Irregular Boundaries Research Articles

VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential equation can be formulated using variational principles. The semi-inverse method proves to be challenging in finding an appropriate variational principle for nonlinear problems and eliminating extraneous components from the studied model. We consider the coupled fractal–fractional KdV system with arbitrary coefficients and establish its variational formulation to unveil the remarkable insights into the energy structure of the model and interrelationships among coefficients. Encouraging results are obtained for this coupled KdV system.

Generalized variational principles for the modified Benjamin-Bona-Mahony equation in the fractal space

Because variational principles are very important for some methods to get the numerical or exact solutions, it is very important to seek explicit variational formulations for the non-linear PDE. At first, this paper describes the modified Benjamin-Bona-Mahony equation in fractal porous media or with irregular boundaries. Then, by designing skillfully the trial-Lagrange functional, variational principles are successfully established for the modified Benjamin-Bona-Mahony equation in the fractal space, respectively. Furthermore, the obtained variational principles are proved correct by minimizing the functionals with the calculus of variations.

Direct Numerical Simulation of liquid metal forced and mixed convection in a square rod bundle

This paper reports results of Direct Numerical Simulations of fully developed, forced and mixed convection of Liquid Lead Bismuth Eutectic (LBE) around four vertical cylindrical rods arranged in a square lattice at Pr = 0.031. The solutions provided here are placed in a context where very few data are available for low-Prandtl flows, especially in mixed convection conditions, and can hence be useful for the development and validation of advanced turbulent heat transfer models. The equations are discretized using a Finite Volume implementation of a second order projection method. The irregular cylindrical boundaries are handled with an original Immersed Boundary technique. A single friction Reynolds number value is set (Reτ = 180) and buoyancy effects are accounted for by imposing the Rayleigh number, under the Boussinesq approximation. A Ra-value Ra = 2.5 ×104 is selected in order to investigate the main differences between forced and mixed convection at low Prandtl number values. Time-averaged velocity and temperature fields are shown, in order to discuss the main features of the flow and thermal fields. First order statistics are also presented, highlighting the effect of aiding buoyancy on turbulent heat and momentum transport.

RECONSTRUCTION THE DOMAIN OF DEFINITION OF SOMEDIFFERENTIAL OPERATOR ON A DIRECTED GRAPH

In this work it is proposed to study differential operators on a graph as an operator composed of differential operators on one-dimensional arcs and matrix operators on interior vertices of the graph. The work explores some questions concerning the theoretical side of ordinary differential equations with integro-differential conditions on stratified sets like graph. The attention will be paid to reconstruction of the domain of differential operator on directed graph. The reconstruction of the domain of differential operator means a simple specifying the boundary conditions from a known differential equations and its known eigenvalues. The paper studies the case of the second order differential equations with irregular boundary conditions on the vertices of directed graph. To achieve our goal we use the fact that finite set of eigenvalues serves as additional information for reconstruction of the domain of the differential operator on stratified set. The constructive algorithms for reconstructing the domain of definition of differential operator on directed graph are developed. All boundary functions from the spectral data are uniquely restored.

Electrode microstructure design based on a CA-FD hybrid computation framework to alleviate the concentration polarization

