Discontinuous Boundary Research Articles

Warped-Area Reparameterization of Differential Path Integrals

Physics-based differentiable rendering is becoming increasingly crucial for tasks in inverse rendering and machine learning pipelines. To address discontinuities caused by geometric boundaries and occlusion, two classes of methods have been proposed: 1) the edge-sampling methods that directly sample light paths at the scene discontinuity boundaries, which require nontrivial data structures and precomputation to select the edges, and 2) the reparameterization methods that avoid discontinuity sampling but are currently limited to hemispherical integrals and unidirectional path tracing. We introduce a new mathematical formulation that enjoys the benefits of both classes of methods. Unlike previous reparameterization work that focused on hemispherical integral, we derive the reparameterization in the path space. As a result, to estimate derivatives using our formulation, we can apply advanced Monte Carlo rendering methods, such as bidirectional path tracing, while avoiding explicit sampling of discontinuity boundaries. We show differentiable rendering and inverse rendering results to demonstrate the effectiveness of our method.

Phase Transformation Under High Pressure Radiates as a Double Couple Deep Earthquake

AbstractDeep‐focus earthquakes (DFEs) originating at the Mantle‐Transition‐Zone (MTZ) (400–700 km) have a Double Couple (DC) radiation pattern similar to crustal earthquakes; however, their mechanism is different and governed by high pressures (15–25 GPa) at nucleation depths. We present a model of nucleation and growth of regions of phase transformation, undergoing a sudden reduction in volume (5%–10%), “volume collapse.” Successive symmetry‐breaking instabilities minimize the energy spent to move the boundary of phase discontinuity and a collapsing volume expands as a flattened pancake‐like self‐similarly expanding Eshelby ellipsoidal inclusion. At the vanishing of the M integral, expressing the balance of flows of energy across the inclusion boundary, at a critical value of the pressure, an arbitrarily small inclusion nucleates and grows at constant potential energy driven by the pressure acting on the change in volume. The inclusion develops shear eigenstrains that decompose into two DC, placing one on the basal plane to radiate without energy losses. The symmetric volume collapse radiates out as an anti‐symmetric DC, and the radiated energy is obtained as the “excess energy,” of the ambient pressure acting on the “volume collapse,” reduced by the energy consumed for the growth of the pancake surfaces, with a “pressure drop” (p0 − pcr) driving the expansion emitting a DC, even under full isotropy. The solution explains some features of the DFEs, (a) the DC radiation, (b) their large energies (the Mw 8.3 Okhotsk earthquake [2013]), (c) the absence of volumetric radiation, and (d) why they can originate in the MTZ, a long‐standing open problem.

Rapid identification of erosion thinning and scaling thickening of inner wall of circular tube based on inverse heat conduction problem method

Due to the erosion of fluid and the deposition of fouling in pipes, the internal defects of pipelines are widespread and seriously threaten the safety of industrial production. In this paper, an indirect inversion model based on modified one-dimensional correction method (MODCM) is proposed to identify the erosion thinning and fouling deposition of the inner wall of a two-dimensional circular tube. By constructing the relationship between the equivalent thermal conductivity and the geometric parameters of defect, the inversion of defects is transformed into the inversion of the equivalent thermal conductivity, which overcomes the difficulty of re-gridding caused by the change of the geometric domain during the iterative process, and effectively improves the calculation efficiency. In order to explore the validity and timeliness of the constructed models, the numerical experiments are carried out. The influence of measurement errors, thermal conductivity of pipe and thermal conductivity of fouling on the identification results are systematically analyzed. The research results show that the thermal conductivities of pipes and fouling have little effect on the inversion results, and the inversion accuracy decreases with the increase of measurement errors. When the measurement error is σ = 0.5 ℃, the identification error remains about 0.2 %, which shows that the method has good robustness. In addition, compared with the typical direct identification models of Levenberg-Marquardt method (LMM) and conjugate gradient method (CGM), the proposed indirect inversion model is superior in computational efficiency and tracking ability of discontinuous boundaries.

Asymptotics of eigenvalues and eigenfunctions of a discontinuous boundary value problem with a spectral parameter in the transmission condition

We determine asymptotics of eigenvalues and eigenfunctions of a discontinuous boundary value problem with a spectral parameter in the transmission condition.

