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Modern wind turbines are often supported by tubular steel towers made from globally conical, locally cylindrical shells with relatively large diameter-to-thickness ratios—approximately between 100 and 300—which enables the tower material to be used as efficiently as possible. Wind turbine towers face complex loading resulting from both environmental and operational load cases and are sensitive to geometrical imperfections that inevitably arise during the fabrication process. Whereas bending often controls at the base of turbine towers, the upper sections are controlled by combined bending and torsion. Although extensive studies have been conducted on the stability and design of cylinders subjected to isolated actions, investigations into the structural response of thin-walled cylinders under combined actions, such as bending and torsion, remain limited. To address this knowledge gap, an experimental program was carried out to study the structural behavior of thin-walled steel cylinders under combined bending and torsion. A total of 48 cylinders were tested with varying diameter-to-thickness ratios and torsion-to-moment ratios found in wind turbine towers. To gain insights into the imperfection sensitivity of these tests, a laser scanner was used to measure the geometric imperfections of each specimen before testing. The test setup, instrumentation, loading procedures and structural response of the cylinders, including ultimate resistances, load-deformation characteristics, and failure modes, are reported. The primary objective of this study is to provide benchmark test data for the validation of numerical models and the development of advanced design methodologies, such as reference resistance design (RRD), for cylindrical shells under combined bending and torsion. Future work will involve formulating guidelines for using laser-scanned data to evaluate geometric imperfections, developing laboratory- and full-scale wind turbine tower finite element models, and ultimately providing improved design guidance on combined bending and torsion. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical stability analysis by considering the torsion field ϕ 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, Λ 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 Λ CDM era with the best fit value of interaction strength and coupling constant for dust and radiation. [ABSTRACT FROM AUTHOR]

We introduce the notion of conformal trajectories in three-dimensional Riemannian manifolds M 3 . Given a conformal vector field V ∈ (M 3) , a conformal trajectory of V is a regular curve γ in M 3 satisfying ∇ γ ′ γ ′ = q V × γ ′ , for some fixed nonzero constant q ∈ ℝ. In this paper, we study the conformal trajectories in the space forms ℝ 3 , 3 and ℍ 3 . For (non-Killing) conformal vector fields in 3 (respectively, in ℍ 3 ), we prove that conformal trajectories have constant curvature and its torsion is a linear combination of trigonometric (respectively, hyperbolic) functions on the arc-length parameter. In the case of Euclidean space ℝ 3 , we obtain the same result for the radial vector field and characterizing all conformal trajectories. [ABSTRACT FROM AUTHOR]

We prove two results on geometric consequences of the representation of restricted holonomy group of a Hermitian connection. The first result concerns when such a Hermitian manifold is Kähler in terms of the torsion and the irreducibility of the holonomy action. As a consequence we obtain a criterion of when a Hermitian manifold (and connection) is a generalized Calabi–Yau (in the sense that the first Ricci vanishes or equivalently that the restricted holonomy is inside SU (m) ). The second result concerns when a compact Kähler manifold with a generic restricted holonomy group is projective, under some nonnegativity assumptions in terms of the Ricci and other curvatures. [ABSTRACT FROM AUTHOR]

Observations of a high spin selectivity in various helical structures, which is called the chirality-induced spin selectivity, suggest a common mechanism originating from the helical geometry. In this paper, we consider a helical chain of atomic p± orbitals having the tangential angular momentum l = ±1. We show in this model that the coupling of l and the spin gives rise to spin-velocity locking, i.e., directions of spin and group velocity are parallel or antiparallel depending on the chirality of the helix, and consequently, an almost perfect spin selectivity in a specific energy region in a wide range of the curvature and the torsion of the helix. We find that the present spin-velocity locking originates from the helical symmetry in which the Hamiltonian is invariant with respect to a combined operation of the rotation around the helix axis and the translation along the helix axis. Therefore, we expect that spin-velocity locking occurs in a wide variety of helical structures. [ABSTRACT FROM AUTHOR]

The curvature causes a variation in the deflection of the outer and inner sides. The effect of curvature was investigated by casting and testing two specimens with the same section – one straight and the other horizontally curved continuous box girder. ABAQUS software was used to numerically model the box girder in order to verify the model and investigate additional parameters. Numerical modeling is successful with less effort, cost, and time because good results are obtained. The effect of the span-to-depth ratio, the compressive strength of concrete, and the percentage of stirrup steel reinforcement was studied numerically. Increasing the height, compressive strength, and percentage of stirrup steel led to a significant increase in load capacity and stiffness. The load capacity in the curved specimen decreased by 11% compared to the straight one due to the effect of torsional moments. A mathematical model was proposed based on the theory of strut-and-tie modeling (STM), where the span was divided into several panels, the effect of torsion was added, and then the results were compared with the traditional sectional method according to ACI and CEB-FIB. For the straight specimen, the sectional ACI, CEB-FIB, and STM methods were used, which gave theoretical results less than the experimental by 31, 48 and 13%, respectively. For the curved specimen, to get closer to reality, the sectional and STM methods were modified by adding the effect of torsion, and the results were less than the experimental tests by 43, 61 and 22%, respectively.

Abstract Maize is the most grown feed crop in the United States. Due to wind storms and other factors, 5% of maize falls over annually. The longitudinal shear modulus of maize stalk tissues is currently unreported and may have a significant influence on stalk failure. To better understand the causes of this phenomenon, maize stalk material properties need to be measured so that they can be used as material constants in computational models that provide detailed analysis of maize stalk failure. This study reports longitudinal shear modulus of maize stalk tissue through repeated torsion testing of dry and fully mature maize stalks. Measurements were focused on the two tissues found in maize stalks: the hard outer rind and the soft inner pith. Uncertainty analysis and comparison of multiple methodologies indicated that all measurements are subject to low error and bias. The results of this study will allow researchers to better understand maize stalk failure modes through computational modeling. This will allow researchers to prevent annual maize loss through later studies. This study also provides a methodology that could be used or adapted in the measurement of tissues from other plants such as sorghum, sugarcane, etc.