The fast charging capability of lithium-ion batteries is considered as a critical requirement for the widespread replacement of fuel vehicles by electric ones. The high current applied in the fast charging process always causes concentration polarization due to the velocity difference between ionic diffusion and electron transport, which could lead to a low charging efficiency. The ionic diffusion velocities in both solid phase and liquid phase are strongly related to the microstructure of electrode particles. Based on the understanding of the reaction-diffusion mechanism, numerical simulation method is feasible to investigate the effect of microstructure on charging performance more economically. However, a two-dimensional model with the consideration of electrode microstructure consists of a set of highly coupled partial differential equations (PDEs), which is hard to be solved and inefficient with the irregular solid-liquid boundaries. Compared with PDEs, cellular automata (CA) is focused on the interaction between the adjacent discrete elements rather than solving the continuous variables across the whole region. According to this characteristic, mass transfer with complex solid-liquid boundaries can be simulated more conveniently by CA, but on the other hand, the restriction of applied current on the total reaction flux is hard to be considered in the CA model. Therefore, the diffusion part and the reaction part are processed by CA and finite difference (FD) method respectively. A CA-FD hybrid computation framework is proposed to consider the effect of microstructure on charging performances and visualize the concentration evolution inside the electrode particles. Based on this framework, the electrodes with uniform structure, porosity-layered structure and particle size-layered structure are constructed and applied in the charging simulations. According to the simulation results, the layered structures are beneficial for alleviating the concentration polarization in batteries, so that the charging efficiency of the electrodes can be improved without energy density loss by adopting these non-uniform structures in certain scenarios.

Deep Learning-Based Steel Bridge Corrosion Segmentation and Condition Rating Using Mask RCNN and YOLOv8

The application of deep learning (DL) algorithms has become of great interest in recent years due to their superior performance in structural damage identification, including the detection of corrosion. There has been growing interest in the application of convolutional neural networks (CNNs) for corrosion detection and classification. However, current approaches primarily involve detecting corrosion within bounding boxes, lacking the segmentation of corrosion with irregular boundary shapes. As a result, it becomes challenging to quantify corrosion areas and severity, which is crucial for engineers to rate the condition of structural elements and assess the performance of infrastructures. Furthermore, training an efficient deep learning model requires a large number of corrosion images and the manual labeling of every single image. This process can be tedious and labor-intensive. In this project, an open-source steel bridge corrosion dataset along with corresponding annotations was generated. This database contains 514 images with various corrosion severity levels, gathered from a variety of steel bridges. A pixel-level annotation was performed according to the Bridge Inspectors Reference Manual (BIRM) and the American Association of State Highway and Transportation Officials (AASHTO) regulations for corrosion condition rating (defect #1000). Two state-of-the-art semantic segmentation algorithms, Mask RCNN and YOLOv8, were trained and validated on the dataset. These trained models were then tested on a set of test images and the results were compared. The trained Mask RCNN and YOLOv8 models demonstrated satisfactory performance in segmenting and rating corrosion, making them suitable for practical applications.

Weakly supervised deep learning-based concrete aggregates automatic segmentation for assessing separation degree

Vision-based automatic concrete aggregate segmentation helps to facilitate fast quantitative analysis of concrete aggregate shape, gradation, and uniformity. However, existing methods are mainly based on supervised deep learning. Since concrete surface images often contain numerous aggregates with irregular sizes and boundaries, this leads to a time-consuming and labor-intensive data annotation process. To reduce annotation costs, this study proposes a weakly supervised deep learning (WSDL) concrete aggregates segmentation method, which can train accurate pixel-level concrete aggregates segmentation models using only low-cost bounding box-level annotation. A concrete aggregate segmentation dataset containing 1400 images is created and experiments are conducted. The results show that the proposed method can achieve pixel-level concrete aggregate segmentation with an AP50 of 95.27 %. Compared with the supervised deep learning-based method, the annotation cost is reduced by 86.24 %. This study also verifies the feasibility of the proposed method for quantitative evaluation of concrete aggregate segregation degree. Expert systems for automatic analysis of concrete aggregate gradation and uniformity can be developed based on this method in the future.

Investigation of the lattice Boltzmann method to resolve combined radiation-conduction heat transfer in participating media with curved boundaries

PurposePresent study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.Design/methodology/approachThe numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.FindingsFor the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.Originality/valueThe difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

Edge-Driven Multi-Agent Reinforcement Learning: A Novel Approach to Ultrasound Breast Tumor Segmentation.

