Separated Boundary Research Articles

Supercritical Crossover Lines in the Cell Fluid Model

The cell fluid model with a modified Morse potential is studied. The supercritical states are considered with respect to the possibility of the construction of a separation boundary between liquid-like and gas-like behaviors. We will calculate three different lines that can be used for this purpose: the loci of the isothermal compressibility maxima, the loci of the thermal expansion coefficient maxima, and the line, where the effective chemical potential is zero, M = 0. By the symmetry of the functionals for the partition functions, the condition M = 0 in fluids is analogous to the absence of an external field in the Ising model.

On Non-Linear Differential Systems with Mixed Boundary Conditions

For the constructive analysis of locally Lipschitzian system of non-linear differential equations with mixed periodic and two-point non-linear boundary conditions, a numerical-analytic approach is developed, which allows one to study the solvability and construct approximations to the solution. The values of the unknown solution at the two extreme points of the given interval are considered as vector parameters whose dimension is the same as the dimension of the given differential equation. The original problem can be reduced to two auxiliary ones, with simple separable boundary conditions. To study these problems, we introduce two different types of parametrized successive approximations in analytic form. To prove the uniform convergence of these series, we use the appropriate technique to see that they form Cauchy sequences in the corresponding Banach spaces. The two parametrized limit functions and the given boundary conditions generate a system of algebraic equations of suitable dimensions, the so-called system of determining equations, which give the numerical values of the introduced unknown parameters. We prove that the system of determining equations define all possible solutions of the given boundary value problems in the domain of definition. We established also the existence of the solution based on the approximate determining system, which can always be produced in practice. The theory was presented in detail in the case of a system of differential equations consisting of two equations and having two different solutions.

Wind Turbine Enhancement via Active Flow Control Implementation

The present research enhances the efficiency of an airfoil section from the DTU-10MW Horizontal Axis Wind Turbine (HAWT) via Active Flow Control (AFC) implementation and when using synthetic jets (SJ). The flow around two airfoil sections cut along the wind turbine blade and for a wind speed of 10 m/s is initially simulated using the CFD-2D-RANS-Kω-SST turbulence model, from where the time-averaged boundary layer separation point and the associated vortex shedding frequency are obtained. On a second stage of the paper, and considering one of the two airfoil sections, the boundary layer separation point previously determined is used to locate the SJ groove as well as the groove width; the three remaining AFC parameters, momentum coefficient, jet inclination angle, and jet pulsating frequency, are parametrically optimized. Thanks to the energy assessment presented in the final part of the paper, the study shows that a considerable power increase of the airfoil section can be obtained when attaching the former separated boundary layer. The extension of the optimization process to the rest of the blade sections where the boundary layer is separated would lead to an efficiency increase of the HAWT. The Reynolds numbers associated to the respective airfoil sections analyzed in the present manuscript are Re = 14.088×106 and Re = 14.877×106, the characteristic length being the corresponding chord length for each airfoil.

Substantive Legitimate Expectations: Re-shaping the Boundaries of Judicial Reach in Public Law Remedies in Commonwealth Jurisdictions

Abstract A legitimate expectation is a state of affairs established in a court of law, usually in proceedings for judicial review, in which a public authority that has made a promise, or has acted in terms of a regular practice, as to the conduct of public affairs, is held to the promise or practice, and can only be allowed to resile from the promise, or deviate from the practice, if it has accorded a beneficiary of the promise or practice, a prior hearing. Thus, the presence of a legitimate expectation imports an obligation on the part of an authority to accord a hearing to affected parties, the obligation to observe the audi alteram partem rule (simply the audi rule). For a long time, the only favorable result for a claimant of a legitimate expectation was the setting aside of the decision of the public authority on procedural grounds. This is what is described in this Article as the orthodox approach. With time courts in some countries, notably England, began enforcing the promises and practices, in the sense of granting relief in line with the legitimate expectations, thus granting substantive outcomes. This came amid some spirited reluctance, as it was thought that this was against principle. The main objection was that granting such relief amounted to usurpation of executive power and was judicial overreach into an area reserved for the executive, and therefore breaking the boundaries of separation of powers. Notwithstanding these objections, courts have continued to grant substantive relief. This Article argues that granting substantive outcomes is the proper province of the judiciary and does not amount to judicial overreach, and that substantive outcomes in many cases provide appropriate protection to individuals in cases of broken promises and disappointed expectations. It will be argued that the courts in many countries have in the past, without saying so, in fact granted substantive relief. It is time that an express exposition be made to the effect that substantive relief in cases of proved legitimate expectations is available as a remedy, for the guidance of public administrators and the public alike.