Abstract Background Control of humeral torsion can present a challenge, especially intraoperatively during closed reduction and fixation of humeral shaft fractures or 2-part surgical neck fractures of the proximal humerus. The objective of this study is to develop and validate an indirect method for the assessment of humeral torsion using an index that is linearly correlated with rotational arm position and can be derived from only a single plain radiographic image of the proximal humerus. Methods The Humeral Head Offset Index (HHOI) is calculated as the ratio of the medial and lateral offset of the humeral head measured from the outer cortices of the shaft on a plain radiographic or fluoroscopic image. The relationship of HHOI with humeral torsion was first verified on a sawbone model with radiopaque characteristics under fluoroscopic control. Different degrees of retroversion were simulated through manual rotation of the humerus with a digital protractor in 5° increments until 40° internally rotated and then in 5° increments until 40° externally rotated from the neutral position. The same procedure was subsequently performed digitally on Digitally Reconstructed Radiographs (DRRs) from computed tomography (CT) dataset of the sawbone. Next, the HHOI index was applied to eight randomly selected patients with total humerus CT using the same method. Spearman’s rho was calculated for the bivariate analysis of correlation between the simulated degree of retroversion and the HHOI. Strength of correlation was classified according to Koo and Li. Interrater and intrarater reliability of three blinded observers with repetition of measurement after three months were analyzed by assessing the intraclass correlation coefficient (ICC). Results Both in the sawbone model and in DRRs, we demonstrated a high to very high significant linear correlation between simulated retroversion and the HHOI. ICC values demonstrated excellent interrater reliability and excellent intrarater reliability for measurement of the HHOI. Conclusions The HHOI is a new, simple, reliable index that has a linear relationship to the rotation of the humerus and can therefore allow an indirect control of humeral torsion in comparison to the contralateral side.

Background: Torsion of the right middle lobe following right upper lobectomy is a rare but potentially fatal complication. To prevent this, fixation of the right middle lobe has been suggested. This study was performed to examine the impact of right middle lobe fixation on postoperative outcomes and bronchial changes. Methods: We enrolled patients who underwent curative-intent video-assisted thoracic surgery (VATS) right upper lobectomy for lung cancer from 2019 to 2022. Participants were grouped based on whether they did or did not receive right middle lobe fixation. Bronchial angles were measured using preoperative and postoperative chest computed tomography images, and postoperative outcomes and bronchial changes were compared between the 2 groups. Results: The study included a total of 50 patients, with 17 (34%) undergoing right middle lobe fixation. All procedures were performed using VATS. No significant differences between groups were observed in preoperative characteristics or postoperative outcomes. After surgery, both groups exhibited a significant increase in the right bronchus intermedius angle and a significant decrease in the branch angle. The postoperative right bronchus intermedius angle was significantly larger in the group without right middle lobe fixation compared to the group with fixation (47.38°±10.98° vs. 39.41°±9.21°, p=0.014). Three cases of atelectasis occurred in the group that did not undergo fixation while no cases were observed in the fixation group; however, this difference was not statistically significant. Conclusion: Fixation of the right middle lobe reduced postoperative angulation of the right bronchus intermedius, which may help prevent postoperative atelectasis.

The spatial rigidity and strength of precast multi-story buildings are largely determined by the rigidity of the shear bonds connecting the vertical load-bearing reinforced concrete structures. When a horizontal load is applied in asymmetrical in-plan load-bearing systems of multi-story buildings, torsion occurs. In vertical shear bonds, especially those located furthest from the center of rigidity, a torque appears. This article presents the results of experimental studies of welded joints of precast buildings under the action of shear and torsion. The research study has been conducted using full-scale samples of shear bonds. The samples have been loaded with a static load vertical shear force and horizontal torsion moment. Various loading conditions are considered. Deformation diagrams of shear bonds were obtained. The limit state of a welded joint under shear and shear with torsion is described. The obtained experimental data on the rigidity of shear connections can be used in mathematical models for determining the stress-strain state of load-bearing systems of panel multi-story buildings.

Wandering spleen is a rare condition in children that is often caused by the loss or weakening of the splenic ligaments. Its clinical presentation is variable; 64% of children with wandering spleen have splenic torsion as a complication. A 13-year-old boy who had been showing abdominal pain in the hypogastric region accompanied by vomit and an enormous tumefaction in the suprapubic region came to our observation. Considering the ovoid morphology at ultrasound exam, the echostructure and the marked reduction of parenchymal vascularization, suspicion for torsion of an ectopic spleen arose. Ultrasound evaluation has a primary role in the diagnosis of a suspected wandering spleen and, to avoid potentially life-threatening complications, immediate surgery is often times required.

Let n = p r be a prime power ideal of F q [ T ] with r ≥ 2 . We study the rational torsion subgroup T (p r) of the Drinfeld modular Jacobian J 0 (p r) . We prove that the prime-to- q (q - 1) part of T (p r) is equal to that of the rational cuspidal divisor class group C (p r) of the Drinfeld modular curve X 0 (p r) . As we completely computed the structure of C (p r) , it also determines the structure of the prime-to- q (q - 1) part of T (p r) . [ABSTRACT FROM AUTHOR]

A 17‐year‐old patient with acute testicular pain had no blood flow observed on scrotal ultrasound Doppler on either side, suggestive of bilateral torsion. The patient underwent immediate scrotal surgical exploration, and a numerical anomaly was observed during surgery—there were two testicles on each side, and all four exhibited torsion. After detorsion, circulation was recovered, and three of four testicles were kept. One dystrophic testis was removed. [ABSTRACT FROM AUTHOR]