A segmentation model of the ultrasound (US) images of breast tumors based on virtual agents trained using reinforcement learning (RL) is proposed. The agents, living in the edge map, are able to avoid false boundaries, connect broken parts, and finally, accurately delineate the contour of the tumor. The agents move similarly to robots navigating in the unknown environment with the goal of maximizing the rewards. The individual agent does not know the goal of the entire population. However, since the robots communicate, the model is able to understand the global information and fit the irregular boundaries of complicated objects. Combining the RL with a neural network makes it possible to automatically learn and select the local features. In particular, the agents handle the edge leaks and artifacts typical for the US images. The proposed model outperforms 13 state-of-the-art algorithms, including selected deep learning models and their modifications.

Garnet–Quartz Inclusion Thermobarometry and Lu–Hf Chronology Detail the Pre-Ultra-High Pressure Metamorphic History of the Grapesvare Nappe, Scandinavian Caledonides

Abstract The subduction–exhumation history of the Grapesvare nappe in the northern Seve Nappe Complex (Scandinavian Caledonides) is recorded by late Cambrian/Early Ordovician ultra-high pressure (UHP) and subsequent amphibolite facies metamorphic events. Records of these events obscured earlier metamorphic episodes that are important for understanding the tectonics of the orogen. To extract the pre–UHP metamorphic records, garnet Lu–Hf geochronology, Titanium-in-Quartz thermobarometry, and Quartz-in-Garnet elastic thermobarometry were applied to garnet porphyroblasts in metasedimentary rocks and eclogite. Metasedimentary rocks contain chemically homogeneous garnet (Grt-M1) with shape-matured quartz inclusions. In some rocks, these garnets are overgrown by garnet with bell-shaped Mn-zoning (Grt-M2) containing irregularly-shaped quartz inclusions. This evolution is interpreted as partial dissolution of Grt-M1 and subsequent growth of Grt-M2. Garnet in the eclogite is volumetrically dominated by eclogite-facies garnet (Grt-E1) that envelope remnants of an older, chemically distinct generation (Grt-E0) with highly irregular and diffuse boundaries. Shape-matured quartz inclusions are present within both garnet generations and define a zoning pattern that is not reflective of the chemical zoning. Collectively, these characteristics are interpreted as replacement of Grt-E0 by Grt-E1 via interface-coupled dissolution–reprecipitation, with the latter inheriting the shape-matured quartz inclusions of the former. Pressure–temperature (P–T) conditions extracted from the quartz inclusions in Grt-M1 and Grt-E0/E1 are 1.08 to 1.21 GPa at 645°C to 695°C and 0.94 to 1.03 GPa at 605°C to 640°C, respectively. These conditions are interpreted as cooling of the rocks from a high temperature metamorphic history, altogether preceding subduction of the Grapesvare nappe. The quartz inclusions in Grt-M2 record 1.04 to 1.21 GPa at 620°C to 675°C, interpreted as prograde metamorphic growth of Grt-M2 during subduction at 495.7 ± 3.2 Ma. Subsequent eclogite-facies metamorphism was responsible for the formation of Grt-E1 at the expense of Grt-E0. The collective results indicate a prolonged polymetamorphic history of the Grapesvare nappe prior to UHP metamorphism that has not been recognized previously.

On the origins of developmental robustness: modeling buffering mechanisms against cell-level noise.

During development, cells are subject to stochastic fluctuations in their positions (i.e. cell-level noise) that can potentially lead to morphological noise (i.e. stochastic differences between morphologies that are expected to be equal, e.g. the right and left sides of bilateral organisms). In this study, we explore new and existing hypotheses on buffering mechanisms against cell-level noise. Many of these hypotheses focus on how the boundaries between territories of gene expression remain regular and well defined, despite cell-level noise and division. We study these hypotheses and how irregular territory boundaries lead to morphological noise. To determine the consistency of the different hypotheses, we use a general computational model of development: EmbryoMaker. EmbryoMaker can implement arbitrary gene networks regulating basic cell behaviors (contraction, adhesion, etc.), signaling and tissue biomechanics. We found that buffering mechanisms based on the orientation of cell divisions cannot lead to regular boundaries but that other buffering mechanisms can (homotypic adhesion, planar contraction, non-dividing boundaries, constant signaling and majority rule hypotheses). We also explore the effects of the shape and size of the territories on morphological noise.

