Type Boundary Research Articles

Ferroelectric domain percolation in polycrystals

Ferroelectric materials possess the ability to switch between polarization states on application of external fields. This switching is facilitated via movement of domains walls and is a critical factor in the performance metrics of these materials. Hence, the interaction of domain walls with microstructural features such as grain boundaries can influence their performance. Experimentally, domain continuity has only been observed over a few grains with no information of the domain percolation length in larger polycrystals. For domain continuity to be energetically feasible, conditions of ferroelectric polarization continuity and domain wall plane matching need to be satisfied at the grain boundary. In this work, we have studied the extent of continuity of domains within modelled polycrystals. It is shown that under tighter conditions of plane matching and uncompensated polarization charge, favorable grain boundary character can have considerable impact on the domain percolation. However, when the conditions of domain continuity are relaxed, due to higher charge and geometric tolerance, domain percolation throughout the polycrystal is a likely phenomenon. It is shown that percolation of domains through a polycrystalline ferroelectric could be tailored by microstructural control of the grain boundary types and defect chemistry control of the charge compensation mechanisms. The ability to manipulate the length-scale of correlated domain wall motion may lead to new opportunities in ferroelectric functional device design. Additionally, these results can be extended to study the effect of grain boundary character on other material phenomena that involve planar interactions at grain boundaries, including ferroelastic twin boundaries and slip plane continuity.

Resource Estimation in Multi-Unit Mineral Deposits Using a Multivariate Matérn Correlation Model: An Application in an Iron Ore Deposit of Nkout, Cameroon

Modeling the spatial dependence structure of metal grades in the presence of soft boundaries between geological domains is challenging in any mineral resource estimation strategy. The aim of this work was to propose a structural model adapted to this type of geological boundary, based on a multivariate Matérn model that fits the observed direct (within domain) and cross (between domains) correlation structures of metal grades. The methodology was applied to a case study of an iron deposit located in southern Cameroon. Cross-validation scores show that accounting for the grade correlation across domain boundaries improved the traditional workflow, where the grade was estimated in each domain separately. The scores were significantly better when we also ensured that the mean grade was locally invariant from one domain to another to reflect the grade continuity across the domain boundary.

Shock vibration and damage responses of nuclear island subjected to an aircraft crash

Although more attention has been given towards the analysis of large commercial aircraft impacts since the September 11 attacks, little work has been done on the vibration response of internal structures and equipment of nuclear power plants (NPPs) during an impact. With a focus on new NPPs, this paper develops a remeshing algorithm for contact surfaces, which utilizes the advantages of scaled boundary finite element (SBFE) polyhedral elements to fully realize the potential of Octree and structured grid discretization methods. The vibration response of nuclear island internal structures is examined. The influence of the interaction between the foundation and the structure on the overall dynamic response is analyzed. Meanwhile, different ranges of foundation size are investigated for balance between computational efficiency and accuracy. The vibration propagation mechanism is found by studying the influence of different artificial boundary types and damping conditions of foundation. The results show that the interaction has a significant influence on the vibration response, and that a foundation size of 1B (height of the steel containment vessel) on all sides provides the optimal balance between computational and accuracy requirements. Furthermore, the damping ratio of the foundation plays a key role in vibration propagation. Finally, the combined bonding method is highly flexible, and allows cross-scale integration of different mesh sizes.

Asymptotic analysis of Sturm-Liouville problem with Robin and two-point boundary conditions

We analyze the initial value problem and get asymptotic expansions for solution. We investigate the characteristic equation for Sturm-Liouville problem with one classical Robin type boundary condition and another two-point nonlocal boundary condition. Finally, we obtain asymptotic expansions for eigenvalues and eigenfunctions.

