Theory Diagrams Research Articles

Development of the interlayer alloy using for TLP diffusion bonding of GH3230 superalloy based on the CALPHAD method

The hot-end components of aero-engines and gas turbines not only require high-temperature alloys capable of withstanding extreme temperatures, but also demand welds with high-temperature-resistant properties. In this study, the CALPHAD method was employed, utilizing the thermodynamic theory of phase diagrams with Thermo-Calc software and the corresponding database, to design the interlayer composition for superalloy TLP diffusion connections. The optimization aimed to determine the interlayer material's solidus-liquidus and compound phase content, resulting in the selection of a new nickel-based interlayer material containing B as MPD, with Co and W as strengthening elements. Using GH3230 alloy as the research subject, TLP diffusion bonding experiments were conducted at a welding temperature of 1200 °C with a holding time of 4 h. The weld zone exhibited no defects, and the microstructure was identical to that of the GH3230 base metal, consisting entirely of a solid solution. High-temperature tensile tests revealed that fractures consistently occurred in the GH3230 base metal, indicating that the weld's strength significantly exceeded that of the base metal. The average tensile strength of GH3230 high-temperature alloy bar tensile simulated specimens is 899 MPa at room temperature and 213 MPa at high temperature. In addition, the 90° three-point bend test showed no cracking in the weld area, indicating adequate plasticity.

A Scaling Relation, Zm-Type Deconfinement Phases, and Imaginary Chemical Potentials in Finite Temperature Large-N Gauge Theories

Abstract We show that the effective potentials for the Polyakov loops in finite temperature SU$(N)$ gauge theories obey a certain scaling relation with respect to temperature in the large-N limit. This scaling relation strongly constrains the possible terms in the Polyakov loop effective potentials. Moreover, by using the effective potentials in the presence of imaginary chemical potentials or imaginary angular velocities in several models, we find that phase transitions to $Z_m$-type deconfinement phases ($Z_m$ phase) occur, where the eigenvalues of the Polyakov loop are distributed $Z_m$ symmetrically. Physical quantities in the $Z_m$ phase obey the scaling properties of the effective potential. The models include Yang–Mills (YM) theories, the bosonic BFSS matrix model, and ${\mathcal {N}}=4$ supersymmetric YM theory on $S^3$. Thus, the phase diagrams of large-N gauge theories with imaginary chemical potentials are very rich and the stable $Z_m$ phase would be ubiquitous. Monte-Carlo calculations also support this. As a related topic, we discuss the phase diagrams of large-N YM theories with real angular velocities in finite volume spaces.

Optimizing gate control coordination signal for urban traffic network boundaries using multi-agent deep reinforcement learning

The macro-aggregated dynamic characteristics of urban network traffic flow encapsulated embodied in macroscopic fundamental diagram theory provide a concise perspective for network-level traffic control. However, accurately translating inter-regional macro-traffic flow control into fine-grained control at each intersection along the boundary remains challenging. To address this issue, a regional boundary intersections collaborative control method is proposed, leveraging the model-free data-driven advantages of multi-agent deep reinforcement learning. First, the proposed model develops a real-time communication module using a bi-directional long short-term memory model and an attention mechanism, enabling intersections to capture spatiotemporal features of the boundary traffic flow. Second, the feedback reward mechanism of the boundary intersection agent is meticulously constructed by considering the traffic state of the protected region, the boundary control pressure, and the traffic pressure of the intersection. The proposed model fosters cooperation at boundary intersections and delicately balances their macro-micro control contradictions based on mastering the boundary state information of the road network. Data-driven boundary gating control can fine-regulate the traffic flow distribution of the network from the perspective of macro-micro to promote its operation efficiency. The simulation experiments verify the effectiveness of the proposed multi-agent signal collaborative control method.

