping effect was derived, and the formulation process did not involve any sectoral coordinate operation. The deducing process of the total strain energy of RHS beam-columns was further discussed and recommended to describe the torsion performance of composite and irregular thin-walled members. Based on the FE program verified against test data and theoretical solution, the accuracy of the provisions of HSS RHS beam-columns given in Eurocode3 and GB50017-2017 was assessed. The comparison of numerical program against codified design provisions revealed that the resistance prediction in Eurocode3 was still serviceable for HSS RHS beam-columns, in conjunction with the torsional rigidity according to the Plate-Beam theory. [ABSTRACT FROM AUTHOR]

The design of the torsion-loaded toroidal shell segment with two functionally graded carbon nanotube-reinforced composite (FG-CNTRC) coatings and the corrugated core is presented. Round and trapezoidal shapes of the corrugated core are considered. A homogenization model for the corrugated core is applied to predict the stiffnesses of the corrugated core. The total potential energy equation, according to the Donnell shell theory, is established. The Ritz energy method is applied to determine the expressions of the buckling and postbuckling responses. The numerical investigations present the significantly beneficial effects of FG-CNTRC coatings and corrugated core on the buckling responses of the shells. [ABSTRACT FROM AUTHOR]

Signal beam combiners play a pivotal role in enhancing the output power of fiber lasers, which have wide-ranging applications from industrial processing to medical and military uses. This paper explores the influence of fiber twist angle and non-uniform symmetric arrangement on the performance of 19 × 1 fiber signal combiners. A simulation model was developed to analyze the impact of these parameters under adiabatic tapering conditions and the principle of brightness conservation. The model allowed for a systematic investigation of how varying twist angles and non-uniform spacings affect the combiner's performance metrics, such as transmission efficiency and beam quality. The study found that an optimal balance between high transmission efficiency (up to 98.5%) and good beam quality (minimum M2 factor of 1.06) can be achieved when the twist angle is kept below 60° and the non-uniform spacing is maintained within 10–30 μm. These conditions ensure minimal degradation of the beam quality while maximizing the transmission efficiency of the combiner. These findings offer valuable insights into the optimization of signal combiner design, which is critical for advancing high-power fiber laser systems. By carefully controlling the fiber twist angle and non-uniform spacing, designers can achieve superior performance in fiber laser applications, thereby enhancing the overall efficiency and reliability of these systems. This research contributes to the broader field of optical engineering by providing a deeper understanding of the underlying principles that govern the performance of signal combiners. [ABSTRACT FROM AUTHOR]

Over the past decade, the physics literature on torsionful non-relativistic gravity has burgeoned; more recently, philosophers have also begun to explore this topic. As of yet, however, the connections between the writings of physicists and philosophers on torsionful non-relativistic gravity remain unclear. In this article, we seek to bridge the gap, in particular by situating within the context of the existing physics literature a recent theory of non-relativistic torsionful gravity developed by philosophers Meskhidze and Weatherall (Philos Sci, , 2023) we also discuss the philosophical significance of that theory. [ABSTRACT FROM AUTHOR]

This study investigates the influence of various transverse reinforcement configurations on the torsional performance of glass fiber reinforced plastic (GFRP) reinforced concrete beams. A comprehensive experimental investigation includes five specimens, each characterized by unique transverse reinforcement designs in terms of stirrup spacing and inclination angles. The implementation of transverse torsional reinforcements within the beams exhibited a remarkable post-cracking hardening response, contributing to enhanced strength recovery. The experimental findings are subsequently compared with a reliable three-dimensional finite element model developed using the ABAQUS software. Finally, a parametric study is conducted to examine the influence of concrete and GFRP bar strength, along with longitudinal and transverse reinforcement ratios, on the torsional behavior of GFRP reinforced concrete beams. The results emphasize the significant impact of concrete tensile strength and transverse reinforcement on the cracking torque, while the parameters related to longitudinal reinforcement have only marginal effects. [ABSTRACT FROM AUTHOR]

Teleparallel gravity, an empirically equivalent counterpart to general relativity, represents the influence of gravity using torsional forces. It raises questions about theory interpretation and underdetermination. To better understand the torsional forces of teleparallel gravity, we consider a context in which forces are better understood: classical spacetimes. We propose a method of incorporating torsion into the classical spacetime context that yields a classical theory of gravity with a closed temporal metric and spacetime torsion. We then prove a result analogous to the Trautman degeometrization theorem: that every model of Newton–Cartan theory gives rise, non-uniquely, to a model of this theory. [ABSTRACT FROM AUTHOR]