Simplification and Regularization Algorithm for Right-Angled Polygon Building Outlines with Jagged Edges

Building outlines are important for emergency response, urban planning, and change analysis and can be quickly extracted from remote sensing images and raster maps using deep learning technology. However, such building outlines often have irregular boundaries, redundant points, inaccurate positions, and unclear turns arising from variations in the image quality, the complexity of the surrounding environment, and the extraction methods used, impeding their direct utility. Therefore, this study proposes a simplification and regularization algorithm for right-angled polygon building outlines with jagged edges. First, the minimum bounding rectangle of the building outlines is established and populated with a square grid based on the smallest visible length principle. Overlay analysis is then applied to the grid and original buildings to extract the turning points of the outlines. Finally, the building orientation is used as a reference axis to sort the turning points and reconstruct the simplified building outlines. Experimentally, the proposed simplification method enhances the morphological characteristics of building outlines, such as parallelism and orthogonality, while considering simplification principles, such as the preservation of the direction, position, area, and shape of the building. The proposed algorithm provides a new simplification and regularization method for right-angled polygon building outlines with jagged edges.

Laser absorption tomography based on unstructured meshing

Laser absorption tomography is an imaging technique used to monitor gas flow and combustion processes. The measurement plane is typically discretized using square pixels in which the flow field is assumed to be uniform. This approach can introduce large discretization errors compared to a finite element mesh with linear interpolation, especially when the domain has an irregular and non-rectangular boundary. In this work, we assess the influence of triangular mesh and quadrilateral mesh schemes on reconstruction accuracy. Our theoretical analysis and numerical studies demonstrate that linear interpolation yields superior performance compared to the conventional uniform-pixel method, and the error can be reduced from 0.250 to 0.097 and 0.160 to 0.105 for triangular and quadrilateral meshes, respectively. Non-body-fitted mesh can increase error by 70 % –99 % . The experiment also proves the superiority of body-fitted meshes with linear interpolation. Moreover, triangular mesh exhibits better noise immunity than quadrilateral mesh. The reconstruction quality appears to be insensitive to the mesh quality for the quadrilateral mesh.

A correction function-based kernel-free boundary integral method for elliptic PDEs with implicitly defined interfaces

This work addresses a novel version of the kernel-free boundary integral (KFBI) method for solving elliptic PDEs with implicitly defined irregular boundaries and interfaces. We focus on boundary value problems and interface problems, which are reformulated into boundary integral equations and solved with the matrix-free GMRES method. In the KFBI method, evaluating boundary and volume integrals only requires solving equivalent but much simpler interface problems in a bounding box, for which fast solvers such as FFTs and geometric multigrid methods are applicable. For the simple interface problem, a correction function is introduced for both the evaluation of right-hand side correction terms and the interpolation of a non-smooth potential function. A mesh-free collocation method is proposed to compute the correction function near the interface. The new method avoids complicated derivation for derivative jumps of the solution and is easy to implement, especially for the fourth-order method in three space dimensions. Various numerical examples are presented, including challenging cases such as high-contrast coefficients, arbitrarily close interfaces and heterogeneous interface problems. The reported numerical results verify that the proposed method is both accurate and efficient.