Engineering method for quantifying the coupling effect of transmission tower-line system under strong winds

For transmission tower-line (TL) systems, the coupling effect between line cables and towers under strong winds is significant. This paper presents a method to quantify the coupling effect. Assuming that effective separation of line cables and towers is attainable, this work transforms the coupling effect into the transferred load from the line cable to the target tower, the coupling participation mass of the line cable, and the additional damping. The effective separation conditions are defined through an optimization method minimizing the residual errors of the wind-induced response and dynamic characteristics between the separated bodies and the TL system. A typical TL system is considered and analyzed for its structural dynamic characteristics and wind-induced response. Particularly, the quantities associated with the coupling effect of the TL system are estimated. It reveals that the transferred dynamic load component parallel to the line cable which is overlooked in current codes is significant and highly sensitive to the separation boundary conditions of line cables. Furthermore, the coupling participation mass of the conductor is more prominent than that of the ground wire. The proposed method is feasible for quantifying the TL coupling effect and incorporating it into the wind-induced response analysis of transmission line structures.

Comments on wormholes and factorization

In AdS/CFT partition functions of decoupled copies of the CFT factorize. In bulk computations of such quantities contributions from spacetime wormholes which link separate asymptotic boundaries threaten to spoil this property, leading to a “factorization puzzle.” Certain simple models like JT gravity have wormholes, but bulk computations in them correspond to averages over an ensemble of boundary systems. These averages need not factorize. We can formulate a toy version of the factorization puzzle in such models by focusing on a specific member of the ensemble where partition functions will again factorize.As Coleman and Giddings-Strominger pointed out in the 1980s, fixed members of ensembles are described in the bulk by “α-states” in a many-universe Hilbert space. In this paper we analyze in detail the bulk mechanism for factorization in such α-states in the topological model introduced by Marolf and Maxfield (the “MM model”) and in JT gravity. In these models geometric calculations in α states are poorly controlled. We circumvent this complication by working in approximate α states where bulk calculations just involve the simplest topologies: disks and cylinders.One of our main results is an effective description of the factorization mechanism. In this effective description the many-universe contributions from the full α state are replaced by a small number of effective boundaries. Our motivation in constructing this effective description, and more generally in studying these simple ensemble models, is that the lessons learned might have wider applicability. In fact the effective description lines up with a recent discussion of the SYK model with fixed couplings [1]. We conclude with some discussion about the possible applicability of this effective model in more general contexts.

Research on compressor cascade flow field modeling method based on finite volume flux-informed neural network

For compressor cascade flow field modeling, there exists strong velocity shear in the leading edge separation flow, boundary layer, and wake, which leads to increased modeling errors. To improve the accuracy of the flow field modeling method, this paper introduces the concept of numerical flux from the finite volume method into the loss function to implement Euler equation physics-informed learning, and a finite volume flux-informed neural network (FVFI-net) is constructed. Selecting a high-load, large-turning-angle compressor cascade as the study object, a comparative analysis is conducted on the advantages and disadvantages of purely data-driven, weak physical constraint, and finite volume flux-informed methods in compressor cascade flow field modeling. The study found that compared to purely data-driven and weak physical constraint methods, FVFI-net can reduce the average error of aerodynamic parameters in the flow field by approximately 45.6% and 29.5%, respectively, at a 0° angle of attack. For the flow separation problem occurring at the suction side leading edge and the blade wake area caused by a 5° angle of attack, FVFI-net can effectively reduce modeling errors near the leading edge, in the wake region, and near the periodic boundaries, thus reducing the average error of the aerodynamic parameters of the flow field by about 49.2%and 31.3%, respectively, compared to pure data-driven and weak physical constraint methods.