Modeling holes and voids in three dimensions using a single element within the Extended Finite Element framework

This paper introduces a highly efficient computational approach using the extended finite element method to model three-dimensional mechanics of holes and voids. The defect is encapsulated within a single element with a tailored exponential enrichment function that captures the behavior near the discontinuity boundary and can account for the pressure acting on the void’s surface through an equivalent nodal force vector. The method’s results were compared against analytical solutions and conventional finite element method results for problems involving single and multiple holes. The comparison demonstrated that the method provides accurate stress concentration estimates while adhering to computational constraints.

HTC-Net: A hybrid CNN-transformer framework for medical image segmentation

Automated medical image segmentation is a crucial step in clinical analysis and diagnosis, as it can improve diagnostic efficiency and accuracy. Deep convolutional neural networks (DCNNs) have been widely used in the medical field, achieving excellent results. The high complexity of medical images poses a significant challenge for many networks in balancing local and global information, resulting in unstable segmentation outcomes. To address the challenge, we designed a hybrid CNN-Transformer network to capture both the local and global information. More specifically, deep convolutional neural networks are introduced to exploit the local information. At the same time, we designed a trident multi-layer fusion (TMF) block for the Transformer to fuse contextual information from higher-level (global) features dynamically. Moreover, considering the inherent characteristic of medical image segmentation (e.g., irregular shapes and discontinuous boundaries), we developed united attention (UA) blocks to focus on important feature learning. To evaluate the effectiveness of our proposed approach, we performed experiments on two publicly available datasets, ISIC-2017, and Kvasir-SEG, and compared our results with state-of-the-art approaches. The experimental results demonstrate the superior performance of our approach. The codes are available at https://github.com/Tanghui2000/HTC-Net.

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

This paper investigates fracture mechanics in particle-reinforced composites by using the extended finite element method enhanced by the consecutive-interpolation quadrilateral element. These composite materials have discontinuous boundaries such as cracks, voids, holes, and soft inclusions. And the extended consecutive-interpolation quadrilateral element (XCQ4) is employed to model these boundaries in two-dimensional linear elastic deformation problems. XCQ4 combines the enrichment functions in the traditional extended finite element method with the consecutive interpolation on a 4-node quadrilateral element. This element uses both nodal values and averaged nodal gradients as interpolated conditions. In fracture analysis, the stress intensity factors (SIFs) are important parameters that must be defined. In this study, the values of SIFs at the crack tips are evaluated with the help of the interaction integrals approach. The obtained numerical results are compared with other reliable results showing high accuracy and convergence rate of the XCQ4 element.

A novel cross-layer dual encoding-shared decoding network framework with spatial self-attention mechanism for hippocampus segmentation

Accurate segmentation of the hippocampus from the brain magnetic resonance images (MRIs) is a crucial task in the neuroimaging research, since its structural integrity is strongly related to several neurodegenerative disorders, such as Alzheimer’s disease (AD). Automatic segmentation of the hippocampus structures is challenging due to the small volume, complex shape, low contrast and discontinuous boundaries of hippocampus. Although some methods have been developed for the hippocampus segmentation, most of them paid too much attention to the hippocampus shape and volume instead of considering the spatial information. Additionally, the extracted features are independent of each other, ignoring the correlation between the global and local information. In view of this, here we proposed a novel cross-layer dual Encoding-Shared Decoding network framework with Spatial self-Attention mechanism (called ESDSA) for hippocampus segmentation in human brains. Considering that the hippocampus is a relatively small part in MRI, we introduced the spatial self-attention mechanism in ESDSA to capture the spatial information of hippocampus for improving the segmentation accuracy. We also designed a cross-layer dual encoding-shared decoding network to effectively extract the global information of MRIs and the spatial information of hippocampus. The spatial features of hippocampus and the features extracted from the MRIs were combined to realize the hippocampus segmentation. Results on the baseline T1-weighted structural MRI data show that the performance of our ESDSA is superior to other state-of-the-art methods, and the dice similarity coefficient of ESDSA achieves 89.37%. In addition, the dice similarity coefficient of the Spatial Self-Attention mechanism (SSA) strategy and the dual Encoding-Shared Decoding (ESD) strategy is 9.47%, 5.35% higher than that of the baseline U-net, respectively, indicating that the strategies of SSA and ESD can effectively enhance the segmentation accuracy of human brain hippocampus.

Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems

In recent years, physics-informed neural networks (PINNs) have emerged as an alternative to conventional numerical techniques to solve forward and inverse problems involving partial differential equations (PDEs). Despite its success in problems with smooth solutions, implementing PINNs for problems with discontinuous boundary conditions (BCs) or discontinuous PDE coefficients is a challenge. The accuracy of the predicted solution is contingent upon the selection of appropriate hyperparameters. In this work, we performed hyperparameter optimization of PINNs to find the optimal neural network architecture, number of hidden layers, learning rate, and activation function for heat conduction problems with a discontinuous solution. Our aim was to obtain all the settings that achieve a relative L2 error of 10% or less across all the test cases. Results from five different heat conduction problems show that the optimized hyperparameters produce a mean relative L2 error of 5.60%.

Discontinuous quarter-point boundary elements revisited: Computation of T-stress in two-dimensional cracked components

This paper analyzes the use of discontinuous quarter-point quadratic elements in a dual or hypersingular boundary element context to compute the T-stress for cracked 2-D isotropic components. The performance of this approach has been demonstrated in the past for stress intensity factors (SIFs) computation and, herein, it is revisited to assess its adequacy for T-stress evaluation. To this end, novel direct extrapolation formulas that determine the T-stress from the computed nodal displacements at the collocation nodes of the discontinuous quarter-point element are proposed, and their accuracy and effectiveness is satisfactorily tested by several numerical examples involving 2-D cracked Carbon NanoTube (CNT) reinforced composites. SIFs extrapolated from the computed nodal crack opening displacements and T-stress evaluated from the computed stresses at internal points (close to the crack-tip) are also presented for completeness. The proposed techniques are a valid and easy-to-implement alternative to the interaction integral approaches when determining SIFs and T-stress.

N-body simulation of planetary formation through pebble accretion in a radially structured protoplanetary disk

Abstract In the conventional theory of planet formation, it is assumed that protoplanetary disks are axisymmetric and have a smooth radial profile. However, recent radio observations of protoplanetary disks have revealed that many of them have complex radial structures. In this study, we perform a series of N-body simulations to investigate how planets are formed in protoplanetary disks with radial structures. For this purpose, we consider the effect of continuous pebble accretion onto the discontinuity boundary within the terrestrial planet-forming region (∼0.6 au). We find that protoplanets grow efficiently at the discontinuity boundary, reaching the Earth mass within ∼104 yr. We confirm that giant collisions of protoplanets occur universally in our model. Moreover, we find that multiple planet-sized bodies form at regular intervals in the vicinity of the discontinuity boundary. These results indicate the possibility of the formation of solar system-like planetary systems in radially structured protoplanetary disks.

Mechanical properties and failure analysis of 3D-printing micron-scale ceramic-based triply periodic minimal surface scaffolds under quasi-static-compression and low-speed impact loads

Numerous developments in additive manufacturing have endowed triply periodic minimal surface (TPMS) structures with excellent mechanical properties, providing possibilities for the wide application prospects of such scaffolds in repairing bone defects. However, current studies mainly focus on the basic mechanical and biomedical properties of TMPS with relatively large scale and low precision made from conventional materials such as stainless powder. Therefore, challenges exist in manufacturing ceramic-based TPMS bone scaffolds that stratify the precision requirements for human bones at the micron scale and further investigating their dynamic mechanical properties. Herein, we successfully design and fabricate two TPMS scaffolds named TPMS-B and TPMS-C with microstructures similar to that of human bone utilizing advanced 3D-printing technology. The experiments reveal that TPMS-C outperforms conventional porous scaffold (Normal-A) and TPMS-B for certain parameters such as specific strength and specific energy absorption. Moreover, the numerical simulation analysis illustrates that structural asymmetry and discontinuous boundaries are the main causes of completely destructive disparities in TPMS-C when exposed to given loads. Meanwhile, the cytocompatibility and osteogenic differentiation of the three scaffolds are verified. The objective of this work is to reveal the mechanical properties and failure analysis of novel 3D-printing materials that can be used to fabricate advanced TPMS bone scaffolds for bone defects treatment.