Carbon segregation and cementite precipitation at grain boundaries in quenched and tempered lath martensite

Tempering is widely applied to make carbon atoms beneficially rearrange in high strength steel microstructures after quenching; though the nano-scale interaction of carbon atoms with crystallographic defects is hard to experimentally observe. To improve, we investigate the redistribution of carbon atoms along martensite grain boundaries in a quenched and tempered low carbon steel. We observe the tempering-induced microstructural evolution by in-situ heating in a transmission electron microscope (TEM) and by compositional analysis through atom probe tomography (APT). Probe volumes for APT originate from a single martensite packet but in different tempering conditions, which is achieved via a sequential lift-out with in-between tempering treatments. The complementary use of TEM and APT provides crystallographic as well as chemical information on carbon segregation and subsequent carbide precipitation at martensite grain boundaries. The results show that the amount of carbon segregation to martensite grain boundaries is influenced by the boundary type, e.g. low-angle lath or high-angle block boundaries. Also, the growth behavior of cementite precipitates from grain boundary nucleation sites into neighboring martensite grains differs at low- and high-angle grain boundaries. This is due to the crystallographic constraints arising from the semi-coherent orientation relationship between cementite and adjacent martensite. We also show that slower quenching stabilizes thin retained austenite films between martensite grains because of enhanced carbon segregation during cooling. Finally, we demonstrate the effect of carbon redistribution along martensite grain boundaries on the mechanical properties. Here, we compare micro-scale Vickers hardness results from boundary-containing probe volumes to nanoindentation results from pure bulk martensite (boundary-free) probe volumes.

The weak Stokes problem associated with a flow through a profile cascade in Lr$L^r$‐framework

AbstractWe study the weak steady Stokes problem, associated with a flow of a Newtonian incompressible fluid through a spatially periodic profile cascade, in the ‐setup. The mathematical model used here is based on the reduction to one spatial period, represented by a bounded 2D domain Ω. The corresponding Stokes problem is formulated using three types of boundary conditions: the conditions of periodicity on the “lower” and “upper” parts of the boundary, the Dirichlet boundary conditions on the “inflow” and on the profile and an artificial “do nothing”‐type boundary condition on the “outflow.” Under appropriate assumptions on the given data, we prove the existence and uniqueness of a weak solution in and its continuous dependence on the data. We explain the sense in which the “do nothing” boundary condition on the “outflow” is satisfied.

The boundaries between personal life and professional role: a proposal to apply some principles of the Structural Family Therapy by Salvador Minuchin to teachers

ABSTRACT The aim of the present study was to apply some principles of the Structural Family Therapy by Salvador Minuchin to teachers. Specifically, we considered the teacher as a system consisting of two communicating subsystems – one pertaining to personal characteristics and skills, and one pertaining to characteristics and skills related to the professional role – and we explored the boundaries between personal life and professional role, proposing the existence of three types of boundaries that are in line with the original classification by Minuchin: rigid, diffuse, and clear. Moreover, through a semi-structured interview, we conducted an initial empirical investigation about the perception and the representation of the boundaries between personal life and professional role in a sample of 9 kindergarten, primary, and middle school teachers (M professional experience = 16.33 years, SD = 9.60 years). The emerged results, even if limited in number, encouraged the development of further dimensional assessment strategies, as well as the development of training courses on teachers’ emotional and relational competence in which they can reflect on the importance of clear boundaries that allow an adaptive exchange of information between personal and professional areas.

МЕТОДЫ И ПРИНЦИПЫ ПОСТРОЕНИЯ ПОЛНЫХ И НЕПРОТИВОРЕЧИВЫХ БАЗ ЗНАНИЙ ПРИ ДИФФЕРЕНЦИАЛЬНОЙ ДИАГНОСТИКЕ ДВУХ БЛИЗКИХ ПО СИМПТОМАТИКЕ ЗАБОЛЕВАНИЙ