We define a congruence module Ψ A (M) associated to a surjective O -algebra morphism λ : A → O , with O a discrete valuation ring, A a complete noetherian local O -algebra regular at p , the kernel of λ , and M a finitely generated A -module. We establish a numerical criterion for M to have a free direct summand over A of positive rank. It is in terms of the lengths of Ψ A (M) and the torsion part of p / p 2 . It generalizes results of Wiles, Lenstra, and Diamond, that deal with the case when the codimension of p is zero. Number theoretic applications include integral (non-minimal) R = T theorems in situations of positive defect conditional on certain standard conjectures. Here R is a deformation ring parametrizing certain Galois representations and T is a Hecke algebra. An example of a positive defect situation is that of proving modularity lifting for 2-dimensional ℓ -adic Galois representations over an imaginary quadratic field. The proofs combine our commutative algebra results with a generalization due to Calegari and Geraghty of the patching method of Wiles and Taylor–Wiles and level raising arguments that go back to Ribet. The results provide new evidence in favor of the intriguing, and as yet fledgling, torsion analog of the classical Langlands correspondence. We also prove unconditional integral R = T results for Hecke algebras T acting on weight one cohomology of Shimura curves over ℚ. This leads to a torsion Jacquet–Langlands correspondence comparing integral Hecke algebras acting on weight one cohomology of Shimura curves and modular curves. In this case the cohomology has abundant torsion and so our correspondence cannot be deduced by means of the classical Jacquet–Langlands correspondence. [ABSTRACT FROM AUTHOR]

In this paper a porous fluid-saturated cylinder subjected to a finite twist deformation is analyzed. The material of the skeleton of the porous cylinder is hyperelastic of Ogden-type and assumed nearly incompressible. The twist is applied to the cylinder in a fast rate so that the fluid pressure develops in the pores of the cylinder. The main objective of this paper is to study the stresses and the fluid pressure in the cylinder over a short period of time after the twist has been applied, or to study the initial response. The analytical expressions for the stress components and the fluid pressure are derived for Ogden material with arbitrary material parameters. The quantitative picture for the stress state is given and the signs of the normal stresses are explained. The stress arising in some imaginary fibers that were initially parallel to the axis of the cylinder is obtained. The present problem is similar to the torsion problem of a totally incompressible and nonporous cylinder in a sense that the total stresses are identical in both problems. But decomposition of the total stresses into the fluid pressure and the effective stresses, which is specific for the fluid-saturated body, can be found only using the present analysis. [ABSTRACT FROM AUTHOR]

We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the normaliser and centraliser structure of these. For toral subgroups, we give an effective classification algorithm. For non-toral elementary abelian subgroups, we focus on algebraic groups of exceptional type with a view to future applications, and in this case we provide tables explicitly describing the subgroups and their local structure. We then describe how to transfer results to the corresponding finite groups of Lie type using the Lang-Steinberg Theorem; this will be used in forthcoming work to complete the classification of elementary abelian p-subgroups for torsion primes p in finite groups of exceptional Lie type. Such classification results are important for determining the maximal p-local subgroups and p-radical subgroups, both of which play a crucial role in modular representation theory. [ABSTRACT FROM AUTHOR]

This study focused on evaluating the confinement requirements for glass fiber–reinforced polymer (GFRP) reinforcement in circular reinforced concrete (RC) columns subjected to seismic forces, including torsional effects. Seven large-scale GFRP-RC columns were tested under axial and quasi-static cyclic lateral loading. The test parameters included torsion-to-bending moment ratio (tm) and transverse reinforcement spacing and configuration (spiral and hoops). The experimental results revealed that introducing torsion to the loading scheme reduced the lateral load resistance and drift capacity of the columns. The study recommends adopting a spiral pitch equal to one-sixth of the effective core diameter, as per the Canadian provisions for FRP-RC structures. This spiral pitch significantly enhanced peak lateral load, torque, drift, and twist capacities while ensuring column stability at high drift ratios and preventing complex modes of failure under seismic loading, including torsion. The GFRP spirally reinforced columns consistently surpassed the drift threshold requirements specified by the Canadian provisions for FRP-RC structures. In contrast, hoop-reinforced columns failed at lower drifts, with a notable lap-splice failure observed in columns under tm of 0.4. It was concluded that using GFRP hoops with a lap splice length of 40 times the bar diameter is inadequate for columns subjected to seismic conditions with torsional effects. [ABSTRACT FROM AUTHOR]