Towards Sustainable Urban Mobility: Voronoi-Based Spatial Analysis of EV Charging Stations in Bangkok

This study leverages the efficacy of Voronoi diagram theory within a mixed-methods approach to thoroughly examine the spatial distribution, service coverage, and optimal locations for expanding electric vehicle (EV) charging infrastructure in Bangkok. Drawing on data from field surveys and public data providers, our analysis unfolds in four key stages. Firstly, we delve into the spatial distribution of charging stations, scrutinizing density, proximity to various road types, and land use through the lens of Voronoi diagrams. Secondly, the application of Voronoi diagrams informs the evaluation of service boundaries. Thirdly, utilizing this effective tool, we assess population density per parking slot or charging head to anticipate future EV adoption. Finally, the study introduces an approach to identify suitable locations for new charging stations through the application of overlapping Voronoi circles. Findings reveal a clustered distribution of charging stations along roads, particularly in the central business district, showcasing the efficiency of Voronoi diagrams in spatial analysis. Residential areas and urban commercial zones also host significant charging station concentrations. Notably, service coverage in inner Bangkok surpasses that of middle and outer areas, highlighting underserved regions. Prospective areas for new charging stations, identified through Voronoi analysis, include Bang Khae, Phra Khanong, Min Buri, and Huai Khwang. This research, rooted in the application of Voronoi diagram theory, offers vital insights for various stakeholders involved in urban infrastructure planning. By employing Voronoi diagrams within Geographic Information Systems (GIS), the study contributes to strategically placing charging stations, optimizing spatial understanding, and enhancing resource allocation. This GIS-based approach not only supports the rise of electric vehicles but also promotes sustainable urban development practices through the efficient utilization of spatial data and analysis techniques.

A Lagrangian approach for variable speed limit implementation in C-ITS framework

With the development of Cooperative-Intelligent Transport System (C-ITS) technologies, new strategies based on embedded technologies have emerged to manage road networks. This paper focuses on adapting to this connectivity context a Variable Speed Limit (VSL) system to detect shockwaves and anticipate their propagation based on the kinematic wave theory to dampen them. We provide an alternative framework to adapt the VSL strategy, well-suited for Eulerian approaches, into a Lagrangian context. While the Eulerian approach is based on Loop Detector (LD) and macroscopic traffic indicators (e.g. flow, density), our Lagrangian approach relies on Road Side Units (RSUs) that record the GPS traces shared by Connected Vehicles (CVs). Based on the combination of CV trajectories, Fundamental and Space-Time Diagrams theory, shockwave estimation and prediction processes directly operate on congestion waves, which release the estimation issue for traffic density. The simulation-based analysis reveals that the performance of the Lagrangian approach is comparable to the Eulerian configurations.

Theory of strain phase equilibria and diagrams

Chemical phase equilibria and phase diagrams are well established and have served as indispensable guides for designing materials through chemical tuning. However, a general thermodynamic theory for strain phase equilibria remains elusive despite extensive studies which have revealed dramatic impacts of mechanical strain on the stability of phases and domain states in solid-state materials. Here, we establish the thermodynamic theory of strain equilibria and a general framework for efficiently constructing multidomain and multiphase diagrams of arbitrarily strained solids under incoherent conditions. As examples, we obtain temperature-strain phase diagrams of ferroelectric PbTiO3, strongly correlated VO2, and unconventional ferroelectric Hf0.5Zr0.5O2. We reveal the analogs of the Gibbs phase rules, multiple- and multi-critical points, common-tangent construction, and level rule in strain equilibria to those in the familiar chemical phase equilibria. Our strain equilibria theory offers a powerful framework for predicting the thermodynamic stability of structural phases and domains in strained solids and for guiding the strain engineering of their functional properties.

A machine learning approach to evaluate the influence of higher-order generalized variables on shell free vibrations

This work focuses on deriving guidelines for choosing structural theories for composite shells using Convolutional Neural Networks (CNN). The Axiomatic/Asymptotic Method (AAM) is used to evaluate higher-order structural theories’ accuracy and computational efficiency based on polynomial expansions. AAM exploits the Carrera Unified Formulation to derive the finite element matrices and obtain natural frequencies. The outcomes of AAM concerning the accuracy and computational cost are used to train CNN for various composite shell configurations. The trained network can then be used as a substitute for finite element models to estimate the accuracy of a given structural theory. The results are provided via Best Theory Diagrams (BTD), in which the set of generalized displacement variables to retain the best accuracy can be read for a given amount of nodal degrees of freedom. Verification is carried out using results from FEM. The results proved the computational efficiency of CNN and highlighted the influence of the shell thickness for the proper choice of the structural theory. Third-order terms and transverse stretching are often necessary to obtain acceptable accuracy.