Subject, topic, purpose. The article discusses methods, principles and approaches to the construction of complete and consistent expert knowledge bases in differential classification problems based on psychologically correct ways of obtaining information from an expert. Methodology. The problems of transferring knowledge from an expert to a computer program are considered. The most important characteristics of the knowledge extraction procedure are its psychological correctness, the completeness of the extraction and presentation of knowledge, as well as the consistency (infallibility) of the knowledge base. Since the main source of information is a person, in order to comply with this rule, the use of his logic of thinking must be a prerequisite. Results of the work. Rational methods and algorithms for the formation of large knowledge bases for the differential diagnosis of two diseases similar in symptoms are proposed on the basis of a psychologically correct method of interviewing an expert who solves the usual diagnostic task for him by a complete description of the case in text form. The results of Monte Carlo statistical modeling of the process of extracting expert knowledge for such tasks are presented within the framework of an algorithm based on the search for boundaries separating two diseases according to the binary approximation scheme from the so-called average object having half of the signs most characteristic of one disease and half of the signs most characteristic of another disease with a different number of used signs and three types of possible boundaries between diseases. Scope of application of the results. The results of the work are of applied importance for the construction of automated workplaces of practitioners in order to improve the quality of diagnostic conclusions and optimize the treatment of patients. Conclusions. Psychologically correct principles of knowledge extraction, methods and algorithms described in the article allow you to quickly and reliably build complete and consistent knowledge bases of large volume in various areas of differential diagnosis of diseases to create appropriate automated doctor’s workplaces, which will improve the quality of medical decisions, especially in difficult cases.

MIXED BOUNDARY VALUE PROBLEMS FOR THE HELMHOLTZ EQUATION

We consider a new approach to investigating the mixed boundary value problem (BVP) for the Helmholtz equation in the case of a three-dimensional unbounded domain Ω−⊂ℝ3 with compact boundary surface S=∂Ω−, which is divided into two disjoint parts, SD and SN, where the Dirichlet and Neumann type boundary conditions are prescribed respectively. Our approach is based on the classical potential method. We look for a solution to the mixed boundary value problem in the form of a linear combination of the single layer and double layer potentials with densities supported on the Dirichlet and Neumann parts of the boundary, respectively. This approach reduces the mixed BVP to a system of integral equations containing neither extensions of the Dirichlet or Neumann data nor a Steklov–Poincaré type operator involving the inverse of the single layer boundary integral operator, which is not available explicitly for arbitrary boundary surfaces. The right-hand sides of the resulting boundary integral equations system are functions coinciding with the given Dirichlet and Neumann data of the problem under consideration. We show that the corresponding pseudodifferential matrix operator is bounded and coercive in the appropriate L2-based Bessel potential spaces. Consequently, the operator is invertible, which implies the unconditional unique solvability of the mixed BVP in the class of functions belonging to the Sobolev space W2, loc1(Ω−) and satisfying the Sommerfeld radiation conditions. We also show that the pseudodifferential matrix operator thus obtained is invertible in the Lp-based Besov spaces and prove that under appropriate boundary data a solution to the mixed BVP possesses the Cα-Hölder continuity property in the closed domain Ω¯− with α=12−𝜀, where 𝜀>0 is an arbitrarily small number.

Sequence Stratigraphy and Sedimentary Environment of the Shiranish Formation, Duhok region, Northern Iraq

The Shiranish Formation is cropped out in several areas in northern Iraq. A stratigraphic and facies study was conducted within the Duhok region to determine the sedimentary environment. Three microfacies, reflecting the various subenvironments within different shelf parts of the deep sea, have been identified within the Shiranish Formation. Four depositional environments are identified: slope, the toe of slope, deep shelf, and deep-sea or cratonic deep basin. The Shiranish Formation in the Duhok region, Northern Iraq, was deposited in an open shelf carbonate platform. The Shiranish Formation sequence is divided into six third-order cycles in the study area. These asymmetrical cycles reflect an imbalance between the relative level of the sea and the production of carbonate, and each one reflects a rise in the sea level following a period of standstill. There is a two-sequence boundary type SB-2 that defines the surface. The Shiranish sequence developed in a high-subsidence area that played the main role in the evolution of the formation. It was deposited on a carbonate platform with high subsidence due to major transgression, wherever the successive sea-level rise and stillstand episodes persist.

