Near-boundary Region Research Articles

Multi-fidelity simulation of aeroengine across wide operation range using auxiliary fully coupled method

Multi-fidelity simulations for the design point or equilibrium lines of aeroengines are implemented using fully coupled methods, simultaneously optimizing computational resources and speed. Fully coupled methods remove the requirement of characteristic maps by directly incorporating computational fluid dynamics models of subcomponents into the thermodynamic model of an aeroengine. However, poor convergence remains an urgent problem for fully coupled methods, particularly when performing multi-fidelity simulations in the near-boundary region. In response to this challenge, an auxiliary fully coupled method was developed in this study. This auxiliary method introduces a parametric priori knowledge and auxiliary coordinate transformations into the existing direct fully coupled method. An automated multi-fidelity simulation platform was established in-house and validated using the KJ66 turbojet engine. The simulation results of the equilibrium line were then compared with experimental data to validate the high accuracy and reliability of the multi-fidelity simulation. Moreover, two fundamental selection schemes for matching parameters (mass flow or static pressure, transferred between the computational fluid dynamics and thermodynamic models) were implemented and systematically compared. The results demonstrate that the adaptive selection of matching parameters extends the application of multi-fidelity simulations to a broader operation range. In addition, the auxiliary fully coupled method was applied to a multi-fidelity simulation of a wider operation range, such as an adjustable nozzle area and variable power extraction. It was also compared with the existing direct fully coupled method with respect to the stable convergence scope. For the mass-flow matching scheme, the maximum stable convergence scope of the direct method was extended from 105 % to 315 % by the auxiliary method. For the static-pressure matching scheme, the auxiliary method also broadened the maximum stable convergence scope of the direct method from 55 % to 190 %. The comparison reveals that the auxiliary fully coupled method exhibits a wider range of far-off-design conditions, including the near-boundary region.

Near-boundary error reduction with an optimized weighted Dirichlet–Neumann boundary condition for stochastic PDE-based Gaussian random field generators

Random field generation through the solution of stochastic partial differential equations is a computationally inexpensive method of introducing spatial variability into numerical analyses. This is particularly important in systems where material heterogeneity has influence over the response to certain stimuli. Whilst it is a convenient method, spurious values arise in the near boundary of the domain due to the non-exact nature of the specific boundary condition applied. This change in the correlation structure can amplify or dampen the system response in the near-boundary region depending on the chosen boundary condition, and can lead to inconsistencies in the overall behaviour of the system. In this study, a weighted Dirichlet–Neumann boundary condition is proposed as a way of controlling the resulting structure in the near-boundary region. The condition relies on a weighting parameter which scales the application to have a more dominant Dirichlet or Neumann component, giving a closer approximation to the true correlation structure of the Matérn autocorrelation function on which the formulation is based on. Two weighting coefficients are proposed and optimal values of the weighting parameter are provided. Through parametric investigation, the weighted Dirichlet–Neumann approach is shown to yield more consistent correlation structures than the common boundary conditions applied in the current literature. We also propose a relationship between the weighting parameter and the desired length-scale parameter of the field such that the optimal value can be chosen for a given problem.

Tameness, Strings, and the Distance Conjecture

The Distance Conjecture states that an infinite tower of modes becomes exponentially light when approaching an infinite distance point in field space. We argue that the inherent path-dependence of this statement can be addressed when combining the Distance Conjecture with the recent Tameness Conjecture. The latter asserts that effective theories are described by tame geometry and implements strong finiteness constraints on coupling functions and field spaces. By exploiting these tameness constraints we argue that the region near the infinite distance point admits a decomposition into finitely many sectors in which path-independent statements for the associated towers of states can be established. We then introduce a more constrained class of tame functions with at most polynomial asymptotic growth and argue that they suffice to describe the known string theory effective actions. Remarkably, the multi-field dependence of such functions can be reconstructed by one-dimensional linear test paths in each sector near the boundary. In four-dimensional effective theories, these test paths are traced out as a discrete set of cosmic string solutions. This indicates that such cosmic string solutions can serve as powerful tool to study the near-boundary field space region of any four-dimensional effective field theory. To illustrate these general observations we discuss the central role of tameness and cosmic string solutions in Calabi-Yau compactifications of Type IIB string theory.