Silver selenide (Ag2Se) flexible films are promising near‐room‐temperature thermoelectric candidates for low‐grade heat harvesting. However, existing Ag2Se films are generally attached on substrates, which impedes further flexibility improvement of the films and constrains the scenarios of applications. Here a cost‐effective and scalable strategy is presented, which combines screen printing and annealing, for synthesizing freestanding Ag2Se inorganic films with different densities of pores. High‐density pores and thin thickness endow the films with high flexibility, while films with low‐density pores obtain higher power factor. Furthermore, by utilizing the porous microstructure, a composite structure consisting of a Ag2Se conductive network and an organic polydimethylsiloxane (PDMS) skeleton is fabricated, which further improves films’ stability under bending and torsion. Finally, a flexible thermoelectric generator comprising five Ag2Se/PDMS legs and encapsulated PDMS outputs a voltage of 20.2 mV and a maximum power of 810 nW (the corresponding power density is 5.4 W m−2) at a temperature difference of 30 K, verifying potential application at near room temperature. This work offers a useful paradigm for fabricating substrate‐free Ag2Se porous films with high flexibility for near‐room‐temperature thermoelectric applications. [ABSTRACT FROM AUTHOR]

Highlights In this paper, a universal mechanical model for the torsional behavior of fiber bundle was established, grounded in the principles of spatial geometry and continuum mechanics, incorporating differential geometry formulas. The model was validated through self‐designed experimental equipment and finite element simulations using Ansys Workbench, showing strong agreement between predicted torsional fracture behavior and experimental results. The study further examined the contributions of fiber bending, torsion, and tension to the overall torque, revealing that torsion plays the dominant role. Additionally, the effect of filament count on the torsional performance of fiber bundles was analyzed, demonstrating that while the number of fibers significantly influences stress distribution, its impact on overall torque is minimal. A universal mechanical model for fiber bundle torsional is proposed. High consistency between simulation and experimental results. Examined filament count effect on torsional strength. More filaments reduce stress concentration, improving performance. [ABSTRACT FROM AUTHOR]

The subject of KCC theory is a second‐order ordinary differential equation, it is sometimes difficult to convert the high dimensional system into an equivalent second‐order system because of the analytical requirements of KCC theory. By means of the Euler‐Lagrange extension of a flow on a Riemannian manifold, this paper gives five geometric invariants of some three‐dimensional systems with great convenience, and focus on the analysis of two of them. The results show that the hyperbolic equilibria corresponding to the seven standard forms of three‐dimensional linear systems are Jacobi unstable. This is completely different from what we got before in two‐dimensional systems, where Jacobi stable and Jacobi unstable correspond to focus and node, respectively. All equilibria of classical Lü chaotic system and Yang‐Chen chaotic system are Jacobi unstable. Meanwhile, in three‐dimensional linear case, the torsion tensors at any point of the trajectory are identically equal to zero, but the two nonlinear systems have nonzero torsion tensors components. [ABSTRACT FROM AUTHOR]

The technology of manufacturing aluminum alloy workpieces using additive friction stir deposition (AFS‐D) has been thoroughly investigated. The ambiguous influence of deformation processing modes on the material density was found. Examination of the microstructure in the central zone of the specimens reveals the absence of microdefects typically associated with workpieces obtained through casting or powder metallurgy methods. It has been observed that the distribution of microhardness is significantly affected by the direction of specimen construction, with approximately a 20% difference in values between the periphery and the central part of the specimen. Specimens produced using the AFS‐D method exhibit a homogeneous microstructure characteristic of deformable aluminum alloys. Notably, a uniform distribution of intermetallides on the specimen surface has been identified. This outcome is likely a result of the alloy undergoing recrystallization during the severe plastic deformation process, leading to the formation of an ultradisperse structure. It is important to emphasize that the selection of technological parameters for AFS‐D should consider not only the magnitude of pressure and deformation but also the deformation speed. [ABSTRACT FROM AUTHOR]

Previous studies have compared the use of the Slocum- jig to the deformity reduction device (DRD) jig for the correction of distal femoral deformities of varying degrees in the frontal plane. The objective of the current study is to further investigate the use of the mini DRD jig in comparison to the Slocum jig for correction of varying degrees of torsional deformities of the distal femur. Femoral models (n = 60) were developed based on a CT scan of an approximately 16.5 kg normal canine femur. Models were created with a standard varus deformity of 15 degrees, and external torsional deformities of 15, 20, or 30 degrees. Using center of rotation of angulation (CORA) methodology, corrective osteotomies were planned and performed on each of the 3D printed models based on the group assigned. Modeling clay was applied the proximal femur to mimic visualization of a routine lateral surgical approach, while retaining the ability to palpate surgical landmarks. Post-correction anatomic lateral distal femoral angle (aLDFA) and femoral torsion angle (FTA) were measured and recorded. The mean post-correction FTA of groups using the DRD jig for correction were consistently closer to the ideal value compared to those using the Slocum jig, although these differences were not always statistically significant. Correction of external torsion between the DRD jig and the Slocum jig was significantly different in groups 1 and 2 (P = 0.026 and P = 0.046), but not in group 3. For the correction of varus deformity, no significant difference was found between the two jig types in any group. Results of this study suggest jig selection during distal femoral osteotomy for correction of torsional deformity may result in varying precision of post-correction alignment. Clinical significance of this variance remains unclear, and intra-operative visual assessment of alignment should be implemented to guide corrections. [ABSTRACT FROM AUTHOR]

Previous models of circular ring segment joints have been inadequate in describing their loading capacity due to the lack of consideration for the interaction between shear force and bending moment. Consequently, these models have led to over‐ or underestimation of the joints' capacity. The increasing use of dry joint connection technology in wind turbine towers and prefabricated segmental bridge constructions necessitates the development of advanced computational models for these connections. This study presents a new model that considers the effects of bending moment, shear force, and torsion on the loading capacity of circular ring segment joints. Numerical simulations were conducted to validate the developed model under different load combinations, and the results demonstrate excellent agreement between the model predictions and numerical simulations. [ABSTRACT FROM AUTHOR]