Kernel-Based Methods for Solving Time-Dependent Advection-Diffusion Equations on Manifolds

In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM) and ghost point diffusion maps (GPDM), to solve the time-dependent advection-diffusion PDE on unknown smooth manifolds without and with boundaries. The core idea is to directly approximate the spatial components of the differential operator on the manifold with a local integral operator and combine it with the standard implicit time difference scheme. When the manifold has a boundary, a simplified version of the GPDM approach is used to overcome the bias of the integral approximation near the boundary. The Monte-Carlo discretization of the integral operator over the point cloud data gives rise to a mesh-free formulation that is natural for randomly distributed points, even when the manifold is embedded in high-dimensional ambient space. Here, we establish the convergence of the proposed solver on appropriate topologies, depending on the distribution of point cloud data and boundary type. We provide numerical results to validate the convergence results on various examples that involve simple geometry and an unknown manifold.

Short Proofs of Explicit Formulas to Boundary Value Problems for Polyharmonic Equations Satisfying Lopatinskii Conditions

This paper deals with Lopatinskii type boundary value problem (bvp) for the (poly) harmonic differential operators. In the case of Robin bvp for the Laplace equation in the ball B1 a Green function is constructed in the cases c>0, c∉−N, where c is the coefficient in front of u in the boundary condition ∂u∂n+cu=f. To do this a definite integral must be computed. The latter is possible in quadratures (elementary functions) in several special cases. The simple proof of the construction of the Green function is based on some solutions of the radial vector field equation Λu+cu=f. Elliptic boundary value problems for Δmu=0 in B1 are considered and solved in Theorem 2. The paper is illustrated by many examples of bvp for Δu=0, Δ2u=0 and Δ3u=0 in B1 as well as some additional results from the theory of spherical functions are proposed.

DPBET: A dual-path lung nodules segmentation model based on boundary enhancement and hybrid transformer

Accurate segmentation of lung nodules is an important basis for the subsequent differentiation of benign and malignant pathological types, which is conducive to early detection of lung cancer. Due to the local feature extraction characteristics of convolution and the limited receptive field of continuous down-sampling, the existing deep convolutional neural networks (CNN) for lung nodules segmentation cause the loss of information of lesion boundaries and locations. To address this issue, a dual-path lung nodules segmentation model based on boundary enhancement and hybrid transformer (DPBET) is proposed in this paper. The model consists of a global path, an edge path, and a feature aggregation module. In the global path, a de-redundant transformer module with explicit guidance is proposed, called Cascade-Axial-Prune Transformer (CAP-Trans). It is combined with CNN to form a hybrid architecture to generate a global representation of the target lesion. In the edge path, an edge detection operator is introduced to construct a lung nodule edge enhancement dataset, which improves the dataset utilization while providing more prior knowledge of the target lesion boundar. In addition, the Down-Attention Sample (DASample) as a basic encoding block is designed to effectively perceive local features of different ranges and scales in the down-sampling process of lung nodule feature extraction. Finally, a feature aggregation module is designed to fuse the outputs of the two paths to get the final segmentation result. Our DPBET can delineate the boundaries of various types of pulmonary nodules, with an average DSC of 89.86% and an average Sensitivity of 90.50% on the public dataset LIDC-IDRI. Compared with the state-of-the-art approaches, a substantial improvement has been achieved. The experimental results demonstrate that DPBET can use edge enhancement to promote the global-edge consistency relationship, and the network architecture is effective in lung nodule segmentation.

Vacancy clustering effect on the electronic and transport properties of bilayer graphene nanoribbons

Experimental realizations of two-dimensional materials are hardly free of structural defects such as e.g. vacancies, which, in turn, modify drastically its pristine physical defect-free properties. In this work, we explore effects due to point defect clustering on the electronic and transport properties of bilayer graphene nanoribbons, for AA and AB stacking and zigzag and armchair boundaries, by means of the tight-binding approach and scattering matrix formalism. Evident vacancy concentration signatures exhibiting a maximum amplitude and an universality regardless of the system size, stacking and boundary types, in the density of states around the zero-energy level are observed. Our results are explained via the coalescence analysis of the strong sizeable vacancy clustering effect in the system and the breaking of the inversion symmetry at high vacancy densities, demonstrating a similar density of states for two equivalent degrees of concentration disorder, below and above the maximum value.