One-loop beta-functions of quartic enhanced tensor field theories

Enhanced tensor field theories (eTFTs) have dominant graphs that differ from the melonic diagrams of conventional tensor field theories. They therefore describe pertinent candidates to escape the so-called branched polymer phase, the universal geometry found for tensor models. For generic order d of the tensor field, we compute the perturbative β-functions at one-loop of two just-renormalizable quartic eTFT coined by + or ×, depending on their vertex weights. The models + has two quartic coupling constants , and two 2-point couplings (mass, Za ). Meanwhile, the model × has two quartic coupling constants and three 2-point couplings (mass, Za , ). At all orders, both models have a constant wave function renormalization: Z = 1 and therefore no anomalous dimension. Despite such peculiar behavior, both models acquire nontrivial radiative corrections for the coupling constants. The RG flow of the model + exhibits a particular asymptotic safety: is marginal without corrections thus is a fixed point of arbitrary constant value. All remaining couplings determine relevant directions and get suppressed in the UV. Concerning the model ×, is marginal and again a fixed point (arbitrary constant value), λ, µ and Za are all relevant couplings and flow to 0. Meanwhile is a marginal coupling and becomes a linear function of the time scale. This model can neither be called asymptotically safe or free.

Non-admissible irreducible representations of 𝑝-adic 𝐺𝐿_{𝑛} in characteristic 𝑝

Let p > 3 p>3 and F F be a non-archimedean local field with residue field a proper finite extension of F p \mathbb {F}_p . We construct smooth absolutely irreducible non-admissible representations of G L 2 ( F ) \mathrm {GL}_2(F) defined over the residue field of F F extending the earlier results of the authors for F F unramified over Q p \mathbb {Q}_{p} . This construction uses the theory of diagrams of Breuil and Pašk u ¯ \bar {\mathrm {u}} nas. By parabolic induction, we obtain smooth absolutely irreducible non-admissible representations of G L n ( F ) \mathrm {GL}_n(F) for n > 2 n>2 .

Theta -diagram technique for {mathcal {N}}=1, d=4 superfields

We describe a diagrammatic procedure to carry out the Grassmann integration in super-Feynman diagrams of 4d theories expressed in terms of {mathcal {N}}=1 superfields. This method is alternative to the well known D-algebra approach. We develop it in detail for theories containing vector, chiral and anti-chiral superfields, with the type of interactions which occur in {mathcal {N}}=2 SYM theories with massless matter, but it would be possible to extend it to other cases. The main advantage is that this method is algorithmic; we implemented it as a Mathematica program that, given the description of a super Feynman diagram in momentum space, returns directly the polynomial in the momenta produced by the Grassmann integration.

Braided quantum electrodynamics

The homotopy algebraic formalism of braided noncommutative field theory is used to define the explicit example of braided electrodynamics, that is, U(1) gauge theory minimally coupled to a Dirac fermion. We construct the braided L∞-algebra of this field theory and obtain the braided equations of motion, action functional and conserved matter current. The modifications of the electric charge conservation law due to the braided noncommutative deformation are described. We develop a braided generalization of Wick’s theorem, and use it to compute correlation functions of the braided quantum field theory using homological perturbation theory. Our putative calculations indicate that the braided theory does not contain the non-planar Feynman diagrams of conventional noncommutative quantum field theory, and that correlators do not exhibit UV/IR mixing.

Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States.

The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.

Feynman diagrams in four-dimensional holomorphic theories and the Operatope

We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the “Operatope”). We derive a set of quadratic recursion relations which appear to fully determine the final answer. Our strategy can be applied to a very general class of twisted supersymmetric quantum field theories.