AbstractWe provide necessary and/or sufficient conditions for the stable Hom functors to be finitely presented. When the covariant Hom functor modulo projectives is finitely presented, its defect is isomorphic to the Bass torsion of the fixed argument. When the contravariant Hom functor modulo injectives is finitely presented, its defect is isomorphic to the cotorsion of the fixed argument. We also give a sufficient condition for the sub-stabilization of the tensor product to be finitely presented. A finite presentation of the tensor product leads to an unexpected application to injective modules. [ABSTRACT FROM AUTHOR]

The fiber-reinforced polymer (FRP) strengthening of reinforced concrete (RC) elements with torsional deficiencies has not yet been extensively studied. Existing studies have primarily focused on rectangular RC beams. The few studies on L or T-shaped beams have used open-form retrofitting methods. However, premature debonding of the retrofitting from concrete surfaces often leads to detachment before achieving enhanced torsional capacity. This study introduces an innovative application of closed-form FRP retrofitting for RC T-beams against torsion. Two novel closed-form torsional upgrading methods were proposed and investigated through a comprehensive experimental program involving eight large-scale T-beams. One method employs FRP ropes embedded in transverse grooves near the surface, while the other combines U-shaped EB-FRP strips with FRP ropes. Additionally, two configurations were examined replicating scenarios where the upper part of the slab is accessible or inaccessible. The results demonstrate that the closed-form methods improve torsional strength by 9% to 25% and twist at failure by 92% to 536% compared to unstrengthened beams, with beams retrofitting through the slab exhibiting superior performance. Step-by-step technical guidelines of the proposed methods are presented to minimize construction defects and ensure effective implementation in real RC structures. [ABSTRACT FROM AUTHOR]

In this study, high-pressure torsion (HPT) processing is applied to the as-cast Al0.5CoCrFeNi high-entropy alloy (HEA) for 1, 3, and 5 turns. Microstructural observations reveal a significant refinement of the second phase after HPT processing. This refinement effect is influenced by the number of processing turns and the distance of the processing position from the center. As the number of processing turns or the distance of the processing position from the center increases, the fragmentation effect on the second phase becomes more pronounced. The hardness of the alloy is greatly enhanced after HPT processing, but there is an upper limit to this enhancement. After increasing the number of processing turns to 5, the increase in hardness at the edge becomes less significant, while the overall hardness becomes more uniform. Additionally, the strength of the processed alloy is significantly enhanced, while its ductility undergoes a noticeable decrease. With an increase in the number of processing turns, the second phase is further refined, resulting in improvement of strength and ductility. [ABSTRACT FROM AUTHOR]

In this paper, we have presented bulk viscous cosmological model of the universe in the modified gravity in which the Lagrangian of the gravitational action contains a general function F (T) , where T denotes torsion, for flat Friedmann–Robertson–Walker spacetime with isotropic fluid. We have studied cosmological solution in F (T) theory of gravity, especially of a particular preference F (T) = T + f (T) = (1 + γ) T + α T 2 , where γ and α are coupling constants, in the presence of bulk viscosity described by Eckart theory, Truncated Israel Stewart theory and Full Israel Stewart theory. The physical and geometrical prospectives of the models in Eckart, Truncated Israel Stewart theory and Full Israel Stewart theory are deliberated in details. The investigation of the variation of bulk viscous pressure, energy density, scale factor, Hubble parameter and deceleration parameter with cosmic growth is furnished in the relevant theories. The models are analyzed by comparison with recent observational data. The cosmological models are well-matched with observations. [ABSTRACT FROM AUTHOR]

The subgroup G ≤ A is absolute direct summand (ADS) if, for every G -high subgroup H ≤ A (i.e. maximal with respect to the property G ∩ H = 0), we have A = G ⊕ H , and A itself is an ADS group if all of its summands inherit this property. In this paper, we characterize the structure of ADS abelian groups, which can be defined as groups such that members of the decomposition into two direct summands are mutually injective. In particular, an ADS abelian group is either divisible, or a direct sum of an indecomposable torsion-free group and a divisible torsion group, or a torsion group such that each p -component is a direct sum of cyclic p -groups of the same length or of Prüfer groups. [ABSTRACT FROM AUTHOR]

Let Λ be a finite-dimensional algebra over a field. We describe how Buan and Marsh’s τ-exceptional sequences can be used to give a “brick labeling” of a certain poset of wide subcategories of finitely generated Λ-modules. When Λ is representation-directed, we prove that there exists a total order on the set of bricks which makes this into an EL-labeling. Motivated by the connection between classical exceptional sequences and noncrossing partitions, we then turn toward the study of (well-separated) completely semidistributive lattices. Such lattices come equipped with a bijection between their completely join-irreducible and completely meet-irreducible elements, known as rowmotion or the “κ-map.” Generalizing known results for finite semidistributive lattices, we show that the κ-map determines exactly when a set of completely join-irreducible elements forms a “canonical join representation.” A consequence is that the corresponding “canonical join complex” is a flag simplicial complex, as has been shown for finite semidistributive lattices and lattices of torsion classes. Finally, we demonstrate how Jasso’s τ-tilting reduction of finite-dimensional algebras can be encoded using the κ-map. We use this to define κd-exceptional sequences for finite semidistributive lattices. These are distinguished sequences of completely join-irreducible elements which we prove specialize to τ-exceptional sequences in the algebra setting. [ABSTRACT FROM AUTHOR]