Two-Stage Caving Characteristics of Complex Irregular Goaf: A Case Study in China

Different from the goaf formed by normal mining, the goaf formed by the continuous caving of the lower illegal goafs is extremely irregular and unstable, which leads to the difference in the goaf caving characteristics. Taking the complex irregular goaf of the Shirengou Iron Mine in China as the research object, the 3D laser scanning technology is used to detect the goaf shape and analyze the cause of the formation. Then, the caving characteristics of the goaf are analyzed by the methods of the numerical simulation, the monitoring of the crash of the caving rock, and the monitoring of the deformation of the arch foot. The simulation results show that the transverse expansion of the irregular goaf boundary is mainly along the perpendicular to the direction of the ore body strike when the goaf caves upward in the initial stage. Additionally, the monitoring results show that the caving characteristics can be divided into two stages: the paroxysmal caving stage and the periodicity caving stage. The paroxysmal caving characteristics are intense and irregular, while the periodicity caving characteristics have obvious periodicity, which is mainly reflected in the periodic alternation between the mass caving and the temporary stability. The interval period of the goaf mass caving is about 15–30 days and is changed by the progress of filling treatment. The conclusions in this work reveal the particularity of the caving characteristics in the complex irregular goaf and contribute to the improvement of the caving characteristics and the prediction of mass caving.

Chromium in minerals as tracer of the polycyclic evolution of eclogite and related metabasite from the Pohorje Mountains, Slovenian Eastern Alps

AbstractSignificantly different peak pressure–temperature (P–T) conditions (18–26 kbar and 630–760°C versus 29–37 kbar and 750–940°C) have previously been published for eclogite and related metabasites from the south‐eastern flank of the Pohorje Mountains in Slovenia. These rocks can show a bimodal distribution of chromium in the rock‐forming minerals, particularly garnet, the role of which in their metamorphic evolution is unclear. Therefore, we studied an eclogite and a related rock with clinopyroxene containing only 17 mol% jadeite + acmite (sample 18Ca35a). KαCr intensity maps of garnet particularly in sample 18Ca35a show a sharp irregular boundary between the core (Gt1) and the mantle (Gt2). Gt1 of millimetre‐sized garnet in this rock is nearly Cr‐free and unzoned, whereas Gt2 is of different composition (0.22 wt.% Cr2O3) and slightly zoned. Nearly Cr‐free amphibole, (clino)zoisite, kyanite and staurolite inclusions are present in Gt1. The matrix consists of garnet and Cr‐bearing clinopyroxene, (clino)zoisite and amphibole. Thermodynamic modelling suggests peak P–T conditions of 22.5 ± 2 kbar at 710 ± 25°C (Gt1) and 23 ± 2 kbar at 700 ± 25°C (Gt2) in both samples. We interpret these findings to suggest that olivine‐ and hornblende‐bearing gabbros with some chromite experienced early metamorphism in the eclogite facies, when Gt1 formed. The rock was subsequently exhumed and cooled leading to significant garnet corrosion. A second stage of metamorphism, recognized by mappable Cr contents in garnet, led to the growth of Gt2 and other Cr‐bearing minerals at the expense of chromite relics, which survived stage I. The peak P–T conditions of stage II are compatible with those previously derived by same authors and support the view that probably no ultrahigh‐pressure eclogite exists in the Pohorje Mountains. We relate the two metamorphic events to the Cretaceous and Palaeogene high‐pressure events recently reported from micaschists of the Pohorje Mountains.

Specificity autocorrelation integration network for surface defect detection of no-service rail

Rails are critical to the safe transportation of railway system, and their surface quality is a vital aspect to consider. Existing defect detection methods struggle to identify irregular defect boundaries and distinguish the similarity of foreground and background. To address these issues, depth images are introduced to detect rail defects. However, the existing RGB-D SOD methods usually fuse two modalities without considering modality-specific characteristics. In this paper, we propose a specificity autocorrelation integration network (SAINet) for surface defect detection of rails. SAINet enhances defect detection performance by exploring autocorrelation features of a single modality and the specificity of each modality. Two decoders are carefully designed to capture the specific characteristics of each modality. Moreover, we propose a cross-modal autocorrelation attention fusion (CAAF) to effectively utilize the two modalities of information. It obtains autocorrelation features of RGB images through dilated convolution and attention modules, introducing depth features to locate defects more accurately. We design a multi-modal feature integration block (MFIB) to supplement the cross-modal features with modality-specific features output by each individual decoder, in order to boost SOD performance. SAINet's performance is verified on the NEU RSDDS-AUG dataset. Our network achieves the best results compared to the 25 state-of-the-art methods. We also validate SAINet's generalization performance on six other benchmark datasets, where the experiments show it competes well on these datasets. The code and results are available at https://github.com/VDT-2048/SAINet.