Static analysis and boundary effect of FG-CNTRC cylindrical shells with various boundary conditions using quasi-3D shear and normal deformations theory

In this paper, static analysis and the stress concentration phenomenon of functionally graded carbon nanotubes reinforced composite cylindrical shells with various boundary conditions are explored by using higher-order shear-normal deformation theory and an analytical approach. Five types of distributions of reinforced carbon nanotubes are considered, that is, uniform and four kinds of functionally gradient distribution of carbon nanotubes along with the thickness of the shell. Effective material properties of carbon nanotubes reinforced composite are estimated to the rule of mixture. The governing equations for FG-CNTRC cylindrical shells with various boundary conditions are solved analytically using simple trigonometric series and the Laplace transform. Moreover, the transverse shear and normal stress are reconstructed using 3D linear elasticity equilibrium equations. The present model is validated by comparing its numerical results with those of published works, including the 3D exact model. Using higher-order shear-normal deformation theory, this article has focused on investigating the stress concentration phenomenon, the distribution of stress components in the near-boundary region, and also assessing the effects of various parameters on the stress state of the FG-CNTRC cylindrical shells.

SPECTRA OF ATTENUATED TOTAL REFLECTION OF NITRIDED SiO2/Si STRUCTURES

We studied the behavior of nitrogen in silicon dioxide films on single-crystal silicon substrates by the attenuated total reflection (ATR) method and time-of-flight secondary ion mass spectrometry. Nitrogen was introduced into a dielectric formed by pyrogenic oxidation at a temperature of 850 ºС in an atmosphere of wet oxygen by implantation of N+ ions with an energy of 40 keV at doses of 2.5‧1014 and 1.0‧1015 cm–2,
 followed by rapid thermal annealing at a temperature of 1000 or 1050 ºС with a duration of 15 s in air. Nitridization of some of the samples was carried out during thermal annealing in a nitrogen atmosphere with the addition of a small amount of oxygen at a temperature of 1200 ºС for 120 minutes. It is established that during heat treatments, the majority of nitrogen atoms diffuse to the SiО2/Si interface and accumulate in the near-boundary region of the oxide. The ATR spectra show an absorption band with maxima at ~2320 and 2360 cm–1, which is probably due to vibrations of double cumulative bonds of the O=Si=N− type. The formation of these bonds is due to the interaction of nitrogen with dangling bonds at the silicon-dielectric interface, as a result of which uncompensated or strained bonds are replaced by more stable ones. The resulting stronger chemical bonds prevent charge accumulation on the surface of the SiО2/Si interface.

MD simulation of interactions of atomic displacement cascades with β-Nb precipitates in a zirconium matrix

In this work, we investigated the effect of spherical binary precipitates and needle-shaped nanoparticles of β-Nb on the evolution of cascade processes in the Zr matrix using the method of molecular dynamics and many-body interatomic potentials. For a case of spherical precipitates, the formation of the interphase region with length of ~ 10 Å was observed. The fraction of the Zr atoms in the precipitate increased during the cascade processes. The Nb atoms, which were initially inside the precipitate, did not leave the boundaries of the interphase region after relaxation of the model crystallite. After the cascade process, the Nb atoms were detected Zr matrix at a distance of no more than 5 Å from interphase boundary. Point defects, as well as their clusters, are formed mainly near the surface of the precipitate. In a case of needle-shaped nanoparticles, a slight “blurring” of the particle boundaries with an increase in the number of niobium atoms in the near- boundary region were observed. After the atomic displacement cascade, part of the niobium atoms moved from nanoparticle into the near-boundary region. Only a few niobium atoms moved into the α-phase matrix outside the near-boundary region. No cases of significant dissolution of the nanoparticle were observed. We also observed the formation of clusters consisting of a mixture of vacancies and SIAs in the structure of the nanoparticle.

A physical protocol for observers near the boundary to obtain bulk information in quantum gravity

We consider a set of observers who live near the boundary of global AdS, and are allowed to act only with simple low-energy unitaries and make measurements in a small interval of time. The observers are not allowed to leave the near-boundary region. We describe a physical protocol that nevertheless allows these observers to obtain detailed information about the bulk state. This protocol utilizes the leading gravitational back-reaction of a bulk excitation on the metric, and also relies on the entanglement-structure of the vacuum. For low-energy states, we show how the near-boundary observers can use this protocol to completely identify the bulk state. We explain why the protocol fails completely in theories without gravity, including non-gravitational gauge theories. This provides perturbative evidence for the claim that one of the signatures of holography - the fact that information about the bulk is also available near the boundary - is already visible in the low-energy theory of gravity.