In the present study, twinning-induced plasticity (TWIP) steels with varying grain size and distribution were obtained by adjusting the thermomechanical methods such as pre-torsion, pre-strain and heat treatment. The advantage of gradient structure design over traditional grain refinement lies in its ability to optimize material strength while reducing ductility loss. Furthermore, the hydrogen embrittlement (HE) behavior of TWIP steels with various grain sizes and distributions was investigated under in-situ hydrogen charging conditions. The results revealed that the gradient structural specimen with finer equiaxed grains in the edge region exhibited lower lattice distortion, fewer stress concentration points and delayed plastic deformation. This decelerated the initiation and propagation of cracks, thus optimizing HE resistance and demonstrating comprehensive mechanical properties superior to all the other investigated specimens in the hydrogen environment. [Display omitted] • Quasi in-situ observation of deformation characteristics. • Gradient design can make steels have superior comprehensive mechanical properties. • Gradient structural materials exhibit the good HE resistance. • In-situ hydrogen charging is more likely to cause HE vs hydrogen pre-charging. • Grain refinement can improve HE resistance. [ABSTRACT FROM AUTHOR]

This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it N -bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the N -bein behaves like a 'square root' of the quantum geometric tensor. Using it, we present a quantum geometric tensor of two states that measures the possibility of moving from one state to another after two consecutive parameter variations. This new tensor determines the commutativity of such variations through its anti-symmetric part. In addition, we define a connection different from the Berry connection, and combining it with the N -bein allows us to introduce a notion of torsion and curvature à la Cartan that satisfies the Bianchi identities. Moreover, the torsion coincides with the anti-symmetric part of the two-state quantum geometric tensor previously mentioned, and thus, it is related to the commutativity of the parameter variations. We also describe our formalism using differential forms and discuss the possible physical interpretations of the new geometrical objects. Furthermore, we define different gauge invariants constructed from the geometrical quantities introduced in this work, resulting in new physical observables. Finally, we present two examples to illustrate these concepts: a harmonic oscillator and a generalized oscillator, both immersed in an electric field. We found that the new tensors quantify correlations between quantum states that were unavailable by other methods. [ABSTRACT FROM AUTHOR]

Background: Control of humeral torsion can present a challenge, especially intraoperatively during closed reduction and fixation of humeral shaft fractures or 2-part surgical neck fractures of the proximal humerus. The objective of this study is to develop and validate an indirect method for the assessment of humeral torsion using an index that is linearly correlated with rotational arm position and can be derived from only a single plain radiographic image of the proximal humerus. Methods: The Humeral Head Offset Index (HHOI) is calculated as the ratio of the medial and lateral offset of the humeral head measured from the outer cortices of the shaft on a plain radiographic or fluoroscopic image. The relationship of HHOI with humeral torsion was first verified on a sawbone model with radiopaque characteristics under fluoroscopic control. Different degrees of retroversion were simulated through manual rotation of the humerus with a digital protractor in 5° increments until 40° internally rotated and then in 5° increments until 40° externally rotated from the neutral position. The same procedure was subsequently performed digitally on Digitally Reconstructed Radiographs (DRRs) from computed tomography (CT) dataset of the sawbone. Next, the HHOI index was applied to eight randomly selected patients with total humerus CT using the same method. Spearman's rho was calculated for the bivariate analysis of correlation between the simulated degree of retroversion and the HHOI. Strength of correlation was classified according to Koo and Li. Interrater and intrarater reliability of three blinded observers with repetition of measurement after three months were analyzed by assessing the intraclass correlation coefficient (ICC). Results: Both in the sawbone model and in DRRs, we demonstrated a high to very high significant linear correlation between simulated retroversion and the HHOI. ICC values demonstrated excellent interrater reliability and excellent intrarater reliability for measurement of the HHOI. Conclusions: The HHOI is a new, simple, reliable index that has a linear relationship to the rotation of the humerus and can therefore allow an indirect control of humeral torsion in comparison to the contralateral side. [ABSTRACT FROM AUTHOR]

Cosmological reconstruction is a powerful technique in modified gravity invented to find the analogy of different cosmological epochs in modified gravity. In this paper, I present the modified holographic reconstruction scheme for f(T,풯 ) theory of gravity where T and 풯 are the torsion scalar and trace of energy–momentum tensor in the context of flat FRW universe. For this reconstruction, I consider Hubble horizon as an infrared cutoff and focus on a particular model f(T,풯 ) = T + γg(풯 ) (a correction to the teleparallel action depending on the matter content). Within this framework, I consider both the power law scale factor as well as the well-established cosmological bouncing scenario. Further, I explore various gravitational Lagrangians that can be reconstructed to yield analytical solution for symmetric, superbounce, oscillatory, singular bounce and matter bounce settings. The viability of these reconstructed models is then assessed through the EoS parameter ωDE and the ωDE − ωDE′ plane (ωDE′ = dωDE dln a ). Notably, all the results align well with recent observational data. [ABSTRACT FROM AUTHOR]

A module over a ring R is pure projective provided it is isomorphic to a direct summand of a direct sum of finitely presented modules. We develop tools for the classification of pure projective modules over commutative noetherian rings. In particular, for a fixed finitely presented module M, we consider Add ⁡ ( M ) {\operatorname{Add}(M)} , which consists of direct summands of direct sums of copies of M. We are primarily interested in the case where R is a one-dimensional, local domain, and in torsion-free (or Cohen–Macaulay) modules. We show that, even in this case, Add ⁡ ( M ) {\operatorname{Add}(M)} can have an abundance of modules that are not direct sums of finitely generated ones. Our work is based on the fact that such infinitely generated direct summands are all determined by finitely generated data. Namely, idempotent/trace ideals of the endomorphism ring of M and finitely generated projective modules modulo such idempotent ideals. This allows us to extend the classical theory developed to study the behaviour of direct sum decomposition of finitely generated modules comparing with their completion to the infinitely generated case. We study the structure of the monoid V * ⁢ ( M ) {V^{*}(M)} , of isomorphism classes of countably generated modules in Add ⁡ ( M ) {\operatorname{Add}(M)} with the addition induced by the direct sum. We show that V * ⁢ ( M ) {V^{*}(M)} is a submonoid of V * ⁢ ( M ⊗ R R ^ ) {V^{*}(M\otimes_{R}\widehat{R})} , this allows us to make computations with examples and to prove some realization results. [ABSTRACT FROM AUTHOR]

