Equivalent Theory Research Articles

Elastoplastic limit analysis of functionally graded materials pipe elbows to predict the damage under in-plane bending moment using XFEM-Technic

Functionally Graded Materials (FGMs) have become a vast field of research, due to their wide range of applications and numerous advantages. The use of FGMs has recently expanded, particularly in the reinforcement of tubular structures. Pipe elbows are among the most important elements in a piping system, responsible for reducing stresses and balancing pressure inside pipes. However, due to significant deformations, most frequently caused by bending moment loads, elbows are more prone to exceeding their stress limits. It is for this reason that the analysis of these tubular structures has attracted the interest of many researchers. As a result, the study of their reinforcement can only be carried out through the study of their damage. In other words, to unlock the difficulties of numerically predicting their responses. The aim of our study is to use the finite element method with the proposed meshing technique in the ABAQUS calculation code, to analyze the behavior of a 90° elbow tubular structure, attached to two straight sections, made of functionally graded FGM Al/SiC (Aluminum/Silicon Carbide) material, with a continuous gradual variation of properties in the direction of wall thickness, per row of finished elements along the entire geometry of the tubular structure, in order to simulate a real pipe system installation. The structure is loaded by two modes of in-plane bending moment (Closing and Opening), with an imposed rotational displacement. The aim of this analysis is to evaluate, firstly, the effects of different grading concepts for the FGM Al/SiC material couple in the model geometry (Simple and Symmetrical Concepts), and secondly, the effect of different power exponent indices (n) of the volume fraction, on the elasto-plastic response up to the damage of the tubular structure. The constitutive behavioral law of our model is based on Von Mises’ equivalent stress flow theory with a hardening variable in incremental form. In addition, the TTO (Tamura-Tomota-Ozawa) model was used to describe the elastic-plastic behavior of the FGM, and the XFEM technique was also applied for crack initiation and propagation. The results obtained under moment-rotation conditions show a significant effect on the response as well as on the level of damage, the effect is also remarkable on the ovalization at the bend cross-section. The approach and reliability of the results obtained were based on a comparison with experimental results, which show good agreement, compared with our numerical model.

A size-distinguishing miniature electromagnetic tomography sensor for small object detection

Electromagnetic tomography (EMT) is an emerging imaging technique that presents the property distribution of conductive or magnetic materials based on signals from the coil array on the EMT sensor. However, conventional EMT researches generally involve large-size EMT sensors, which are ineffective in detecting and discerning the size of small objects due to limited spatial resolution, sensitivity and relatively high noise level. As such, this paper presents a novel miniature EMT sensor, which incorporates 8 small coils around the circumference for imaging and 2 larger horizontal coils that generate a vertical field for target size distinction. Moreover, a novel equivalent theory is proposed to approximate the effect of the horizontal coils by the cumulative effect of the 8 small coils. An EMT testing system is established with the proposed sensor array and the multi-channel instrument developed in our lab. Experiments based on multiple sample distributions and different reconstruction algorithms validate the ability of the sensor to detect and distinguish the size of small objects of different materials. Furthermore, the equivalent theory was validated through the experiments.

Filtered colimit elimination from Birkhoff's variety theorem

Birkhoff's variety theorem, a fundamental theorem of universal algebra, asserts that a subclass of a given algebra is definable by equations if and only if it satisfies specific closure properties. In a generalized version of this theorem, closure under filtered colimits is required. However, in some special cases, such as finite-sorted equational theories and ordered algebraic theories, the theorem holds without assuming closure under filtered colimits. We call this phenomenon “filtered colimit elimination,” and study a sufficient condition for it. We show that if a locally finitely presentable category A satisfies a noetherian-like condition, then filtered colimit elimination holds in the generalized Birkhoff's theorem for algebras relative to A.

Infinite-Volume Gibbs States of the Generalized Mean-Field Orthoplicial Model

The generalized mean-field orthoplicial model is a mean-field model on a space of continuous spins on Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^n$$\\end{document} that are constrained to a scaled (n-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n-1)$$\\end{document}-dimensional ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-sphere, equivalently a scaled (n-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n-1)$$\\end{document}-dimensional orthoplex, and interact through a general interaction function. The finite-volume Gibbs states of this model correspond to singular probability measures. In this paper, we use probabilistic methods to rigorously classify the infinite-volume Gibbs states of this model, and we show that they are convex combinations of product states. The predominant methods utilize the theory of large deviations, relative entropy, and equivalence of ensembles, and the key technical tools utilize exact integral representations of certain partition functions and locally uniform estimates of expectations of certain local observables.