The Effect of the Interaction of Excitations with the Interface between Nonlinear Media with a Switching on the Formation of Localized States

Models of contacting media with stepwise nonlinearity are considered in the presence of interaction of excitations with the interface as a planar defect. In such media, an instantaneous switching from one level to another occurs when the field amplitude reaches a certain threshold value. New types of localized states with specific structure and properties are found. The structure of such states is determined by the formation of domains in the near-boundary regions, in which the values of certain parameters of the media differ from those in other regions. It is shown that, in the presence of interaction of excitations with the interface, new phenomena may occur that are related to the structural features of the field of localized states. The conditions for the existence of localized states are changed. The field can be maximized not only in the near-boundary region but also at the interface between a medium with stepwise nonlinearity and a linear medium. In the medium with stepwise nonlinearity containing a planar defect, the interaction of excitations with this defect leads to a decrease in the amplitude in the plane of the defect. As the intensity of interaction with the defect increases at a fixed localization energy, the domain width increases. It is shown that the threshold value of the total energy flow starting from which localized states exist and a domain is formed can be controlled by the intensity of the interaction of excitations with the interface.

Surface Waves at the Boundary of a Medium with a Refractive Index Switching and a Crystal with the Diffusion-Type Photorefractive Nonlinearity

It is formulated a model, within which, regularities for formation of nonlinear surface waves with a specific field structure are described. It is shown that there are two new types of waves of chosen polarization, which propagate along the contact of a photorefractive crystal with diffusion nonlinearity and a nonlinear optical medium with switching. Nonlinearity in this medium is modelled by a stepwise changing the refractive index depending on the field amplitude. The field structure in the obtained surface waves consists of three components in different regions of contacting media. The propagation of a localized light beam along the boundary at the near-boundary region results in formation of an area of a finite width, which has a refractive index that is different from the remaining medium. The field exponentially decreases in the region behind this domain when moving away from the near-boundary region. In a photorefractive crystal, the field can decrease with oscillations or without oscillations. The dependence of the propagation constant on optical characteristics of media and guiding parameters is derived in the explicit analytical form.

A moving immersed boundary method for simulating particle interactions at fluid-fluid interfaces

A sharp interface immersed boundary method coupled to a volume-of-fluid method and suitable for moving boundary problems is presented. A discrete-forcing approach is used, in which the velocity reconstruction in the near-boundary region is performed using piece-wise continuous bi-quadratic functions. A method is proposed for coupling the volume-of-fluid equation to the immersed boundary method that allows for the boundary to move, as well as appropriate boundary conditions for imposing contact angles. Numerical simulations of both static and moving boundary problems are performed, which demonstrate the efficacy of the proposed method. Validation is performed by comparing numerical results with experimental data and theoretical models available in the literature.

Double-deck structure in the problem of a compressible flow along a plate with small localized irregularities on the surface

We consider the stationary problem of flow of a viscous compressible subsonic fluid along a flat plate with small localized (hump-type) irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of the flow in the thin boundary layer (i.e., in the near-boundary region).

SOME NEW TYPES OF APPROXIMATIONS VIA MINIMAL STRUCTURE

In this paper, we use the notions of a minimal structure approximation space (short MSAS)and the notion of near open sets to introduce a new approximation of uncertain sets as a mathematicaltool to modify the approximations. Relationships between these types are established via proof andcounter examples. Also, some basic concepts of near approximations set are investigated and studied therelations between these different types of sets in MSAS. This set is a specific importance to help withthe modifications of an approximation space via adding new concepts and facts. Finally, we use thisconcept to introduce the definitions of near lower approximation, near upper approximation, nearboundary region, near rough and near exact sets and study some of the properties of this notion.