The fine aggregate matrix (FAM), consisting of asphalt binder, mineral filler, fine aggregate, and air voids, plays a major role in the mechanistic response of asphalt mixtures. The behavior of FAM is significantly affected by multiple factors including fine aggregate gradation, asphalt binder type, mineralogical type of the fine aggregate, test temperature, and aging. In this study, three asphalt binders, six fine aggregate gradations, two mineralogical types of fine aggregate, and one field aging effect were considered to prepare FAM samples. A modified multiple stress creep recovery (MSCR) test was used to investigate the high temperature viscoelastic behavior of FAMs by using the torsion bar fixture of a dynamic shear rheometer (DSR), and an appropriate range of creep stress loading in the MSCR test for FAMs was controlled within 1.2 kPa to 25.6 kPa. The results showed that the F-AC13 specimen had the strongest stress sensitivity, especially at the phase of large creep stress. The F-AC20 and F-SUP20 specimens had excellent high temperature viscoelastic performance. The viscoelastic properties of the FAMs were consistent with the properties of their asphalt binder. The FAMs with fine basalt aggregate had better deformation resistance, and the FAMs with fine limestone aggregate had better elastic recovery. The nonrecoverable creep compliance Jnr values of the FAM specimens had more sensitivity to the temperature change, and the percentage recovery %R values increased slightly with increasing temperature. After field aging, the FAM specimens had better deformation resistance and worse elastic recovery. A multifactor analysis of variance (ANOVA) was selected to comprehensively evaluate the significance of these influence factors on the FAM performance. The fine aggregate gradation, asphalt binder, and creep stress had significant effects on the viscoelastic behavior of FAMs. Therefore, improvement of the asphalt binder and fine aggregate gradation can directly enhance the performance of FAMs. The applied creep stress was also a critical condition of the MSCR test for the measurement of FAM performance. [ABSTRACT FROM AUTHOR]

In the presence of spacetime torsion, the momentum components do not commute; therefore, in quantum field theory, summation over the momentum eigenvalues will replace integration over the momentum. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin, the separation between the eigenvalues increases with the magnitude of the momentum. Consequently, this replacement regularizes divergent integrals in Feynman diagrams with loops by turning them into convergent sums. In this article, we apply torsional regularization to the self-energy of a charged lepton in quantum electrodynamics. We show that torsion eliminates the ultraviolet divergence of the standard self-energy. We also show that the infrared divergence is absent. In the end, we calculate the finite bare masses of the electron, muon, and tau lepton: 0.4329 MeV , 90.95 MeV , and 1543 MeV , respectively. These values constitute about 85% of the observed, re-normalized masses. [ABSTRACT FROM AUTHOR]

In this paper, the accurate free vibration characteristics of thin-walled box beam are discussed and the kinematic model is established by using fine shear deformation theory. The model adopts the in-plane and out-of-plane displacement fields including extension, torsion, warping and distortion, as well as the transverse shear due to bending and warping due to torsion. One-dimensional high-order beam theory is applied to the dynamic solution of thin-walled box beam, and the analytical solution of high free vibration modes of multi-deformation coupled modes under different boundary conditions is derived. The results show that warping, distortion and shear deformation play an important role in the free vibration characteristics of thin-walled box beam, and the validity of the model is verified. In addition, finite element software (ANSYS) is used for finite element simulation. The application of vibration mode in the structure design of thin-walled box beam is summarized, especially in the case of higher natural frequency. The calculation method is in good agreement with the finite element results. [ABSTRACT FROM AUTHOR]

Although the mechanisms of molluscan shell growth have been studied using mathematical models, little is known about the molecular basis underpinning shell morphogenesis. Here, we performed Wnt activation experiments to elucidate the potential roles of Wnt signaling in the shell growth of Lymnaea stagnalis. In general, we observed following three types of shell malformations in both dose- and developmental stage-dependent manners: (i) cap-shaped shell, (ii) cap-shaped shell with hydropic soft tissues, and (iii) compressed shell with a smaller number of coiling. We analyzed the morphologies of these malformed shells using the growing tube model, revealing that the compressed malformations show significantly larger values for T (torsion), with no significant changes in the values for the remaining parameters E (expansion) and C (curvature). We also found that cap-shaped malformations have significantly larger values for E, suggesting that the effects of BIO on shell formation may change during growth. Since the changes in T and/or E parameter values can greatly alter the shell morphologies from a planispiral or a cap-shaped one to various three-dimensional helices, changes in shell developmental processes possibly controlled by Wnt signaling may account for at least a part of the evolution of diverse shell forms in molluscs. [ABSTRACT FROM AUTHOR]

Although the mechanisms of molluscan shell growth have been studied using mathematical models, little is known about the molecular basis underpinning shell morphogenesis. Here, we performed Wnt activation experiments to elucidate the potential roles of Wnt signaling in the shell growth of Lymnaea stagnalis. In general, we observed following three types of shell malformations in both dose- and developmental stage-dependent manners: (i) cap-shaped shell, (ii) cap-shaped shell with hydropic soft tissues, and (iii) compressed shell with a smaller number of coiling. We analyzed the morphologies of these malformed shells using the growing tube model, revealing that the compressed malformations show significantly larger values for T (torsion), with no significant changes in the values for the remaining parameters E (expansion) and C (curvature). We also found that cap-shaped malformations have significantly larger values for E, suggesting that the effects of BIO on shell formation may change during growth. Since the changes in T and/or E parameter values can greatly alter the shell morphologies from a planispiral or a cap-shaped one to various three-dimensional helices, changes in shell developmental processes possibly controlled by Wnt signaling may account for at least a part of the evolution of diverse shell forms in molluscs. [ABSTRACT FROM AUTHOR]