Composite materials have gained significant attention in various engineering fields due to their unique mechanical properties and versatility. This review focuses on the torsional properties of composite materials, exploring the fundamental aspects that govern their behavior when subjected to torsional loads. Torsional properties, including shear modulus, fiber orientation, anisotropy, torsional strength, manufacturing considerations, and testing methodologies, are examined in detail. Understanding the torsional behavior of composites is crucial for optimizing their performance in applications ranging from aerospace to sports equipment. This review paper provides a concise overview of the key considerations and parameters involved in assessing the torsional properties of composite materials, offering a foundation for further research and application in this field. [ABSTRACT FROM AUTHOR]

A set of exact solutions is suggested for the Poisson equation in a plane region of a certain form for describing a flow of Newtonian incompressible liquid in a channel at low Reynolds numbers. The motion of an ideal liquid in a region bounded by a rotating contour, torsion of a rod, deflection of a membrane at zero displacement on the boundary of its region, and heating of a rod under certain conditions are equivalent to a mathematically formulated problem of such a flow. A possibility is demonstrated to construct approximate solutions to the said problem for certain sections of a channel, having a parabolic segment of the contour, using exact solutions to this problem. Examples are given for the construction of flow regions in a prismatic channel resting on a parabolic contour. [ABSTRACT FROM AUTHOR]

This study is based on a theory for analyzing non-uniform torsion in thin-walled beams made of homogeneous elastic material with arbitrary cross-sections by incorporating the effect of the shear deformation of a cross-section. Utilizing the Finite Element Method (FEM), the proposed numerical approach addresses non-uniform torsion by breaking down a 3D analysis into 2D cross-sectional and 1D modeling components. Initially, the geometric constants of the cross-section were computed using a 9-node isoparametric element in 2D FEM. Subsequently, a 1D FEM employing a linear isoparametric element calculated the twist angle, torsion warping parameters, and stress results. The stress field was determined through a local analysis of the 2D cross-section. Notably, the 2D FEM component aligns with contemporary trends in commercial software, thereby bolstering the potential and practical applicability of the proposed numerical approach. Its verification and validation through numerical analyses using MATLAB underscore the efficacy and reliability of the method in analyzing non-uniform torsion behavior in structural design, particularly under diverse boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we present two different ways for computing the Kauffman bracket skein module of S 1 × S 2 , KBSM S 1 × S 2 , via braids. We first extend the universal Kauffman bracket type invariant V for knots and links in the Solid Torus ST, which is obtained via a unique Markov trace constructed on the generalized Temperley–Lieb algebra of type B, to an invariant for knots and links in S 1 × S 2 . We do that by imposing on V relations coming from the braid band moves. These moves reflect isotopy in S 1 × S 2 and they are similar to the second Kirby move. We obtain an infinite system of equations, a solution of which is equivalent to computing KBSM S 1 × S 2 . We show that KBSM S 1 × S 2 is not torsion free and that its free part is generated by the unknot (or the empty knot). We then present a diagrammatic method for computing KBSM S 1 × S 2 via braids. Using this diagrammatic method, we also obtain a closed formula for the torsion part of KBSM S 1 × S 2 . [ABSTRACT FROM AUTHOR]

Inertial sensors act as inertial references in space gravitational wave detection missions, necessitating that their internal test mass (TM) maintains minimal residual acceleration noise. High-energy particles and cosmic rays in space, along with ion pumps in ground-based torsion pendulum experiments, can cause charge accumulation on the TM surface, leading to increased residual acceleration noise. Consequently, a charge management system was introduced to control the TM's charge. The complex light path propagation within the electrode housing (EH) makes the TM's charging and discharging process difficult to theoretically calculate and fully simulate. To address this issue, we propose a simulation method for charging and discharging inertial sensors within ultraviolet (UV) charge management systems. This method innovatively considers the impact of photoelectron emission angle and the TM's position offset from symmetry on performance. The method also simulates charging and discharging rates over time under conditions of symmetry and preliminarily examines factors affecting the TM's equilibrium potential. Simulation results indicate that this method effectively models the charge management system's operation, providing a valuable reference for system design. [ABSTRACT FROM AUTHOR]

In this case report, we described a rare complication—lung torsion after esophageal atresia repair in a newborn. Torsion of the lung is a critical condition in which either the entire lung or a lung lobe twists, leading to occlusion of blood vessels and airways. The patient's clinical condition was poor after the primary operation. An emergency thoracotomy showed 180° torsion of the right upper lobe (RUL) and right middle lobe (RML). After detorsion, perioperatively, the lung was gradually reperfused and had a normal appearance. After surgery, the patient was unstable, which culminated in a fatal end (bradycardia, reperfusion injury). Immediate intervention can preserve the affected lung or lung lobe. However, pulmonary torsion typically has a poor prognosis due to misdiagnosis and delayed treatment. Additionally, diagnosis in the neonatal period is even more challenging because the clinical symptoms are nonspecific. In any case, the question is whether detorsion is the right solution or whether a segmentectomy is necessary. [ABSTRACT FROM AUTHOR]

Pulmonary sequestration with torsion is a rare condition. We describe a seven‐month‐old baby presenting excessive crying for pulmonary sequestration with torsion. Contrast‐enhanced chest computed tomography demonstrated an oval‐shaped mass in the posteromedial right lower chest, no systemic arterial supply was evident. The edge of the mass showed slight linear reinforcement, and its interior had no reinforcement. Thoracoscopic segmentectomy was carried out and histology confirmed pulmonary sequestration with torsion. [ABSTRACT FROM AUTHOR]