FGM concept used in damage analysis of heat-treated elbows under out-of-plane combined bending moment

The elbow is presented in pressurized tubular structures as a connecting element, generally subjected to bending moments either out-of-plane or in-plane, in closure or opening. Another mode of bending moment that can also occur in these tubular structures is the combined bending moment between out-of-plane and in-plane in closure, or out-of-plane and in-plane in opening. In this work, to better present the potential severity caused by this loading mode, an elbow structure attached by straight tubular sections made of X60 steel is analyzed and its damage under this combined bending moment with orientations between the plane and out-of-plane of the structure is discussed. A reinforcement proposal will be made in the second part of this work. Indeed, the structure is pretreated thermally at the elbow, resulting in a graded structure along the thickness with two different material constituents: the base metal and the thermally affected zone (HAZ). Based on the concept of Functionally Graded Materials (FGM), the gradation is by volume fraction between the base metal and the HAZ, following a power law function of a volume fraction index (n). This graded property is introduced along the thickness by finite element layers. The elastic-plastic behavior of the HAZ-base metal mixture is modeled using the Voce model and the Von Mises equivalent stress flow theory. Using the XFEM technique(extended finite element method), the damage of the pressurized and thermally treated structure under a combined out-of-plane bending moment shows that these parameters condition the response and the level of damage.

Terahertz wide-band wide-angle absorber and polarization converter based on VO2 metamaterial

In this study, a Terahertz wide-band wide-angle absorber and polarization converter based on VO2 metamaterial is proposed. The device is simulated by using full-wave electromagnetic computing software CST. The device functions as a wide-band absorber while VO2 is in the metallic mode. In the 1.82 THz to 4.27 THz band, the absorption efficiency exceeds 90% and the relative bandwidth reaches 81.4%. The absorption mechanism is analyzed bying equivalent circuit theory. Additionally, the absorber can work at large polarization angle and incident angle. While VO2 is in the insulated mode, the design can convert the incident y-polarized terahertz wave into the x-polarized state and realize the transformation of linear polarization. Polarization conversion efficiency (PCR) exceeds 90% in the band of 1.57 THz to 3.82 THz, with a relative bandwidth of 83.5%. The device also supports large incidence angle tolerances. These results show that the disigned metamaterial device has potential applications in absorption, polarization conversion and imaging.

Investigation into the Variation Law of Network Fracture Conductivity in Unconventional Oil and Gas Reservoirs

The network fracturing technique is a key technology for increasing effective reservoir volume and enhancing production in shale oil and gas. The fracture network’s conductivity is one of the crucial factors affecting the efficient development of shale gas. To evaluate the variation patterns and influencing factors of the conductivity of network fractures, this study employed a proppant conductivity evaluation system and an equivalent theory testing method. It investigated the conductivity of propped and self-propped fractures under different angles and numbers of fractures. Experimental results showed that fractures with proppant support had higher conductivity than unsupported fractures. Smaller angles between secondary and main fractures resulted in greater conductivity. The conductivity of multi-fracture structures increased with the number of fractures. Under low-closure pressure conditions, self-propped fractures exhibited significantly higher conductivity than propped fractures, but this trend reversed under high closure pressure. This experimental research provides guidance for constructing network fractures with high conductivity in unconventional oil and gas reservoir fracturing.

A sandwich-structured 1-3 type piezoelectric composite material for enhancing reliability

This study proposes a sandwich structure 1-3 piezoelectric composite, incorporating flexible silicone rubber to enhance the thickness vibration mode of piezoelectric ceramics. Rigid aluminum nitride (AlN) is employed to bolster the mechanical stability of the composite. Utilizing equivalent parameter theory, we establish a mathematical model for the sandwich structure composite material. The impact of the piezoelectric phase size and the volume fraction of AlN on several performance parameters of the material are analyzed, including the thickness electromechanical coupling coefficient, density, sound velocity, and characteristic impedance. The sandwich structure piezoelectric composite was fabricated using the "cutting and filling" technique. Experimental outcomes reveal that this material demonstrates concentrated thickness vibration modes, with a thickness electromechanical coupling coefficient reaching as high as 0.72, a 16.6 % increase compared to traditional 1-3 piezoelectric composites. Results from thermal shock tests and tensile tests suggest that the sandwich structure 1-3 piezoelectric composite has considerable potential for use in highly reliable low-frequency receiving transducers.