Thin-walled channel beams such as cold-formed steel purlins are primarily used to withstand wind forces in the roofing and walling systems of buildings. Traditionally, these types of members are usually designed for bending moments, with the effects of torsion ignored. However, the loading on thin-walled channels can be much more complicated than simple bending actions. Because of the position of the shear centre outside the section, channels can undergo bending and torsion when subjected to vertical load on the top flange. The applied torsion may cause significant stresses in the channel, which may need to be accounted for in design. There appears to be no research on quantifying the effects of torsion on thin-walled channels subjected to a uniformly distributed load acting on the top flange. In this paper, a theoretical solution is derived for calculating the longitudinal stresses in thin-walled channels subjected to torsion caused by a uniformly distributed load acting on the top flange. The theory is validated by modelling the channels in a finite-element analysis. The theoretical results include calculations of the twist rotation, bimoment, sectorial coordinate and longitudinal stresses, while the results from the finite-element analysis include the twist rotation and longitudinal stresses. The results show that the longitudinal stresses caused by torsion can significantly exceed those caused by the bending moment. Practical advice is also given for engineers on how to minimize torsion in cold-formed steel purlins. [ABSTRACT FROM AUTHOR]

In this study, we explore the sweeping surfaces in Euclidean 3-space, utilizing the modified orthogonal frames with non-zero curvature and torsion, which allows us to consider the spine curves even if their second differentiations vanish. If the curvature of the spine curve of a sweeping surface has discrete zero points, the Frenet frame might undergo a discontinuous change in orientation. Therefore, the conventional parametrization with the Frenet frame of such a surface cannot be given. Thus, we introduce two types of modified sweeping surfaces by considering two types of spine curves; the first one's curvature is not identically zero and the second one's torsion is not identically zero. Then, we determine the criteria for classifying the coordinate curves of these two types of modified sweeping surfaces as geodesic, asymptotic, or curvature lines. Additionally, we delve into determining criteria for the modified sweeping surfaces to be minimal, developable, or Weingarten. Through our analysis, we aim to clarify the characteristics defining these surfaces. We present graphical representations of sample modified sweeping surfaces to enhance understanding and provide concrete examples that showcase their properties. [ABSTRACT FROM AUTHOR]

Let K be a non-cyclotomic imaginary quadratic field with class number 1 and E / K an elliptic curve with E (K) [ 2 ] ≃ ℤ / 2 ℤ ⊕ ℤ / 2 ℤ. In this paper, we determine the torsion groups that can arise as E (L) tor where L is any quadratic extension of K. [ABSTRACT FROM AUTHOR]

We give a practical method to compute the 2-torsion subgroup of the Jacobian of a non-hyperelliptic curve of genus 3, 4 or 5. The method is based on the correspondence between the 2-torsion subgroup and the theta hyperplanes to the curve. The correspondence is used to explicitly write down a zero-dimensional scheme whose points correspond to elements of the 2-torsion subgroup. Using p-adic or complex approximations (obtained via Hensel lifting or homotopy continuation and Newton–Raphson) and lattice reduction we are then able to determine the points of our zero-dimensional scheme and hence the 2-torsion points. We demonstrate the practicality of our method by computing the 2-torsion of the modular Jacobians J 0 (N) for N = 4 2 , 5 5 , 6 3 , 7 2 , 7 5. As a result of this we are able to verify the generalized Ogg conjecture for these values. [ABSTRACT FROM AUTHOR]

In this paper we define the delocalized L2-analytic torsion form and the delocalized L2-combinatorial torsion form. By using the method of Bismut-Goette, under the conditions of positive Novikov-Shubin invariants, nontrivial finite conjugacy class and the existence of a family of fiberwise Morse functions whose gradient fields satisfy the Thom-Smale transversality condition in every fiber, we prove the Cheeger-Müller type relation between the delocalized L2-analytic torsion form and the delocalized L2-combinatorial torsion form. [ABSTRACT FROM AUTHOR]

Copyright of Revista de Cirugia is the property of Sociedad de Cirujanos de Chile and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Materialwissenschaft und Werkstoffechnik is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We know that all automorphism α of an injective module D can be extended to an automorphism of any module N which embedded D as a submodule. We say then that α satisfies the extension property in the category of module. Extending an automorphism in a given category is both interesting and a difficult problem to solve. However in the category of groups, Schupp [10] proved that only inner automorphisms have the extension property. Ben Yakoub [5], in the category of algebras, has found an automorphism which is not inner but satisfies the extension property. Abdelalim et al. [1–3] solved this problem in a category of mixed modules over a bounded factorization domain, in the category of free modules over an integral domain, and in a category of torsion modules over a unique factorization domain. One of the issues that we think is important is this. What happens to the results of the extension property, if we weaken the conditions on the ring of scalars while widening the category of mixed modules? Let A be an integral Domain. Let M ′ be a free A-module and T a torsion A-module such that ⋂ a ∈ A ∗ a T = { 0 T } . We give a necessary and sufficient condition such that an automorphism α of M = M ′ ⊕ T satisfies the extension property. [ABSTRACT FROM AUTHOR]