Dissipative Instability of Magnetohydrodynamic Sausage Waves in a Compressional Cylindrical Plasma: Effect of Flow Shear and Viscosity Shear

The shear flow influences the stability of magnetohydrodynamic (MHD) waves. In the presence of a dissipation mechanism, flow shear may induce an MHD wave instability below the threshold of the Kelvin–Helmholtz instability, which is called dissipative instability. This phenomenon is also called negative energy wave instability because it is closely related to the backward wave, which has negative wave energy. Considering viscosity as a dissipation mechanism, we derive an analytical dispersion relation for the slow sausage modes in a straight cylinder with a discontinuous boundary. It is assumed that the steady flow is inside and dynamic and bulk viscosities are outside the circular flux tube under photospheric condition. When the two viscosities are weak, it is found that for the slow surface mode, the growth rate is proportional to the axial wavenumber and flow shear, consistent within the incompressible limit. For a slow body mode, the growth rate has a peak at a certain axial wavenumber, and its order of magnitude is similar to surface mode. The linear relationship between the growth rate and the dynamic viscosity established in the incompressible limit develops nonlinearly when the flow shear and/or the two viscosities are sufficiently strong.

Inhibiting segregation enabled outstanding combination of mechanical and corrosion properties in precipitation-strengthened aluminum alloys

Segregation of solutes to grain boundary (GB) is the dominant restriction on enhancement of mechanical properties and corrosion resistance during aging in precipitation-strengthened aluminum alloys. Here, we innovatively introduce the cyclic deformation by the vibration during aging to eliminate the GB segregation, resulting in the formation of the narrow precipitate-free zone (PFZ) widths near the GB, as well as the fine and discontinuous grain boundary precipitations (GBPs). Compared with the traditional peak-aging, the 2014 aluminum alloy treated by thermal cooperative vibration aging (TCVA) exhibits a superb combination of impact toughness and corrosion resistance, and retains the strength and ductility. In addition, the atomic simulations show that TCVA generates numerous vacancies near the GB, but does not change the dislocation density with the increase of cycle time. These results indicate that the vacancy significantly promotes the nucleation and growth of precipitates in the vicinity of GB, resulting in the narrow PFZs and fine discontinuous GBPs. The present work provides the fundamental knowledge and method to inhibit the equilibrium segregation of solutes to GB during aging, and further realizes the precipitation-strengthened aluminum alloys with excellent mechanical and corrosion properties.

Multiple reinforcement measures of flysch landslide.

This work is mainly intended to investigate the flysch landslide reinforcement measures used in the Smokovac-Mateševo section of the North-South Expressway project in Montenegro. Bentley's Plaxis software is used for a numerical analysis of sliding surface parameters of flysch strata in the limit equilibrium state. This study analyzes the slope safety factor for rreinforcement measures such as rock bolts, retaining walls, anti-sliding piles, slope unloading and bolt anchoring and obtains an optimal combination of reinforcement application for the flysch landslide. The effects of seismic action on complex stress and the discontinuous stress boundary conditions arising from various reinforcement measures on landslide stability are also examined. The measures applied in this paper can be used as a reference for flysch landslide reinforcement or other similar slope engineering measures.

A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

The present paper provides a new definition of the dual interpolation curve in a geometric-intuitive way based on adaptive curve refinement techniques. The dual interpolation curve is an implementation of the interpolatory subdivision scheme for curve modeling, which comprises polynomial segments of different degrees. Dual interpolation curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, and continuous and discontinuous boundary representation. In addition, the dual interpolation curve is mainly applied to solve the difficult geometry defeaturing problems for curve modeling in existing computer-aided technology. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual interpolation curve is flexible and convenient for characterizing a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of characterizing the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.