This study examines the impact of high-pressure torsion (HPT) processing at various temperatures on the precipitation behavior of Cu-Cr alloys. The introduction of defects through HPT is observed to promote the precipitation of Cr atoms. Unlike the traditional large-scale precipitation that typically occurs around 400 °C, HPT can induce the precipitation of solute atoms even at room temperature. Furthermore, the temperature at which HPT is performed significantly influences the behavior of the precipitated phase during subsequent aging, ultimately affecting the alloy's overall properties. At elevated temperatures (ETs) and room temperature (RT), Cr atoms tend to aggregate, forming Guinier–Preston (GP) zones or precipitates, which coarsen into incoherent precipitates after annealing. In contrast, when HPT is conducted at liquid nitrogen temperature (LNT), Cr atoms are retained in their original positions, leading to the formation of uniformly distributed, high-density small precipitates post-annealing. This phenomenon results in superior properties for HPT-LNT-treated samples, evidenced by a microhardness of 191.8 ± 3.2 HV and an electrical conductivity of 84.6 ± 1.8% IACS. [ABSTRACT FROM AUTHOR]

Purpose: An increased value of tibiofemoral rotation is frequently observed in patients with patellofemoral instability or maltracking. Nevertheless, the appropriate approach for addressing this parameter remains unclear so far. One potential approach for correcting tibiofemoral rotation is femoral rotational osteotomy. We hypothesized that femoral rotational osteotomy affects tibiofemoral rotation. Methods: All patients who underwent femoral rotational osteotomy between January 2018 and May 2022 were included in this study. Pre‐ and postoperative tibiofemoral rotation and the degree of femoral rotation were measured using two‐dimensional (2D) and three‐dimensional (3D) measurements. The effect of femoral rotation on tibiofemoral rotation was assessed. Results: Forty knees (18 right and 22 left) of 36 patients (28 females and 8 males) were included. Mean preoperative femoral torsion was 32.1 ± 10.1° in 2D and 30.8 ± 10.1° in 3D. Femoral rotation was performed by −14.1 ± 8.3° using 2D measurements and −15.0 ± 8.0° using 3D measurements. Tibiofemoral rotation changed from 9.9 ± 6.2° to 9.7 ± 6.0° (p = n.s.) in 2D, and from 10.2 ± 5.5° to 9.4 ± 5.4° (p = n.s.) in 3D. Conclusion: Tibiofemoral rotation showed no significant changes after femoral rotational osteotomy. Hence, femoral rotational osteotomy cannot be used to correct tibiofemoral rotation in addition to correcting the femoral version. Other surgical techniques need to be evaluated if correction of tibiofemoral rotation is required. Level of Evidence: Level III. [ABSTRACT FROM AUTHOR]

The cochlea, situated within the inner ear, is a spiral-shaped, liquid-filled organ responsible for hearing. The physiological significance of its shape remains uncertain. Previous research has scarcely addressed the occurrence of transverse flow within the cochlea, particularly in relation to its unique shape. This study aims to investigate the impact of the geometric features of the cochlea on fluid dynamics by characterizing transverse flow induced by harmonically oscillating axial flow in square ducts with curvature and torsion resembling human cochlear anatomy. We examined four geometries to investigate curvature and torsion effects on axial and transverse flow components. Twelve frequencies from 0.125 Hz to 256 Hz were studied, covering infrasound and low-frequency hearing, with mean inlet velocity amplitudes representing levels expected for normal conversation or louder situations. Our simulations show that torsion contributes significantly to transverse flow in unsteady conditions, and that its contribution increases with increasing oscillation frequency. Curvature alone has a small effect on transverse flow strength, which decreases rapidly with increasing frequency. Strikingly, the combined effect of curvature and torsion on transverse flow is greater than expected from a simple superposition of the two effects, especially when the relative contribution of curvature alone becomes negligible. These findings may be relevant to understanding physiological processes in the cochlea, including metabolite transport and wall shear stress. Further studies are needed to investigate possible implications for cochlear mechanics. [ABSTRACT FROM AUTHOR]

Nowadays, piezoelectric micro-beam structures are used in various industries, and knowing and analysis of these smart microstructures is important. However, in the modeling of these electromechanical microbeams, the torsion during bending is generally omitted for simplicity. Considering that in some cases, twisting and bending cannot be omitted and must be modeled simultaneously. Therefore, this article presents a coupled bending-torsion model for the first time for static deflection and free vibration analysis of piezoelectric microbeams with nonclassical continuum theories. The governing equations of the motion and boundary conditions of the Timoshenko beam at the micro-scale have been obtained using size-dependent electromechanical theory and Hamilton's principle. In addition, the Laplace transform is used to solve the static equations, while the generalized differential quadratic (GDQ) method is used to discretize and solve the free vibration equations. In the following, the influence of various parameters, such as the effect of size and geometric conditions, on the static displacements and the natural frequency of the microbeam is discussed. [ABSTRACT FROM AUTHOR]

Background: Tissue stimulations greatly affect cell growth, phenotype, and function, and they play an important role in modeling tissue physiology. With the goal of understanding the cellular mechanisms underlying the response of tissues to external stimulations, in vitro models of tissue stimulation have been developed in hopes of recapitulating in vivo tissue function. Methods: Herein we review the efforts to create and validate tissue stimulators responsive to electrical or mechanical stimulation including tensile, compression, torsion, and shear. Results: Engineered tissue platforms have been designed to allow tissues to be subjected to selected types of mechanical stimulation from simple uniaxial to humanoid robotic stain through equal‐biaxial strain. Similarly, electrical stimulators have been developed to apply selected electrical signal shapes, amplitudes, and load cycles to tissues, lending to usage in stem cell‐derived tissue development, tissue maturation, and tissue functional regeneration. Some stimulators also allow for the observation of tissue morphology in real‐time while cells undergo stimulation. Discussion on the challenges and limitations of tissue simulator development is provided. Conclusions: Despite advances in the development of useful tissue stimulators, opportunities for improvement remain to better reproduce physiological functions by accounting for complex loading cycles, electrical and mechanical induction coupled with biological stimuli, and changes in strain affected by applied inputs. [ABSTRACT FROM AUTHOR]