Copyright of Cotton Textile Technology is the property of Cotton Textile Technology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We construct sphere fibrations over (n−1)$(n-1)$‐connected 2n$2n$‐manifolds such that the total space is a connected sum of sphere products. More precisely, for n$n$ even, we construct fibrations Sn−1→#k−1(Sn×S2n−1)→Mk$S^{n-1} \rightarrow \#^{k-1}(S^n \times S^{2n-1}) \rightarrow M_k$, where Mk$M_k$ is a (n−1)$(n-1)$‐connected 2n$2n$‐dimensional Poincaré duality complex that satisfies Hn(Mk)≅Zk$H_n(M_k)\cong {\mathbb {Z}}^k$, in a localised category of spaces. The construction of the fibration is proved for k⩾2$k\geqslant 2$, where the prime 2, and the primes that occur as torsion in π2n−1(Sn)$\pi _{2n-1}(S^n)$ are inverted. In specific cases, by either assuming n$n$ is small, or assuming k$k$ is large we can reduce the number of primes that need to be inverted. Integral results are obtained for n=2$n=2$ or 4, and if k$k$ is bigger than the number of cyclic summands in the stable stem πn−1s$\pi _{n-1}^s$, we obtain results after inverting 2. Finally, we prove some applications for fibrations over N#Mk$N\# M_k$, and for looped configuration spaces. [ABSTRACT FROM AUTHOR]

The release of ground stress brought on by overlying excavation poses a significant threat to regular tunnel operation, especially when the foundation pit intersects the tunnel inclination, and the torsional deformation of the tunnel also needs to be considered. Based on the foundation pit intersecting with the subway tunnel at an angle, the U-shaped soil reinforcing (USR) technique was introduced to limit the tunnel heave produced by overlying excavation. The Topcon MS05A automated monitoring system was used to track the following: (1) the evolution of the tunnel heave over time and space; (2) the convergent deformation of the cross section; and (3) the torsional deformation. The reinforcement efficiency of the USR method was assessed with numerical simulations, and the effect of intersection angles and reinforcement dimensions on the deformation of the underlying tunnel was further discussed. In addition, an optimal design was suggested for the USR method that considers cost. Tunnel deformation utilizing the USR method was reduced by 63.40%, and the maximum heave was observed to be merely 6.5 mm. The influence zone on the tunnel by overlying excavation was up to 2.5 times the excavation widths, and the tunnel always produced clockwise rotation. Backfilling generates significant and sharp distortion, so the backfilling speed must be carefully controlled. The foundation pit spanning the tunnel at a small angle caused a bigger heave and torsion of the tunnel, which should be avoided. The proposed optimization approach can determine the cost based on the tunnel deformation control criteria. This study provided a valuable reference for the protection of adjacent excavations of subway tunnels in deep sandy strata. [ABSTRACT FROM AUTHOR]

Background: Polymers in practical applications often face diverse torsional loads, such as polymeric gears, couplings, scaffolds, etc. Meanwhile, additive manufacturing enables the creation of intricate geometries for specific needs and its application to fabricate various component parts has grown exponentially. Nevertheless, research on cyclic and reversed cyclic torsional loading of additively-manufactured polymers is very limited. Objective: Mechanical characterization of monotonic, cyclic, and reversed cyclic torsion in polylactic acid (PLA), PLA Premium, and PLA Tough materials. Methods: Specimens were 3D-printed with a 0° build orientation using an extrusion technique and two infill orientation angles (± 45° and 0°/90°). Specimens were subjected to underwent monotonic, cyclic, and reversed cyclic torsion until failure. Results: Regardless of material type, ductile fracture governed the behavior under monotonic loading and brittle failure under cyclic and reversed cyclic loadings. Specimens with a ± 45° infill orientation outperformed their 0°/90° counterparts across all materials, with PLA Premium exhibiting superior performance compared to PLA and PLA Tough. Importantly, it was demonstrated that the previously-proposed multilinear idealized shear stress-shear strain curve, developed for monotonic loading of 15 different polymers, also applies to the envelope curves of cyclic and reversed cyclic loading in PLA-based polymers. Thus, it is useful as material model input for numerical simulation purposes. [ABSTRACT FROM AUTHOR]