SOLVING OF ELASTIC DYNAMICAL PROBLEM IN A POROUS FLUID-SATURATED PIECEWISE-HOMOGENEOUS HALF-SPACE BY THE INDIRECT METHOD OF NEAR-BOUNDARY ELEMENTS

Context. Solving the different applied problems of engineering and petroleum geology, geophysics and geodynamics, researchers often use methods based on phenomenon seismic-electrical effect of the second kind, since the electromagnetic field of electrical-kinetic origin is much more informative than the seismic one that generated it, and from it they can determine important petrophysical parameters (for example, porosity and fluid permeability) geological environment. At the first stage of investigation of this effect, the need of solving an elastic-dynamic problem arises, when the object of investigation is the processes of propagation of elastic waves in porous, fluid-saturated piecewise homogeneous media. This task also has an independent meaning for monitoring ecologically dangerous phenomena in the study of deformation processes in soil massifs, especially in mountainous areas, associated with their subsidence due to caverns, earthquakes, filtration of precipitation on the slopes and other phenomena.Objective. Construction of a mathematical model for the propagation of elastic waves in piecewise homogeneous media; creation of software for its numerical implementation and testing of its effectiveness; carrying out numerical investigations of the dependence on the parameters of the medium on the distribution of the displacement components at the boundary of the half-space.Method. We used the Bio theory to create a mathematical model of the problem and the indirect method of near-boundary elements to construct its numerical-analytical solution, last one is based on the theory of methods of boundary integral equations.Results. The software that implements the near-boundary elements method for numerical and analytical modeling of the elastic-dynamic problem has been developed. Computational experiments were carried out to estimate errors of discretization of the near-boundary region and of approximation of the mathematical model.Conclusions. The effect of change of the characteristics of an inclusion (in a form of a parallelepiped), in particular its fluid permeability and porosity, on the distribution of displacement components on the half-space boundary has been investigated. The practical recommendations of the recognition of inclusions have been done.

Double-deck structure of the boundary layer in the problem of a compressible flow along a plate with small irregularities on the surface

We consider the problem of a viscous compressible subsonic fluid flow along a flat plate with small periodic irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of flow in the thin boundary layer (i.e., in the near-boundary region).

Electrical conductivity and grain boundary composition of Gd-doped and Gd/Pr co-doped ceria

We characterize electrical conductivity, microstructure, nano-scale grain boundary structure and chemistry of ceria electrolytes with nominal compositions of Gd0.2Ce0.8O2-δ (GDC) and Gd0.11Pr0.04Ce0.85O2-δ (GPDC). The electrolytes are fabricated using mixed oxide nanopowders synthesized by spray drying. AC impedance spectroscopy was performed from 150°C to 700°C in air to determine grain-interior electrical conductivity. Grain-boundary conductivity was determined below 300°C. The grain-interior conductivity of the GPDC was higher than that of GDC by as much as 10 times, depending on the temperature. The GPDC specific grain-boundary conductivity was measured to be approximately 100 times higher than that of GDC. Energy dispersive X-ray spectroscopy (EDX) and electron energy-loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) confirmed the grain-to-grain compositional uniformity of both materials following heat treatments. Grain boundaries were free of glassy intergranular phases; dopant concentration and Ce oxidation state were found to vary significantly near grain boundaries. Boundary core composition was estimated from STEM EELS to be Gd0.62Ce0.38O2-δ, and Gd0.29Pr0.16Ce0.55O2-δ in GDC and GPDC, respectively. Pr segregation to grain boundaries in the GPDC is hypothesized to enhance conductivity by both decreasing oxygen vacancy migration energy, and inducing mixed ionic–electronic conductivity in the near-boundary region.

Effective hydrodynamics of black D3-branes

The long-wavelength effective field theory of world-volume fluctuations of black D3-branes is shown to be a hydrodynamical system to leading order in a gradient expansion. We study the system on a fiducial `cutoff' surface: the fluctuating geometry imprints its dynamics on the surface via an induced stress tensor whose conservation encapsulates the hydrodynamical description. For a generic non-extremal D3-brane, as we move our cutoff surface from the asymptotically flat near-boundary region to the near-horizon region, this hydrodynamical system interpolates between a non-conformal relativistic fluid and a non-relativistic incompressible fluid. We also consider the dependence on the deviation from extremality of the D3-branes. In the near-extremal case we recover the description in terms of a conformal relativistic fluid encountered in the AdS/CFT context. We argue that this system allows us therefore to explore the various connections that have hitherto been suggested relating the dynamics of gravitational systems and fluid dynamics. In particular, we go on to show that the blackfold effective field theory approach allows us to capture this hydrodynamical behaviour and moreover subsumes the constructions encountered in the fluid/gravity correspondence and the black hole membrane paradigm, providing thereby a universal language to explore the effective dynamics of black branes.