Numerical Modeling of the Interaction of a Monodisperse Gas Suspension with a Shock Wave Moving at an Angle to the Separation Boundary of a Homogeneous Gas and a Gas Suspension

The work is devoted to the study of the influence of the dispersed phase on the dynamics of gas suspensions during numerical modeling of the dynamics of gas suspensions. In this study, based on the continuum technique of dynamics of inhomogeneous media, the interaction of a shock wave propagating from a homogeneous gas with a gas suspension was numerically simulated. For each of the components of the mixture, a complete hydrodynamic system of equations of motion was solved, which included the equations of conservation of density, the equations of conservation of the spatial components of the momentum of the mixture components, and the equations of conservation of energy of the components. The carrier medium was described as a viscous, compressible heat-conducting gas. The mathematical model took into account interfacial heat transfer. The mathematical model also took into account the interphase exchange of momentum, which included the force of aerodynamic drag, the dynamic force of Archimedes and the force of added masses. The system of equations of the mathematical model was integrated using the finite difference method. To suppress numerical oscillations, a nonlinear correction scheme was used. Large volumetric contents of the dispersed phase were considered. The influence of interfacial interaction on the process of shock wave propagation has been studied.

The effect of shortfin mako shark skin at the reattachment of a separated turbulent boundary layer

This smooth flat experimental study investigates the capability of mako shark scales to control flow separation when placed downstream of the onset of turbulent boundary layer separation and within the reattachment region. The objective of the study is to validate the hypothesis that the shark scales' bristling and recoiling would prevent the flow separation on the flank region (the fastest flow region) of the shark. A rotating cylinder was used to induce an adverse pressure gradient over a flat plate to produce a region of separated flow where the shark skin specimen was mounted. Two types of mako shark scales (flank (B2) and between flank and dorsal fin (B1)) were positioned in the preferred flow direction on a flat plate. The B2 scales are slender, 200μm tall, and can bristle up to 50°. In contrast, B1 scales are wider, shorter, and can bristle at 30°. The bristling angle and shape are the main mechanisms by which the scales act to inhibit flow from moving upstream near the wall. Thus, the difference in the bristling angles and structures of the scales is attributed to the fact that the B2 scales function in a thicker boundary layer (behind the shark's gills) where they must bristle sufficiently high into the boundary layer to control the flow separation, and because the adverse pressure gradient in this region is higher where flow separation is more likely. The scales are placed in the reattachment region to elucidate their ability to control and reattach an already separated turbulent flow. The results show that B2 scales placed in the reattachment region reduce the size of the turbulent separation bubble and decrease the turbulent kinetic energy, while B1 scales have the opposite effect.

Mean-flow structures of the turbulent boundary layers bounding a two-dimensional separation bubble

Understanding the mean-flow structures of a separated turbulent boundary layer (TBL) is crucial for turbulence modeling. This study investigates the spatial scaling properties of the total shear stress and mixing length in the TBLs bounding a two-dimensional (2D) separation bubble, aiming to derive analytical descriptions for the entire mean-velocity profiles of the TBLs. For the adverse pressure gradient (APG) TBL upstream of the separation bubble, the total shear stress possesses a two-layer structure with an inner layer adhering to a linear law and an outer layer conforming to a defect power law. In contrast, the mixing length profile consists of four layers, namely the viscous sublayer, the buffer layer, the overlap layer, and the wake region. Each of the layers exhibits a power law or a defect power law relationship with the spatial coordinate normal to the wall. In the four-layer structure, three parameters are sensitive to the variation of the APG: the buffer-layer thickness, the relative magnitude of the mixing length at the boundary layer edge, and a defect power law exponent quantifying the extent of the wake region. For the reattached TBL downstream of the separation bubble, the total shear stress consists of two parts. One part is induced by the pressure gradient and retains the two-layer structure, while the other, engendered by the intense turbulence advected from the separated shear layer, exhibits a dual-power-law distribution. The advected turbulence also significantly alters the four-layer structure of the mixing length, resulting in an augmented buffer layer, a diminished overlap layer, and a wake region that mimics a turbulent mixing layer. Via a dilation ansatz to describe the scaling transition between adjacent layers, the study formulates the complete profiles of the total shear stress and mixing length. The formulation leads to the derivation of novel analytical expressions for the entire mean-velocity profiles of the TBLs. The expressions are in precise accord with the direct numerical simulations of an incompressible 2D separation-bubble flow and a 2D impinging shock wave/TBL interaction. The elucidation of the mean-flow structures through this study is anticipated to facilitate the analysis of turbulence models, thereby enhancing their performance in simulating separated TBLs. The construction of the mean-flow descriptions by inspecting the spatial scaling properties of turbulence paves a promising way for theoretical exploration of complex nonequilibrium TBLs.