New insight into the mandibular nerve at the foramen ovale level for percutaneous radiofrequency thermocoagulation.

Percutaneous radiofrequency thermocoagulation (RFTC) has been widely utilized in the management of trigeminal neuralgia. Despite using image guidance, accurate needle positioning into the target area still remains a critical element for achieving a successful outcome. This study was performed to precisely clarify the anatomical information required to ensure that the electrode tip is placed on the sensory component of the mandibular nerve (MN) at the foramen ovale (FO) level. The study used 50 hemi-half heads from 26 South Korean adult cadavers. The cross-sectioned anterior and posterior divisions of the MN at the FO level could be distinguished based on an irregular boundary and color difference. The anterior division was clearly brighter than the posterior one. The anterior division of the MN at the FO level was located at the whole anterior (38.0%), anteromedial (6.0%), anterior center (8.0%), and anterolateral (22.0%) parts. The posterior division was often located at the whole posterior or posterolateral parts of the MN at the FO level. The anterior divisions covered the whole MN except for the medial half of the posterolateral part in the overwrapped images of the cross-sectional areas of the MN at the FO level. The cross-sectional areas of the anterior divisions were similar in males and females, whereas those of the posterior divisions were significantly larger in males (P = 0.004). The obtained anatomical information is expected to help physicians reduce unwanted side effects after percutaneous RFTC within the FO for the MN.

Generalized finite difference method-based numerical modeling of oil–water two-phase flow in anisotropic porous media

This paper applies generalized finite difference method (GFDM) to a compressible two-phase flow in anisotropic porous media with the aim of further extending the wider application of this class of meshless methods. We develop an implicit Euler scheme in time and a GFDM discretization in space based on two treatments of the anisotropic permeability tensor in continuous function expression and discrete distribution. The effectiveness and generality of GFDM for two-phase flow problems in anisotropic porous media are verified by three examples with rectangular, irregular, and complex boundaries. Also, the computational performance of the method is verified according to the error calculation with L2 absolute error functions in different node collocation schemes. In addition, the sensitivity analysis of the radius of the influence domain to the transient pressure equation (parabolic equation) and the saturation equation (hyperbolic equation) is considered. It generally holds that the larger the radius of the influence domain, the lower the calculation accuracy in the case of Cartesian collocation. This may be a preliminary rule for the radius choice of the influence domain for GFDM. In sum, this work provides an efficient and accurate meshless solver to handle two-phase flow problems in anisotropic porous media under the GFDM framework, which reveals the great application potential of GFDM in reservoir numerical simulation.

Hardware-based security devices using a physical unclonable function created by the irregular grain boundaries found in perovskite calcium titanate

The IoT era necessitated the need for hardware-based security devices due to their strong resistance to hacking compared to software-based systems, which are limited by CPU usage and performance. Hardware-based systems are more unpredictable due to their unique and non-discernible external properties. This research focused on developing a security device based on lead-free metal oxide CaTiO3 perovskite material with irregular electrical characteristics, known as physical unclonable functions. These irregularities were created by increasing the number of grain boundaries on the device surface through high-temperature annealing, resulting in greater adsorbed oxygen. The outcome was a highly random and unique security key using irregular electrical characteristics with 49.53% uniformity and a 46.55% inter-Hamming distance.