An error estimate for finite element approximation to elliptic PDEs with discontinuous Dirichlet boundary data

This note provides an error estimate for finite element approximation to elliptic partial differential equations (PDEs) with discontinuous Dirichlet boundary data. Solutions of problems of this type are not in H1 and, hence, the standard variational formulation is not valid. To circumvent this difficulty, an error estimate of a finite element approximation in the W1,r(Ω) (0<r<2) norm is obtained through a regularization by constructing a continuous approximation of the Dirichlet boundary data.

Renal ultrasound image segmentation method based on channel attention and GL-UNet11

Background and objectiveKidney tumor is one of the common malignant tumors of urinary system. However, rapid and accurate segmentation of kidney tissue is still a challenging problem in the medical image processing field on account of its obscure onset and uncertain and discontinuous boundary of its anatomical structure. We proposed a deep learning method globa-local UNet11 (GL-UNet11) for ultrasonic image segmentation of kidney, renal parenchyma and renal sinus, aiming at the inaccuracy of internal and marginal segmentation in ultrasonic image segmentation. MethodologyWe deepen the UNet network to make it more expressive, and propose a new channel attention network, Global Local network (GL-UNet), which takes into account the influence of global channel and local channel on predicting the importance of each channel, so that the network can better focus on important information. At the same time, the proposed global-local network is added to the convolutional block of the deepened UNet subsampling part, which effectively enhances the features of the important channels. ResultsThe Dice coefficient and the intersection over union (IOU) of our method reached 96.25% and 92.78% in the task of kidney segmentation. In the task of segmentating renal parenchyma, Dice coefficient reached 92.90% and IOU reached 86.75%. In the task of segmentating renal sinus, Dice coefficient reached 90.18% and IOU reached 82.12%, both of which were superior to other deep learning methods. ConclusionThe GL-UNet11 network proposed in this study compared with the previously proposed UNet and Segnet methods and SE-UNet, ECA-UNet and GL-UNet methods proposed in this paper, Great improvement has been made in both quantitative and qualitative parts. It has achieved good segmentation effect on the kidney segmentation data set, which is of great significance for the early detection and prognosis of kidney patients in the future.

Simulating pillar reinforcement using a displacement discontinuity boundary element code

In this study we explore the use of a novel numerical modelling approach to study the effect of pillar reinforcement on pillar stability. Case studies in the literature indicate that tendons, strapping of the pillars, and shotcrete or thin spray-on liners are commonly used to reinforce pillars. No clear methodology exists to select the type of support or to design the capacity of the support required, however. This has led to ongoing collapses in some mines in spite of heavy support being used to reinforce unstable pillars. A limit equilibrium model with confinement on the edge of the pillar was used to simulate the interaction of the support with the failing pillar. The model correctly predicts that an increase in confinement will lead to a decrease in the extent of pillar failure. As the displacement discontinuity boundary element method allows for the efficient solution of large-scale bord-and-pillar layouts, the effect of pillar confinement can now be studied on a mine-wide scale. Accurate calibration of the limit equilibrium model is, however, required before this method can be used for the design of effective pillar support.

Impedance Sensitivity Analysis Based on Discontinuous Isogeometric Boundary Element Method in Automotive Acoustics

Abstract Acoustic sensitivity analysis is an essential technique to determine the direction of structural-acoustic optimization by evaluating the gradient of the objective functions with respect to the design variables. However, acoustic sensitivity analysis with respect to acoustic impedance, which is an important parameter representing the interior absorbent material in automotive acoustics, is lacking in the study. Moreover, acoustic sensitivity analysis implemented with conventional numerical methods is time and effort-consuming in automotive acoustics, due to the large-scale mesh generation. In this work, the impedance sensitivity analysis for automotive acoustics based on the discontinuous isogeometric boundary element method is presented. The regularized boundary integral equation with impedance boundary conditions is established, then the sensitivity is derived by differentiating the boundary integral equation. The efficiency of the proposed method is improved by employing the parallel technique and generalized minimal residual solver. A long duct example with an analytical solution validates the accuracy of the proposed method, and an automotive passenger compartment subjecting to impedance boundary conditions illustrates that the computing time of the proposed method is one order of magnitude less than the conventional method. This work presents an easily implementable and efficient tool to investigate acoustic sensitivity with respect to impedance, showing great potential in the application of automotive acoustics.