Effect of Tripping and Domain Width on Transonic Buffet on Periodic NASA-CRM Airfoils

Transonic buffet is an instability characterized by shock oscillations and separated boundary layers. High-fidelity simulations have typically been limited to narrow domains to be computationally feasible, overly constraining the flow and introducing modeling errors. Depending on the boundary-layer state upstream of the interaction, different buffet features are observed. High-fidelity simulations (implicit large-eddy simulation) were performed on the periodic (infinite) NASA-CRM wing at a moderate Reynolds number to assess the sensitivity of the two-dimensional transonic buffet to boundary-layer state and domain width. Simulations were cross-validated against low-fidelity Reynolds-averaged Navier–Stokes (RANS)/unsteady RANS and global stability analysis, and excellent agreement was found near the onset. By varying the boundary-layer tripping amplitude, laminar, transitional, and turbulent buffet interactions were obtained. All cases consisted of a single shock and low-frequency oscillations (St≈0.07). The transitional interaction also exhibited reduced shock movement, a 15% increase in CL¯, and energy content at higher frequencies (St≈1.3). Spanwise domain studies showed sensitivity at the shock location and near the trailing edge. We conclude that the span width must be greater than the trailing-edge boundary-layer thickness to obtain span-independent solutions. For largely separated cases, the sensitivity to span width increased, and variations across the span were observed. This was found to be associated with a loss of two-dimensionality in the flow.

Optimal design of an inclined barrier for performance improvement of an oscillating water column device with an artificial neural network model

An oscillating water column (OWC) device with a surface-piercing inclined barrier has been studied in irregular waves. This study is to determine the optimal shape of an inclined barrier utilizing an Artificial Neural Network (ANN) model for the performance enhancement of the conventional OWC system. We employed the dual boundary element method (DBEM) as our numerical approach, which resolves two separate boundary integral equations (singular and hyper-singular) formulated at the coincident source points situated on either side of the degenerate barrier boundary. The design parameters affecting the performance of the OWC system have been optimized to maximize the power extraction using the trained ANN model. The training dataset was prepared using the DBEM, which is then used to train and validate the ANN model. Subsequently, the trained model was employed to make predictions using a broader dataset to identify the optimal combination of design parameters that maximize the conversion efficiency. The findings reveal that the well-trained ANN model can learn complex nonlinear relationships, make good predictions with high accuracy using a larger dataset of input conditions, and offer the optimal values of an inclined barrier appropriate for the wave conditions at the sea installation site.

Notes on wormhole cancellation and factorization

In AdS/CFT, partition functions of decoupled CFTs living on separate asymptotic boundaries factorize. However, the presence of bulk wormholes connecting different boundaries tends to spoil the factorization of the bulk partition function, which leads to a disagreement between the two sides. In this paper, we present two examples where wormhole contributions cancel each other in bulk partition function calculations, thus the bulk factorization can be realized. The first example is in 2-dimensional Jackiw–Teitelboim (JT) gravity, where the proposed way of realizing the cancellation resides in the extra complex phases associated with different wormholes. The phases arise due to the degenerate vacua structure. In the example of the Sachdev–Ye–Kitaev (SYK) model, the cancellation can be achieved due to the distribution of the wormhole saddles on a complex plane. The two examples demonstrate a way of realizing bulk partition function factorization by extending the Hilbert space and dressing wormhole saddles with extra phases.