On mixed finite element approximations of shape gradients in shape optimization with the Navier–Stokes equation

AbstractFor shape optimization of fluid flows governed by the Navier–Stokes equation, we investigate effectiveness of shape gradient algorithms by analyzing convergence and accuracy of mixed finite element approximations to both the distributed and boundary types of shape gradients. We present convergence analysis with a priori error estimates for the two approximate shape gradients. The theoretical analysis shows that the distributed formulation has superconvergence property. Numerical results with comparisons are presented to verify theory and show that the shape gradient algorithm based on the distributed formulation is highly effective and robust for shape optimization.

Numerical investigation on origin and evolution of polygonal cracks on rock surfaces

We studied the formation and evolution mechanism of polygonal cracks on rock surfaces under cooling by modelling meso-damage mechanics, continuum mechanics and thermodynamics. Factors that affect rock surface damage include ambient temperature, lithology difference and boundary restrictions. We established and simulated a heterogeneous model with a surface weak layer for three types of boundaries. These were biaxial constraint, uniaxial constraint and free boundary. The initiation and propagation of polygonal cracks were reproduced for varying thickness and homogeneity of the weak layer. The results show that the boundary constraints strongly influence the polygonal cracking. Many polygonal or parallel cracks are generated on the rock surface under biaxial or uniaxial constraint. The unconstrained rock surface displays polygonal cracks at the center and parallel cracks in the surrounding areas. The thicker the surface weak layer, the larger the average area of formed blocks. Small blocks and short cracks are more numerous than large blocks and long cracks. As the heterogeneity index increases, the rock layer is more likely to produce blocks with relatively regular shapes. Quadrilateral, pentagonal and hexagonal blocks dominate regardless of changes in layer thickness and heterogeneity. However, the number of edges of the polygonal blocks is sensitive to rock heterogeneity. The polygons tend to become more complex with increasing inhomogeneity. This study contributes to understanding the complex formation mechanisms of polygonal cracks on rock surfaces in nature. Additionally, the simulations of three-dimensional fracture geometry provide a basis for developing algorithms to generate discrete fractures and blocks in discrete fracture network (DFN) analyses.

Acoustic energy flux analysis of the bifurcated waveguide by varying outlet boundaries

This communication is devoted to the analysis of the energy flux of a two-dimensional waveguide with planar and non-planar surfaces. The main goal is to analyze the effects of reflected and transmitted energy fluxes of the bifurcated waveguide by varying the different types of outlet boundaries. The upper and lower boundaries of the inlet are taken as flexural in nature, whilst the outlet of the duct is varied by soft, rigid and impedance boundary conditions. The benchmark Mode-Matching (MM) technique is applied to solve the underlying boundary value problem (BVP). The system is excited with two types of incident forcing: fluid-borne incident and structure-borne incident. For a flexible inlet bounded by a membrane, the obtained eigenfunctions are linearly dependent and non-orthogonal in character. For sake of this, generalized orthogonality relations (OR) are developed. Additionally, the application of generalized OR led to the appearance of some dependent sums that are tackled using the fixed membrane edge conditions. The application of edge conditions led to the unique solution of the BVP. In the end, the expressions of reflected and transmitted energy fluxes are obtained and analyzed graphically against frequencies for different structural properties of the waveguide. Furthermore, it is shown that the conserved energy flux is valid, and reconstructed matching conditions are found in good accord.