Two-level type theory and applications - ERRATUM

AbstractWe define and develop two-level type theory (2LTT), a version of Martin-Löf type theory which combines two different type theories. We refer to them as the ‘inner’ and the ‘outer’ type theory. In our case of interest, the inner theory is homotopy type theory (HoTT) which may include univalent universes and higher inductive types. The outer theory is a traditional form of type theory validating uniqueness of identity proofs (UIP). One point of view on it is as internalised meta-theory of the inner type theory. There are two motivations for 2LTT. Firstly, there are certain results about HoTT which are of meta-theoretic nature, such as the statement that semisimplicial types up to level n can be constructed in HoTT for any externally fixed natural number n. Such results cannot be expressed in HoTT itself, but they can be formalised and proved in 2LTT, where n will be a variable in the outer theory. This point of view is inspired by observations about conservativity of presheaf models. Secondly, 2LTT is a framework which is suitable for formulating additional axioms that one might want to add to HoTT. This idea is heavily inspired by Voevodsky’s Homotopy Type System (HTS), which constitutes one specific instance of a 2LTT. HTS has an axiom ensuring that the type of natural numbers behaves like the external natural numbers, which allows the construction of a universe of semisimplicial types. In 2LTT, this axiom can be assumed by postulating that the inner and outer natural numbers types are isomorphic. After defining 2LTT, we set up a collection of tools with the goal of making 2LTT a convenient language for future developments. As a first such application, we develop the theory of Reedy fibrant diagrams in the style of Shulman. Continuing this line of thought, we suggest a definition of $(\infty,1)$ -category and give some examples.

Best Theory Diagrams for Laminated Composite Shells Based on Failure Indexes

This paper presents a novel approach to developing 2D structural theories for composite shells. The proposed approach uses the capabilities of the Carrera Unified Formulation (CUF) in conjunction with the Axiomatic/Asymptotic Method (AAM) to obtain the best theories for given structural layouts. Different structural cases are considered to analyze the influence of factors such as boundary conditions, lamination, and thickness on the accuracy of a model. The parameter chosen to evaluate a model’s performance is based on the Failure Indexes (FI) defined by the Hashin Failure criteria for unidirectional fiber composites. The outcome of this procedure is the Best Theory Diagram (BTD), containing the graphical representation of the highest accuracy as a function of the number of adopted unknowns. The results show the importance of higher-order terms to capture stress fields and the influence of thickness on the definition of the best theories.

Construction machinery hydraulic transmission system fault analysis and elimination methods

Abstract The hydraulic system plays the role of power transmission in the working process of construction machinery, but their complex structure leads to their frequent failure, which in turn leads to serious consequences. Therefore, this paper first takes the fault diagnosis and troubleshooting of the hydraulic system of construction machinery as the research theme and introduces the working principle of the hydraulic system of construction machinery and common fault mechanism and common methods of fault monitoring and diagnosis. Secondly, it proposes to analyze the key components of the hydraulic system based on the power bonding diagram theory and establish its bonding diagram model to analyze the working principle and power flow characteristics of key components. Finally, the pressure and velocity characteristic parameters are identified with the help of wavelet technology, and the energy distribution and energy entropy value of the hydraulic cylinder velocity signal are obtained by wavelet packet transform. The simulation results show that the wavelet-based analysis model proposed in this paper has good fault tolerance and robustness for fault diagnosis of the hydraulic system of construction machinery, and the correct rate of hydraulic pump fault diagnosis is up to 97%, with a correct average rate increased by 16%; the correct rate of hydraulic cylinder fault diagnosis is up to 95%, with a correct average rate increased by 13%. The wavelet analysis model can be widely applied to the fault diagnosis of hydraulic systems of various construction machinery, and it effectively improves the performance of hydraulic fault analysis systems and provides a key technology for fault identification and troubleshooting of construction machinery.

Two-level type theory and applications

AbstractWe define and develop two-level type theory (2LTT), a version of Martin-Löf type theory which combines two different type theories. We refer to them as the ‘inner’ and the ‘outer’ type theory. In our case of interest, the inner theory is homotopy type theory (HoTT) which may include univalent universes and higher inductive types. The outer theory is a traditional form of type theory validating uniqueness of identity proofs (UIP). One point of view on it is as internalised meta-theory of the inner type theory. There are two motivations for 2LTT. Firstly, there are certain results about HoTT which are of meta-theoretic nature, such as the statement that semisimplicial types up to level n can be constructed in HoTT for any externally fixed natural number n. Such results cannot be expressed in HoTT itself, but they can be formalised and proved in 2LTT, where n will be a variable in the outer theory. This point of view is inspired by observations about conservativity of presheaf models. Secondly, 2LTT is a framework which is suitable for formulating additional axioms that one might want to add to HoTT. This idea is heavily inspired by Voevodsky’s Homotopy Type System (HTS), which constitutes one specific instance of a 2LTT. HTS has an axiom ensuring that the type of natural numbers behaves like the external natural numbers, which allows the construction of a universe of semisimplicial types. In 2LTT, this axiom can be assumed by postulating that the inner and outer natural numbers types are isomorphic. After defining 2LTT, we set up a collection of tools with the goal of making 2LTT a convenient language for future developments. As a first such application, we develop the theory of Reedy fibrant diagrams in the style of Shulman. Continuing this line of thought, we suggest a definition of $(\infty,1)$ -category and give some examples.