Minimum Principles for Sturm–Liouville Inequalities and Applications

A minimum principle for a Sturm–Liouville (S-L) inequality is obtained, which shows that the minimum value of a nonconstant solution of a S-L inequality never occurs in the interior of the domain (a closed interval) of the solution. The minimum principle is then applied to prove that any nonconstant solutions of S-L inequalities subject to separated inequality boundary conditions (IBCs) must be strictly positive in the interiors of their domains and are increasing or decreasing for some of these IBCs. These positivity results are used to prove the uniqueness of the solutions of linear S-L equations with separated BCs. All of these results hold for the corresponding second-order differential inequalities (or equations), which are special cases of S-L inequalities (or equations). These results are applied to two models arising from the source distribution of the human head and chemical reactor theory. The first model is governed by a nonlinear S-L equation, while the second one is governed by a nonlinear second-order differential equation. For the first model, the explicit solutions are not available, and there are no results on the existence of solutions of the first model. Our results show that all the nonconstant solutions are increasing and are strictly positive solutions. For the second model, many results on the uniqueness of the solutions and the existence of multiple solutions have been obtained before. Our results are applied to prove that all the nonconstant solutions are decreasing and strictly positive.

Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions

Published theoretical data from several models – PHSD/HSD both with and without chiral symmetry restoration (CSR), applied to experimental data on nuclear collisions from BEVALAC/SIS to LHC energies were analyzed using meta-analysis and Kolmogorov criteria. This made it possible to localize possible features of nuclear matter created in central nucleus-nucleus collisions. Ignition of a drop of quark-gluon plasma (QGP) begins already at an energy of about √s<SUB>NN</SUB> = 2 GeV. The assessment showed that this QGP droplet occupies a small fraction, 15% (average radius of about 5.3 fm, if the fireball radius is 10 fm), of the total volume of the fireball created at √s<SUB>NN</SUB> = 2.7 GeV. A drop of exotic matter undergoes a split phase transition – separated boundaries of sharp (1<sup>st</sup> order) crossover and CSR in chiral limit, between QGP and Quarkyonic matter at an energy about √s<SUB>NN</SUB> = 3.5 GeV. The critical endpoint of 2<sup>nd</sup> order probably cannot be reached in nuclear collisions. The triple phase area occupies interval from √s<SUB>NN</SUB> =12 GeV to 15 GeV, the critical endpoint of 1<sup>st</sup> order – at around √s<SUB>NN</SUB> = 20 GeV. The boundary of smooth (2<sup>nd</sup> order) crossover transition with CSR in chiral limit between Quarkyonic matter and QGP was localized between √s<SUB>NN</SUB> = 9.3 GeV and 12 GeV, and between Hadronic and QGP in the interval from √s<SUB>NN</SUB> = 15 GeV to 20 GeV, the boundary of sharp (1<sup>st</sup> order) crossover transition with CSR in chiral limit between Hadronic matter and QGP was localized after √s<SUB>NN</SUB> = 20 GeV. The phase trajectory of the hadronic corona, enveloping the exotic droplet, always remains in the hadronic phase. The possible phase diagram of nuclear matter created in mid-central heavy ion collisions is also presented in the same energy range as for central collisions. Taking into account the quantum nature of the fireball created in nuclear collisions, emphasis is on the existence of events in central nuclear collisions at energy range from √s<SUB>NN</SUB> = 2 GeV to 2.76 TeV, at which no exotic matter is created and nuclear matter in the fireball remains in the hadronic phase throughout its (fireball) evolution.

QUALITY CONTROL METHODS AND MODELS OF POLYMER COMPOSITE MATERIALS

This article analyzes the traditional and modern methods of demolition control applied to structures made of polymer composite materials. Polymer composite materials are designed to ensure the strength of structures with a minimum mass, not subject to corrosion, etc. as there are advantages. But such materials require a special approach in the preparation and creation and the application of new methods, tools and solutions. This is due to the fact that there are many different types of polymer composite materials. Therefore, the development of criteria for the analysis of quality control methods and models, reliability forecasting in the technology of manufacturing products from polymer composite materials is an urgent issue. The authors give recommendations for the selection of methods for a complete assessment of the quality of compositional materials. The analysis of effective methods of quality control and forecasting of reliability of polymer composite materials was carried out. For this purpose, factors for the choice of the method and reliability prediction have been identified, taking into account its complexity for controlling polymer composite materials. Models for controlling polymer composite materials and products made on its basis were selected and on their basis the effectiveness of the application of low-frequency ultrasonic devices at the separation boundaries of controlled environments was determined.