The degeneracies of 1/4 BPS states with unit torsion in heterotic string theory compactified on a six torus are given in terms of the Fourier coefficients of the reciprocal of the Igusa cusp Siegel modular form Φ 10 of weight 10. We use the symplectic symmetries of the latter to construct a fine-grained Rademacher-type expansion which expresses these BPS degeneracies as a regularized sum over residues of the poles of 1 / Φ 10 . The construction uses two distinct SL (2 , Z) subgroups of Sp (2 , Z) which encode multiplier systems, Kloosterman sums and Eichler integrals appearing therein. Additionally, it shows how the polar data are explicitly built from the Fourier coefficients of 1 / η 24 by means of a continued fraction structure. [ABSTRACT FROM AUTHOR]

We compute the Mordell–Weil groups of the modular Jacobian varieties of hyperelliptic modular curves X 1 (M , M N) over every composite field of some quadratic number fields. Also we prove criteria for the existence of elliptic curves over such number fields with prescribed torsion points generalizing the results for quadratic number fields of Kamienny and Najman. [ABSTRACT FROM AUTHOR]

Together with axial and flexural actions, modern-designed reinforced-concrete walls can also be subjected to torsion during rare loading events, such as large-magnitude earthquakes or strong winds. For certain widely used nonplanar open cross-section geometries, this torque is resisted primarily through warping. In some cases, the longitudinal stresses caused by torsional warping can be of the same order of magnitude as those caused by flexure, which postulates a reduction of the in-plane bending moment capacity of the section. This study explores the reduction of bending moment capacity of open reinforced-concrete U-shaped core walls due to the simultaneous application of flexural, axial, and torsional loading. Initial investigations focused on strain gradients through the wall segments of reinforced-concrete U-shaped walls. Using a refined data set from a recent experimental campaign, the commonly assumed linear strain gradient used in the design of reinforced-concrete walls is challenged. Numerical methods that intrinsically rely on the observed strain gradients are then employed to compute, for a range of torque-to-bending-moment ratios, the ultimate bending moment and torque capacities from combined loading scenarios. The numerical results corroborate existing experimental results, indicating a significant reduction (almost half) in ultimate bending moment capacity when a torque equal to approximately 20% of imposed bending is applied. Interaction diagrams between the ultimate torque and bending moment show that it is possible to derive a simple relationship between the two for the purposes of structural design. These results can help formulate guidelines for future international building codes, which in their current form cannot account for the design of open sections governed by warping torsion. [ABSTRACT FROM AUTHOR]

This study aims to develop an analytical model based on the curve beam theory to capture the mechanical response of a multihelix cable considering the internal contact displacements. Accordingly, a double-helix cable subjected to axial tension and torsion is analyzed, and both the line and point contacts between the neighboring wires and strands are considered via an equivalent homogenized approach. Then, the proposed theoretical model is extended to a hierarchical multihelix cable with mutual contact displacements by constructing a recursive relationship between the high- and low-level multihelix structures. The global tensile stiffness and torsional stiffness of the double-helix cable are successfully evaluated. The results are validated by a finite element (FE) model, and are found to be consistent with the findings of previous studies. It is shown that the contact deformations in multihelix cables significantly affect their equivalent mechanical stiffness, and the contact displacements are remarkably enhanced as the helix angles increase. This study provides insights into the interwire/interstrand mutual contact effects on global and local responses. [ABSTRACT FROM AUTHOR]

In a recent paper by A. A. Klyachko, V. Y. Miroshnichenko, and A. Y. Olshanskii, it is proven that the center of any finite strongly verbally closed group is a direct factor. In this paper, we extend this result to the case of finite normal subgroups of any strongly verbally closed group. It follows that finitely generated nilpotent groups with nonabelian torsion subgroups are not strongly verbally closed. [ABSTRACT FROM AUTHOR]

The Witt ring of a complex flag variety describes the interesting – i.e. torsion – part of its topological KO-theory. We show that for a large class of flag varieties, these Witt rings are exterior algebras, and that the degrees of the generators can be determined by Dynkin diagram combinatorics. Besides a few well-studied examples such as full flag varieties and projective spaces, this class includes many flag varieties whose Witt rings were previously unknown, including many flag varieties of exceptional types. In particular, it includes all flag varieties of types G_2 and F_4. The results also extend to flag varieties over other algebraically closed fields. [ABSTRACT FROM AUTHOR]

We introduce the notions of Gorenstein projective τ -rigid modules, Gorenstein projective support τ -tilting modules and Gorenstein torsion pairs and give a Gorenstein analog to Adachi–Iyama–Reiten's bijection theorem on support τ -tilting modules. More precisely, for an algebra Λ , we prove that there is a bijection between the set of Gorenstein projective support τ -tilting modules and the set of functorially finite Gorenstein projective torsion classes. As an application, we introduce the notion of CM- τ -tilting finite algebras and show that Λ is CM- τ -tilting finite if and only if Λ op is CM- τ -tilting finite. Moreover, we show that the Bongartz completion of a Gorenstein projective τ -rigid module need not be a Gorenstein projective τ -tilting module. [ABSTRACT FROM AUTHOR]

Evaluating building damage in mining areas using Interferometric Synthetic Aperture Radar (InSAR) has inherent challenges. This work presents a Delaunay Triangulation of Surface Deformation (DTSD) model that utilizes Permanent Scatter InSAR to analyze various types of deformations in villages. This model created a network of irregular triangles using Delaunay triangulation and PS points as the input. The calculation involved determining the inclination of triangular edges and the torsion of spatial Bezier curves fitted by these edges. The PS points' maximum inclination and curvature values were identified by solving over-determined equations. Results from a slurry injection mine in Huaibei, China, indicate that the various types of deformations in the neighboring communities were below 8 %, and the buildings experienced minimal damage. The DTSD model offers a theoretical framework for monitoring and assessing various types of surface deformation and designing essential zones for building protection. [ABSTRACT FROM AUTHOR]