Ultrahigh-performance concrete (UHPC) is a type of concrete that has gained attention from researchers for its potential use in various structural applications to improve the behavior of concrete structures. Despite this interest, there are limited experimental test results available on how the ratio of stirrups and the dosage of steel fibers affect the torsional behavior of UHPC beams. This study presents an experimental investigation and theoretical prediction of torque capacity (UHPC) of beams with different ratios of stirrups and dosages of steel fibers under pure torsion. One normal-strength concrete (NSC) beam and 10 UHPC beams with 150×200-mm cross sections were tested. The experimental parameters were the dosages of steel fibers (1% and 2%) and the spacings of the stirrups of 0.0, 50,100, 150, and 200 mm. Including the UHPC high tensile strength and volume fraction of steel fibers, an expression for cracking and ultimate torques of UHPC was proposed and verified. Results showed that the UHPC beams have brittle failure modes compared to NSC beams. Results demonstrated that the UHPC beams showed higher initial cracking and ultimate torsional moments than the NSC beam. The additional steel fibers enhance the torsional properties, and this improvement was linearly at the effective stirrup's ratio higher than 0.25%. The 1% or higher steel fiber dosage was confirmed to be enough to substitute the missing strength of the stirrups. Results of previous research and the suggested cracking and ultimate torque equations of UHPC agreed with the experimental results. [ABSTRACT FROM AUTHOR]

Beam-column joints' behavior is a key research focus due to their critical role in maintaining structural integrity and safety during earthquakes. While concentric joints have been extensively studied, eccentric joints, where beams' centerlines deviate from columns' centerlines, remain relatively unexplored. Beam-column joints exhibit more complex behavior, experiencing a significantly higher shear force (approximately six-fold that of a column), along with flexural moments and normal forces. The joint's eccentricity introduces a torsional moment that amplifies shear stress, and the beam is subjected to an out-of-plane moment (around one-sixth of the primary moment). The out-of-plane moment reduces the joint's resistance mechanism by reducing the confinement provided by beams. To examine the influence of beam eccentricity on the ductility, strength, and failure mechanism of beam-column joints, comprehensive nonlinear finite element (FE) analyses were conducted utilizing experimental eccentric beam-column joints, followed by meticulous validation of the developed model. The models employed incompatible mode mesh element and energy-based models for the concrete material behavior, utilizing an explicit solver. The models were used to examine the impact of various geometric parameters, boundary conditions, and axial load levels on behaviors (global and local) of the beam-column joint subassemblies. The examined geometric parameters encompass aspect ratios of joint and column for both joint types (exterior and interior). Joint behaviors were observed to be significantly influenced by the boundary conditions of the column. Furthermore, the aspect ratio of the joint, representing the beam-to-column depth ratio, played a predominant role in determining the joint failure mechanism by limiting their ability to develop beam hinges. Increasing the aspect ratio of the column had a modest effect on the joint's shear strength but improved the joint subassemblies' ductile behavior, despite increasing the joint's torsional moment. Higher column axial load levels increased the joint's shear strength and led to a shift in cracking patterns from diagonal to vertical. Interestingly, the study found that interior joints experienced higher out-of-plane moments. Exterior and interior joints maintained a level of approximately 62.5 % as a ratio between their shear strength across all models. Moreover, it was observed that yielding of joint stirrups correlated with a shear distortion angle of approximately 0.5 × 10 − 2 rad. Restrictions of ACI provisions on the aspect ratio of the joint seem to be conservative for eccentric interior joints. On the other side, the ACI provisions might overestimate eccentric exterior joint shear strengths as the aspect ratio exceeds unity. [ABSTRACT FROM AUTHOR]

In this study, a general method is developed for the torsional vibration of non-circular-shaped nanorods with varying boundary conditions using second-order strain gradient theory. In most of the studies in the literature, the cross section of the rods is considered to be circular. The reason for this is that the use of warping function is inevitable when the cross section geometry is not circular. For circular cross sections after torsion, the warping is very small and is considered to be non-existent. For non-circular sections, cross section warping should be taken into account in mathematical calculations. The cross section geometry is different from circular in this study, and the boundary conditions are not rigid, contrary to most studies in the literature. In this paper, the second-order strain gradient theory and the most general solution method are discussed. In some specific cases, it is possible to transform the problem into many studies found in the literature. The correctness of the algorithm is tested by comparing the resulting solutions with closed solutions found in the literature. The influence of some variables on the torsional frequencies is illustrated by a series of graphical figures, and the superiority of the applied method is summarized. [ABSTRACT FROM AUTHOR]

The characterization of automorphisms having the extension property in the category of modules is an open problem. In earlier works (Abdelalim et al. in: Springer proceedings in mathematics and statistics, vol 311, pp 313–323, 2020, Abdelalim et al. in Discuss Math-Gen Algebra Appl 43, 2023), the authors solved this problem in the category of direct sum of cyclic torsion-free modules over a BFD and in the category of a direct finite sum of cyclic modules with torsion over a UFD. It is natural to see what happens in other categories. In this paper, we extend the result in Abdelalim et al. (Discuss Math-Gen Algebra Appl 43, 2023) to the category of a direct infinite sum of cyclic modules over a BFD with torsions. Let A be a bounded factorization domain (BFD). Consider a direct infinite sum M of cyclic modules over A such that the torsion part of M is a proper submodule of M and let α be an automorphism of M. We give a necessary and sufficient condition such that α satisfies the extension property. [ABSTRACT FROM AUTHOR]