Variations of the shock and secondary flow structure in a transonic compressor cascade with outlet back pressure

The effects of back pressure on the transonic cascade operating state are crucial and can determine the structure of internal shock waves and secondary flows. In this paper, numerical methods validated by experiments were employed to investigate the evolution mechanisms of the inlet flow field, shock structure, secondary flow structure, and cascade performance under different back pressures. Analysis revealed that transonic cascade exhibited unique incidence characteristics in the inlet flow field under both subsonic and supersonic regimes, although these two regimes involved different physical mechanisms. The results revealed that the operating state of the transonic compressor cascade under the unique incidence condition was influenced by the outlet back pressure, and there existed a critical static pressure ratio. The critical static pressure ratio shifted from 1.61 for two-dimensional flow to 1.37 for three-dimensional (3D) flow at M1 = 1.1, due to the corner separation and the characteristics of 3D shocks. The 3D shock structure exhibited a non-uniform distribution along the spanwise direction due to the influence of back pressure and the separated boundary layer. The vortex structures analysis revealed that the secondary flow structure on the sidewalls of the transonic compressor cascade was primarily dominated by corner vortices, whose formation mechanism was related to the interaction between the shock wave and the sidewall boundary layer. Additionally, this interaction also led to the formation of detached shock and lip shock vortex structures. Finally, loss analysis indicated that the wake region of the transonic cascade primarily includes six types of loss, and the total loss of the cascade decreased with the rise in back pressure.

Research on intelligent classification of weld defects based on improved ResNeXt network

Welding technology is widely used in the connection of metal workpieces, and then due to improper operation and other reasons, small defects may occur in the welding, which will lead to welding failure and hazardous accidents. Therefore, it is very important to accurately identify welding defects. The automatic defect identification method based on deep learning learns features directly from the full-focus mapping of weld defects and automatically classifies them; the ResNeXt network is selected for improvement, and the SK convolution unit is introduced into the original ResNeXt-50 network model to enhance the adaptive adjustment of sensory field; in order to alleviate the problem of the point-by-point convolution in the ResNeXt-50 which consumes a large amount of In order to alleviate the problem that point-by-point convolution in ResNeXt-50 consumes a large amount of computation, 1×1 group convolution is used instead of the original point-by-point convolution, and channel rearrangement is introduced to alleviate the problem of weakened information exchange of groups caused by group convolution. After improvement, the ResNeXt-50 network model can achieve a classification accuracy of 98.2%, which is 5.5% more than that of the original ResNeXt-50 on this paper's dataset, and the classification accuracy after T-sne visualization also has obvious separation boundary and clustering effects.

Investigating the Effect of the Separation of Scales in Reduced Order Battery Modelling: Implications on the Validity of the Newman Model

Modelling lithium-ion battery behavior is essential for performance prediction and design improvement. However, this task is challenging due to processes spanning many length scales, leading to computationally expensive models. Reduced order models have been developed to address this, assuming a “separation of scales” between micro- and macroscales. This study compares two approaches: direct microstructure-resolved 3D domain electrochemical modelling and a simplified 1D homogenized model, similar to the Doyle-Fuller-Newman model. The research investigates the validity of the scale separation assumption in continuum electrode-level models by varying scale separation factors, boundary conditions, and geometries. The findings reveal increases in deviation between the 3D models and 1D models for more tortuous, less porous microstructures, especially under higher discharge rates. However, under realistic conditions, with an electrode featuring eight particles across its thickness and typical transport properties, the 3D model predicts only a slight (2%) increase in current compared to the 1D model at a high rate of 7C (approximately j ≈ 350 Am−2). These results suggest that the separation of scales assumption in the DFN model is generally suitable for a wide range of operating conditions. However, 1D models may overlook local variations in electrolyte concentration and potential, crucial for understanding degradation mechanisms.

Oscillatory properties of selfadjoint boundary problems of the fourth order

A series of results and methods is presented, which make it possible to trace the relationship between the number of inner zeros of nontrivial solutions of fourth order selfadjoint boundary problems with separated boundary conditions and the negative inertia index.