Analytical model for transient pressure analysis in a horizontal well intercepting with multiple faults in karst carbonate reservoirs

In recent years, the Shunbei karst-carbonate reservoirs becomes a huge productivity oilfield, which produced over one million tonnes crude oil annually. However, there are difficulties in understanding production contribution of each fault-karst branch in reservoirs, which significantly impacts the efficient development. Multibranched fault-karst reservoirs in the Shunbei have an obvious tree-shaped geostructure, in which the natural fractures and eroded cave develop along multiple large-scale faults. The existing models for pressure transient analysis (PTA) were mainly established for fracture-cave reservoirs only with single fault, which cannot be applicable to characterize the multibranched fault-karst reservoir. To fill this gap, a novel analytical PTA model for horizontal commingled production well in the multibranched fault-karst reservoir was established to describe pressure response and identify flow regimes. First, our model includes the Darcy flow with the fluid compressibility effect in fracture region, and the large-scale vertical storage flow in cave region as well as the horizontal laminar flow in the horizontal wellbore. Then, the accuracy of this PTA model is verified by comparing it with the existing single branch fault-karst pressure model. Further, we applied the model to analyze the Shunbei oilfield case data. Last, the effect of boundary type, fluid compressibility effect, fracture physical properties, and cave spatial distribution on the pressure response are discussed in detail. The sensitivity analysis results show (a) the cave storage flow regime exhibits an obvious unit-slope-line on pressure derivative curve, at the time the skin transient flow constitutes a V-shape characteristic. (b) The number of fracture-cave branches can be directly obtained by counting the number of V-shaped appearances on the pressure derivative curve. (c) The fluid compressibility effect leads to an upward trend on the pressure and its derivative, reservoir engineers should be cautious to explain that characteristic as a closed boundary effect. (d) The cave volume and cave position control the timing of the V-shape occurring. As the cave volume increases, the linear flow regime lasts longer and the V-shaped feature becomes apparent. With the cave distance and cave depth increasing, the V-shape characteristic comes later. This work can provide technical support for accurate characterization of multibranched fault-karst reservoirs, and give a type curve analysis method for rapidly diagnosing the spatial location of each karst cavity by analyzing bottom-hole pressure.

Self-similar diffuse boundary method for phase boundary driven flow

Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such interactions include melting, sublimation, and deflagration, all of which exhibit bidirectional coupling, mass/heat transfer, and topological change of the solid–fluid interface. The diffuse interface method is a powerful technique that has been used to describe a wide range of solid-phase interface-driven phenomena. The implicit treatment of the interface eliminates the need for cumbersome interface tracking, and advances in adaptive mesh refinement have provided a way to sufficiently resolve diffuse interfaces without excessive computational cost. However, the general scale-invariant coupling of these techniques to flow solvers has been relatively unexplored. In this work, a robust method is presented for treating diffuse solid–fluid interfaces with arbitrary boundary conditions. Source terms defined over the diffuse region mimic boundary conditions at the solid–fluid interface, and it is demonstrated that the diffuse length scale has no adverse effects. To show the efficacy of the method, a one-dimensional implementation is introduced and tested for three types of boundaries: mass flux through the boundary, a moving boundary, and passive interaction of the boundary with an incident acoustic wave. Two-dimensional results are presented as well these demonstrate expected behavior in all cases. Convergence analysis is also performed and compared against the sharp-interface solution, and linear convergence is observed. This method lays the groundwork for the extension to viscous flow and the solution of problems involving time-varying mass-flux boundaries.

On numerical solution stability of the Laplace equation in absence of the Dirichlet boundary condition: Benchmark problem proposal

A fundamental 1D steady state diffusion problem using only third type boundary condition also named as the Robin or Fourier type is analysed. In the heat transfer problems this boundary condition is called convective boundary condition using heat transfer coefficient ( α ) as a constant. The main idea of the proposed Benchmark problem is to test the solution accuracy in both limiting cases of α approaching to zero and to infinity. The infinite case limits to Dirichlet boundary condition and should not be the problem, while the zero limit leads to trivial solution of zeros in the absence of the Dirichlet boundary condition. The application of the Benchmark would be in freeze drying, where similar boundary conditions occur. The presented BEM numerical solution failed for α > 1 0 13 in double precision computation for two 2D formulations: cartesian and axisymmetric. The low limit results failed for α < 1 0 − 13 for cartesian formulation. This is expected, while the failure of axisymmetric formulation results already at moderate low α < 1 0 − 3 value is not. The solution stability and accuracy are found strong dependent to the fundamental solution integrals accuracy. The effect of system matrix preconditioner is also studied.