Electrical breakdown mechanism and life prediction of thermal-aged epoxy/glass fibre composites

Epoxy/glass fibre composites possess excellent mechanical and electrical properties and are widely utilised in electrical and electronic power equipment. However, the composites exhibit relatively poor thermal conductivity, causing the temperature of the composites to increase during the operation of power equipment, resulting in a significant reduction in the electrical breakdown strength. Although the effects of thermal aging on polymeric materials have been widely studied, its influence on electrical strength mechanisms has not been investigated at the molecular level. In this study, epoxy/glass fibre composite specimens were subjected to accelerated thermal aging treatment for 360 h at 180 °C. Functional groups, molecular chain dynamics, and electrical breakdown are characterised using infrared spectroscopy, dielectric spectroscopy, and breakdown measurement. Subsequently, electrical breakdown mechanism and life prediction of the thermally aged composites are discussed. During thermal aging, the epoxy resin molecular chains undergo continuous oxidation and chain scission, which generate numerous polar functional groups and short chains and an increase in the free volume. This triggers an enhancement in the chain segmental dynamics, thereby significantly reducing the activation energy of the epoxy resin. After 360 h, activation energy decreased from 0.78 eV to 0.67 eV. The DC breakdown voltages of the specimens decreased from 168.28 kV/mm to 134.91 kV/mm. An insulation life prediction model for thermally aged epoxy/glass fibre composites is established based on the time-temperature equivalence theory. The prediction results indicate that the service life of the operational composites is approximately 11.2 years at 353 K, which is consistent with engineering experience.

Physics-informed transfer learning model for fatigue life prediction of IN718 alloy

To address the challenges posed by inadequate data and data utilization in multiple scenarios of fatigue loading, a Physics-informed Transfer Learning (PITL) model has been developed to predict the fatigue life of IN718 superalloy. Strain-controlled low-cycle fatigue tests were carried out at 400 °C with three distinct strain ratios, which were subsequently segmented for individual transfer learning tests. PITL models with significant engineering value were built by integrating transfer learning methodologies rooted in TrAdaBoost with a physics-based model that hinges on the principles of equivalent strain theory. The findings suggest that PITL models exhibit improved accuracy and greater robustness compared to both transfer learning and physics models.

Research on the water flooding front based on dynamic and static data inversion – a case study

To clarify the movement of the water flooding front in fluvial reservoirs, this research takes the BZ oilfield as an example. By considering the equivalent flow resistance theory for oil–water two-phase flow, the horizontal micro-element equivalent method and the strong heterogeneity of fluvial facies reservoir comprehensively, a calculation model for a non-piston water flooding front in a horizontal well pattern was established. First, five horizontal injection–production well groups in the BZ oilfield were taken as examples to calculate the water breakthrough time for the oil wells. The calculation results are in good agreement with the actual production performance. In detail, the advancing speed of the water flooding front in the high-permeability strip was 0.8–1.6 m/day, and the speed in the low-permeability strip was 0.12–0.35 m/day. When water is seen in the oil well, the advancing speed in the low-permeability strip is reduced, resulting in uneven displacement and the formation of non-dominant potential areas. In addition, the water flooding front advancing distance was simulated to be 300–450 m by establishing a reservoir numerical simulation model, which is close to the result of the proposed model, indicating that the calculation method is reliable. This research is of great significance for predicting the water breakthrough time of horizontal production wells, judging the weak affected area on the mainstream line, and optimizing water injection and tapping reservoir potential in good time.