Cellular covers which originate in homotopy theory are considered here for a very special class: divisible uniserial modules over valuation domains. This is a continuation of the study of cellular covers of divisible objects, but in order to obtain more substantial results, we are restricting our attention further to specific covers or to specific kernels. In particular, for h-divisible uniserial modules, we deal first with covers limited to divisible torsion-free modules (Section 3), and continue with the restriction to torsion standard uniserials (Sections 4–5). For divisible non-standard uniserial modules, only those cellular covers are investigated whose kernels are also divisible non-standard uniserials (Section 6). The results are specific enough to enable us to describe more accurately how to find all cellular covers obeying the chosen restrictions. [ABSTRACT FROM AUTHOR]

Silicene has very good electronic properties and has important applications in the field of microelectronics. The effects of torsional deformation on the structural, electronic and optical properties of B absorbed silicene system are studied by using density functional theory based on the first-principles. The binding energy of the adsorption system under different torsion angles was calculated, and the stability of the system was analyzed. After analyzing the energy band structure, it is found that the band gap of silicene can be adjusted by changing the twist angle. The twist angle affects the amount of electron transfer that occurs between the B-Si bonds. The optical properties of the torsion-adsorption system were studied, including dielectric function, absorption coefficient and reflectivity. The distortion has obvious effects on the absorption spectrum and reflection spectrum, and improves the light transmittance of silicene. [ABSTRACT FROM AUTHOR]

Under earthquake excitations, reinforced concrete (RC) columns could be subjected to lateral drift reversals and a combination of axial forces, bending moments, and torsional effects. This paper investigates the behavior of glass fiber-reinforced polymer (GFRP)-RC columns under seismic-simulated loading, including torsion, which has not been studied previously. Seven large-scale circular GFRP-RC column-footing connections were cast and tested under various combined reversed cyclic loading configurations to examine the effects of torsion-bending moment ratio (tm), transverse reinforcement ratio, and concrete compressive strength. The test results revealed that increasing the tm reduced the lateral load capacity and deformability of the GFRP-RC column, but resulted in a more symmetric torque-twist relationship. Increasing the transverse reinforcement ratio mitigated core damage and provided additional support (for example, spiral turns) for torsion-induced tensile stresses. Moreover, increased concrete compressive strength bolstered torque capacity and torsional stiffness, while, under a tm of 0.4, it resulted in decreased twist capacity. When torsion was present, increasing the concrete compressive strength had an insignificant impact on the bending-shear response, differing from findings for GFRP-RC columns subjected to seismic loading without torsion. [ABSTRACT FROM AUTHOR]

Reinforced concrete (RC) bridge columns often encounter complex combinations of loads, including flexural, axial, shear, and torsional forces, during seismic events, especially in the presence of geometric irregularities such as skewed or curved bridges, unequal spans, or varying column heights. Corrosion-related deterioration in RC structures spurred the adoption of glass fiber-reinforced polymer (GFRP) as a promising alternative to steel reinforcement. This study experimentally investigates the performance of GFRP-RC circular columns under cyclic loading, including torsion with different torsion-to-bending moment ratios (tm and longitudinal reinforcement ratios. The results showed that, with the same reinforcement ratios, the addition of torsion to cyclic bending and shear significantly altered the behavior of the GFRP-RC column in terms of mode of failure, load resistance, drift capacity, and energy dissipation. The inelastic deformability hinge shifted upward with increased tm. Higher tm accelerated stiffness degradation, while increasing the longitudinal reinforcement ratio enhanced lateral load, drift, and twist capacities. [ABSTRACT FROM AUTHOR]

Let G(q) be a twisted or untwisted finite exceptional group of Lie type over GF (q) , either adjoint or simply connected, and let W be the Weyl group of G(q). This paper compiles an extensive data set on the maximal tori of G(q). A systematic labeling is given, via the corresponding conjugacy classes of W, together with a complete list of the structures of the maximal tori in terms of their torsion coefficient decomposition. Additionally the associated admissible graphs and the structure or shape of centralizers of elements in W are given as well as compatible computer files. Also various apparent inconsistencies in the current literature on simply connected groups are discussed and resolved. [ABSTRACT FROM AUTHOR]

This paper proposes a new model for anisotropic compact stars with quintessence in Rastall teleparallel gravity via embedding approach. In the gravity, the acquired field equations encompassing the anisotropic matter source as well as the quintessence field are studied using the specific character of the scalar torsion T for the observed stars candidates PSRJ 1416–2230, 4U 1608–52, CenX–3, EXO 1785–248 and SMC X–1. All of the stellar structures under consideration are said to be advantageously independent of any central singularity and are stable. A thorough graphical analysis reveals that numerous physical properties critical for forming stellar structures are satisfied. [ABSTRACT FROM AUTHOR]