Remote Dynamic Three-Dimensional Scene Reconstruction

Remote dynamic three-dimensional (3D) scene reconstruction renders the motion structure of a 3D scene remotely by means of both the color video and the corresponding depth maps. It has shown a great potential for telepresence applications like remote monitoring and remote medical imaging. Under this circumstance, video-rate and high resolution are two crucial characteristics for building a good depth map, which however mutually contradict during the depth sensor capturing. Therefore, recent works prefer to only transmit the high-resolution color video to the terminal side, and subsequently the scene depth is reconstructed by estimating the motion vectors from the video, typically using the propagation based methods towards a video-rate depth reconstruction. However, in most of the remote transmission systems, only the compressed color video stream is available. As a result, color video restored from the streams has quality losses, and thus the extracted motion vectors are inaccurate for depth reconstruction. In this paper, we propose a precise and robust scheme for dynamic 3D scene reconstruction by using the compressed color video stream and their inaccurate motion vectors. Our method rectifies the inaccurate motion vectors by analyzing and compensating their quality losses, motion vector absence in spatial prediction, and dislocation in near-boundary region. This rectification ensures the depth maps can be compensated in both video-rate and high resolution at the terminal side towards reducing the system consumption on both the compression and transmission. Our experiments validate that the proposed scheme is robust for depth map and dynamic scene reconstruction on long propagation distance, even with high compression ratio, outperforming the benchmark approaches with at least 3.3950 dB quality gains for remote applications.

Mechanism of secondary currents in open channel flows

This paper describes the conditions for initiation and maintenance of secondary currents in open channel flows. By analyzing the Reynolds equation in the wall‐normal and wall‐tangent directions, this study reveals that, like other types of vortices, the secondary currents are originated in the near‐boundary region, and the magnitude (or strength) of secondary flow is proportional to the lateral gradient of near‐wall velocity. The near‐wall secondary flow always moves from the region with lower velocity (or lower boundary shear stress) to the location with higher velocity (or higher boundary shear stress). Subsequently, the near‐boundary secondary flow creeps into the main flow and drives circulation within a region enclosed by lines of zero total shear stress, leading to anisotropy of turbulence in the main flow region. This paper also discusses typical secondary currents in open channel flows and presents the relationship between sediment transport and secondary currents. The formation of sand ridges widely observed on the Earth surface is explained in the light of the proposed relationship.

Excitations and spin correlations near the interface of two three-dimensional Heisenberg antiferromagnets

Magnetic excitations and spin correlations near the interface of two spin-12 Heisenberg antiferromagnets are considered using the spin-wave approximation. When the interaction between boundary spins differs essentially from exchange constants inside the antiferromagnets, quasi-two-dimensional spin waves appear in the near-boundary region. They eject bulk magnons from this region, thereby dividing the antiferromagnets into areas with different magnetic excitations. The decreased dimensionality of the near-boundary modes leads to amplified nearest-neighbor spin correlations in the interface area.

Infrared long nanosecond laser pulse ablation of silicon: Integrated two-dimensional modeling and time-resolved experimental study

Nanosecond (ns) laser ablation may provide good solutions to many industrial silicon micromachining applications. However, most of the previous work is on lasers in ultraviolet (UV) or visible spectral ranges, and ns laser ablation of silicon at the infrared (IR) wavelength has not been well understood, particularly for long ns pulses with durations on the order of ∼100ns. IR ns lasers often have lower costs and less external energy consumption for the same laser energy output than UV or visible lasers, which is desirable for many practical applications. This paper aims to understand the mechanism of IR ns laser ablation of silicon, by combining time-resolved experimental observations with physics-based modeling study. The observation is through a ns-gated intensified charged-coupled devices (ICCD) camera coupled with a microscope tube, while the model is based on two-dimensional (2D) gas dynamic equations for the gaseous phases coupled with the condensed phase heat transfer equation through the Knudsen layer relations. The research shows that the material removal mechanism under the studied laser ablation conditions is surface vaporization in the early stage (yielding a plasma plume above the target), followed by subsequent liquid ejection. The measured plasma front propagation matches reasonably well with the model prediction. The experimentally observed spatial distribution of the plasma radiation intensity is consistent with and has been understood through the model. The study also shows that the observed liquid ejection is induced by the total surface pressure difference between the near-boundary region of the target melt pool and the other remaining region of the pool. The pressure difference is mainly due to the surface vaporization flux drop after laser pulse ends.