Damage investigation in steel pipe under pressure and combined bending moment: Application in structure connected by elbow and reduced tee

Steel tubular structures in pipelines, or those connections such as concentric reductions, reduced tees, and elbows, all differ in their response to loading, they are sometimes solicited to complex and combined loads, which accumulate with the internal pressure to their solicitation cause in certain situation their damage, the objective in this analysis is to numerically predict the mechanical behavior until damage of a complete tubular structure, which contains the connecting elements of an elbow and a reduced tee attached to each other by straight tubular parts, this structure, by its standardized dimensions presents a real design of a main pipeline spigot for a possible supply line, this tubular structure is analyzed in this work under these real pressure conditions, and combined loads probably coming from the weight of a valve, or a pipe flanged to this spigot element or other, in X60 steel This structure is solicited under different combined modes of loading. The elastic-plastic behavior is under Voce’s model and Von Mises’ equivalent stress flow theory, the damage of the structure by crack initiation and propagation is ensured by using the XFEM technique, the response up to damage of the structure is evaluated under the effect of the parameters of the combined loading mode, we present by angular bendingrotation moment curves that these parameters clearly condition the response and the level of damage.

On the Operational Theory of the CPS-Calculus: Towards a Theoretical Foundation for IRs

The continuation-passing style translation often employed by compilers gives rise to a class of intermediate representation languages where functions are not allowed to return anymore. Though the primary use of these intermediate representation languages is to expose details about a program's control flow, they may be equipped with an equational theory in order to be seen as specialized calculi, which in turn may be related to the original languages by means of a factorization theorem. In this paper, we explore Thielecke's CPS-calculus, a small theory of continuations inspired by compiler implementations, and study its metatheory. We extend it with a sound reduction semantics that faithfully represents optimization rules used in actual compilers, and prove that it acts as a suitable theoretical foundation for the intermediate representation of Appel's and Kennedy's compilers by following the guidelines set out by Plotkin. Finally, we prove that the CPS-calculus is strongly normalizing in the simply typed setting by using a novel proof method for reasoning about reducibility at a distance, from which logical consistency follows. Taken together, these results close a gap in the existing literature, providing a formal theory for reasoning about intermediate representations.

Language Features of Song Deli’s Chinese Version of The Theory Of Moral Sentiments from the Perspective of Functional Equivalence Theory

Language Features of Song Deli’s Chinese Version of The Theory Of Moral Sentiments from the Perspective of Functional Equivalence Theory

A unified framework of semi-supervised community detection integrating network topology and node content

Detecting the community structure within networks is important because it aids in the analysis of complex networks. However, the existence of diverse complex structures in the network topology can limit the topological information’s ability to represent communities. For instance, the accuracy of many traditional methods based on topology alone decreases sharply when a link is missing or noisy. To solve the above-mentioned issues simultaneously, we propose a unified framework of semi-supervised community detection integrating content information. Three models are proposed, instead of a special model-handling problem. The framework used performs the same interpretation for a target problem. The inputs contain the adjacent and node content matrix. The proposed models describe the network topology using a non-negative matrix factorization (NMF) algorithm–based generative model or modularity maximization algorithm. Additionally, we use the equivalence theory of the pLSI, and NMF models the content information based on NMF. Community membership is also used as the relationship between communities and node contents. The models uniformly integrate content information and network topology. Further, a constraint matrix that depicts must-links is built by calculating the similarity of neighbors between any two nodes. Must-link pairs can represent the network topology’s prior information. The models’ community memberships are adjusted by using a strong constraint based on the connected component of this matrix. The models also introduce prior information into the topological and content information in the mentioned models. We compared the proposed models with the state-of-the-art community detection models on artificial networks and five real networks. The experimental results show that the proposed models outperformed the models combining topology and content and semi-supervised models. Fusing the topology with the content and the prior information in the models was also effective for community detection. Thus, the models under the framework are more advantageous than other semi-supervised models when incorporating the same amount of prior information into the models. The semi-supervised framework used also has a certain level of competitiveness in detecting communities.

Pre-stress effect of metal bars in low-stress separation technology

This paper proposes a low-stress separation technology based on pre-stress effect. It connects notching and loading to take advantage of the rotating bending fatigue to achieve the cropping of metal bars. The real-time positions of the notching tool and loading hammer are calculated based on energy equivalence theory. Compared to the conventional notching method, it achieves 25.1 % reduction of cutting force in the case of AISI1045 steel bars. A testing platform is set up and the loading curve is designed to meet the requirements of deflection law and fatigue cyclic loading law. The bending stress for the minimum cutting force, crack angle and deviation under different notch parameters, and the reasonable pre-loading of different materials are determined through cropping tests and finite element simulation. Cropping results indicate that the optimized notch angle and depth are 60° and 1.5 mm, respectively.