This research work studies a problem associated with an axisymmetric torsion of an orthotropic layer by a circular rigid disc at the midplane. The orthotropic layer is sandwiched by two identical orthotropic half-spaces with two interfaced cracks. The layer and half-spaces are dissimilar in nature. The mixed boundary value problem is reduced to a system of dual integral equations by Hankel transformation, which are converted to Fredholm integral equations of the second kind. The integral equations are solved numerically by the quadrature rule. The stress intensity factors for crack and disc have been derived and are presented graphically for different thicknesses of orthotropic layer. [ABSTRACT FROM AUTHOR]

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Background: The clinical value of myocardial torsion quantification in prognostic assessment and risk stratification of various cardiovascular diseases is gradually being recognized. However, normal values of left and right ventricular (LV and RV) torsion and torsion rates (TRs) have not been fully determined, and their correlation with age and gender has not been well studied. Purpose: To establish normal ranges of biventricular torsion, peak systolic and diastolic TRs using magnetic resonance feature tracking (MR‐FT) technique based on a large sample of healthy adults, and further investigate their relationship with age and gender. Study Type: Retrospective. Population: 566 Healthy adults (312 males, aged 43 ± 10 years; 254 females, aged 43 ± 11 years). Field Strength/Sequence: 1.5T/gradient echo. Assessment: Biventricular torsion, peak systolic, and diastolic TRs. Statistical Tests: Shapiro–Wilk test, Student's t‐test, Mann–Whitney‐U test, linear regression, intraclass correlation coefficient, Bland–Altman analysis. Differences were regarded as statistically significant at P < 0.05. Results: Women demonstrated greater magnitudes of left ventricle (LV) torsion (1.23 ± 0.44 vs. 1.00 ± 0.42°/cm), peak systolic TR (9.69 ± 3.70 vs. 8.27 ± 3.73°/cm*sec), peak diastolic TR (−7.78 ± 2.82 vs. −6.06 ± 2.44°/cm*sec), and RV torsion (2.20 ± 1.23 vs. 1.65 ± 1.11°/cm*sec), peak systolic TR (16.07 ± 8.18 vs. 12.62 ± 7.08°/cm*sec), peak diastolic TR (−15.39 ± 6.53 vs. −11.70 ± 6.03°/cm*sec). For both genders, the magnitudes of LV and RV torsion, peak systolic, and diastolic TRs increased linearly with age. All the measurements of biventricular torsion, peak systolic and diastolic TRs achieved good to excellent intraobserver and interobserver reproducibility, with all intraclass correlation coefficients >0.70. Data Conclusion: The present study systematically provided age‐ and sex‐stratified reference values for LV and RV torsion and TRs using MR‐FT technique. Women and aging are associated with greater magnitudes of biventricular torsion, peak systolic, and diastolic TRs. Level of Evidence: 3 Technical Efficacy: Stage 2 [ABSTRACT FROM AUTHOR]

We analyze the orbits of a unit mass body in a background Reissner–Nordstr o ¨ m (RN) black hole in d = (3 + 1) from the perspectives of Geometric Torsion (GT) modified gravity theory in (4 + 1) dimensional bulk. A 4-form flux in bulk GT theory in d = (4 + 1) has been shown to ensure a mass dipole correction to the (3 + 1) dimensional gravity theory by Gupta, Kar and Rang recently. We argue that the dipole correction contributes topologically to the known exact geometries in General Theory of Relativity (GTR). Furthermore, the topological correction has been identified with non-Newtonian potential underlying a B 2 ∧ F 2 coupling term to Einstein–Hilbert action. The winding numbers ensured by the BF coupling to d = (3 + 1) action in the framework presumably provide a clue towards a tunneling instanton in theory. [ABSTRACT FROM AUTHOR]

The geometric trinity of gravity comprises three distinct formulations of general relativity: (i) the standard formulation describing gravity in terms of spacetime curvature, (ii) the teleparallel equivalent of general relativity describing gravity in terms of spacetime torsion, and (iii) the symmetric teleparallel equivalent of general relativity (STEGR) describing gravity in terms of spacetime non-metricity. In this article, we complete a geometric trinity of non-relativistic gravity, by (a) taking the non-relativistic limit of STEGR to determine its non-relativistic analogue, and (b) demonstrating that this non-metric theory is equivalent to Newton–Cartan theory and its teleparallel equivalent, i.e., the curvature and the torsion based non-relativistic theories that are both geometrised versions of classical Newtonian gravity. [ABSTRACT FROM AUTHOR]

This paper deals with the study of torsional energy (total squared torsion) at infinitesimal bending of curves and knots in three dimensional Euclidean space. During bending, the curve is subject to change, and its properties are changed. The effect that deformation has on the curve is measured by variations. Here, we observe the infinitesimal bending of the second order and variations of the first and the second order that occur in this occasion. The subjects of study are curves and knots, in particular torus knots. We analyze various examples both analytically and graphically, using our own calculation and visualization software tool. [ABSTRACT FROM AUTHOR]