Unification of Irreversibility and Energy Diagram Theory.

A simultaneous emission-detection phenomenon occurs when a quantum well (QW) diode is biased with a forward voltage and illuminated with a shorter-wavelength light beam. The diode is able to detect and modulate light emitted by itself due to its spectral emission-detection overlap. Here, two identical QW diode units separately function as a transmitter and a receiver to establish a wireless light communication system. In association with energy diagram theory, we explain the irreversibility between light emission and light excitation in the QW diode, which may help us deeply understand various expressions in nature.

Arboreal topological and fracton phases

We describe topologically ordered and fracton ordered states on novel geometries which do not have an underlying manifold structure. Using tree graphs such as the $k$-coordinated Bethe lattice ${\cal B}(k)$ and a hypertree called the $(k,n)$-hyper-Bethe lattice ${\cal HB}(k,n)$ consisting of $k$-coordinated hyperlinks (defined by $n$ sites), we construct multidimensional arboreal arenas such as ${\cal B}(k_1) \square {\cal B}(k_2)$ by the notion of a graph Cartesian product $\square$. We study various quantum systems such as the ${\mathbb Z}_2$ gauge theory, generalized quantum Ising models (GQIM), the fractonic X-cube model, and related X-cube gauge theory defined on these arenas. Even the simplest ${\mathbb Z}_2$ gauge theory on a 2d arboreal arena is fractonic -- the monopole excitation is immobile. The X-cube model on a 3d arboreal arena is fully fractonic, all multipoles are rendered immobile. We obtain variational ground state phase diagrams of these gauge theories. Further, we find an intriguing class of dualities in arboreal arenas as illustrated by the ${\mathbb Z}_2$ gauge theory defined on ${\cal B}(k_1) \square {\cal B}(k_2)$ being dual to a GQIM defined on ${\cal HB}(2,k_1) \square {\cal HB}(2,k_2)$. Finally, we discuss different classes of topological and fracton orders on arboreal arenas. We find three distinct classes of arboreal toric code orders on 2d arboreal arenas, those that occur on ${\cal B}(2) \square {\cal B}(2)$, ${\cal B}(k) \square {\cal B}(2), k >2$, and ${\cal B}(k_1) \square {\cal B}(k_2)$, $k_1,k_2>2$. Likewise, four classes of X-cube fracton orders are found in 3d arboreal arenas -- those on ${\cal B}(2)\square{\cal B}(2)\square {\cal B}(2)$, ${\cal B}(k) \square {\cal B}(2)\square {\cal B}(2), k>2$, ${\cal B}(k_1) \square {\cal B}(k_2) \square {\cal B}(2), k_1,k_2 >2$, and ${\cal B}(k_1) \square {\cal B}(k_2) \square {\cal B}(k_3), k_1,k_2,k_3 >2$.

Improvement of fracture assessment method for pipe girth weld based on failure assessment diagram

The increasing demand for oil and gas resources in China has promoted the rapid construction and development of oil and gas pipeline networks. With an increase in the mileage of high-grade pipeline, the intrinsic safety of pipeline girth weld faces serious challenges, and the existing fracture assessment methods have many shortcomings. The failure assessment diagram of the commonly used fracture assessment method in engineering is taken as the research object. Aiming at deficiency that it cannot accurately consider the strength matching characteristics of girth welds. Based on the failure assessment diagram theory and the equivalent stress-strain relationship method, the influence of crack size, pipeline diameter-thickness ratio, and material parameters on the fracture assessment accuracy of the girth weld is studied. The calculation method of optimized limit load and reference stress is established. Moreover, the improved fracture assessment process of pipeline girth weld is proposed, which makes up for the lack of conservative assessment results in traditional methods and improves the accuracy of fracture assessment girth weld under high-stress conditions.