A study on maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolator.

This paper aims to study the maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolators (CMIs). The maglev force and stiffness of CMIs were analytically computed based on equivalent charge theory, and the transfer function of the system was conducted. The effects of magnet geometry parameters and air gap on the maglev force, stiffness, and vibration transmission characteristics of the CMI system were revealed through parametric analyses. With the increase in magnet length and width, the maximum value of maglev force increases, but the displacement range of near-zero stiffness, amplitude, and phase of the system gradually decrease. With the increase in magnet height, the displacement range of near-zero stiffness increases, while the variation in the amplitude and phase of the system has minimal impact. Meanwhile, in the Halbach array, the height variation of the magnet at different positions has different impacts on the magnetic force. As the air gap increases, the maximum value of maglev force decreases, but the amplitude and phase gradually increase, and the displacement range of near-zero stiffness first rises and then decreases. Finally, an experimental study was carried out to test the vibration attenuation characteristics of CMIs, in which sinusoidal excitation, hammer strike excitation, and random excitation were applied.

Kenneth Rexroth’s Translation of Du Fu Poetry from the Perspective of Functional Equivalence Theory

Kenneth Rexroth, a well-known American poet and translator, has contributed to Du Fu poetry translation in the Western society. From the perspective of Nida’s functional equivalence theory, this research takes Rexroth’s English translations of Du Fu poems as a case to study the translation strategies adopted by Rexroth. This explores translation strategies of Du Fu poetry from the perspective of functional reciprocity theory, and is supposed to provide references for the English translation of the ancient Chinese poetry in the future. The above examples all reflect the faithfulness and accuracy of the free translation under the theory of functional equivalence, and accurately express the connotation of the original poem. Above all, the translator has adopted literal translation when translating the above verse. in order to achieve the requirement of the theory of functional equivalence, which enabled the target readers to have the same experience as the original readers. This was the most fundamental purpose of using the literal translation here.

Plactic-like monoids arising from meets and joins of stalactic and taiga congruences

We study the four plactic-like monoids that arise by taking the meets and joins of stalactic and taiga congruences. We obtain the combinatorial objects associated with the meet monoids, establishing Robinson–Schensted-like correspondences and giving extraction and iterative insertion algorithms for these objects. We then obtain results on the sizes of classes of words equal in plactic-like monoids, show that some of these monoids are syntactic, and characterise their equational theories.

Clarification of the transverse orbital angular momentum of spatiotemporal optical vortices

Advances in the generation and the application of spatiotemporal optical vortices (STOV) are proceeding fast, but fundamental aspects of their nature remain obscure. Bliokh (2023 Phys. Rev. A 107 L031501) (PRA) and Porras (2023 Prog. Electromagn. Res. 177 95) (PIER) provide contradictory results on the transverse orbital angular momentum (OAM) carried by STOVs. We show that the results by Porras in PIER and by Bliokh in PRA refer to different STOVs and are all correct. In PIER, STOVs are elliptical at given cross section and time, or in space-time, but not in three-dimensional space. In PRA, STOVs are elliptical in space but not in space-time. This is evidenced from two dual, equivalent theories on the transverse OAM where a wave packet is seen in space-time evolving with propagation distance or in space evolving in time, that account for all values of the total, intrinsic and extrinsic OAM in PIERS and PRA. However, the intrinsic OAM with respect to the photon wave function center in PRA is not generally conserved, which advocates for the energy center in PIER as the STOV center. We argue that STOVs are generated in experiments to purportedly have elliptical symmetry in space-time. The values provided in PIER should then be taken as the reference for elliptical STOVs, and the theory therein to evaluate the transverse OAM of other wave packets. Hancock et al (2021 Phys. Rev. Lett. 127 193901; 2024 Phys. Rev. X 14 011031) erroneously attribute the transverse OAM of elliptical STOVs in space to the elliptical STOVs in space-time that they consider theoretically and can generate in their experiments.