Local Boundary Research Articles

Inverse Coefficient Problem for the 2D Wave Equation with Initial and Nonlocal Boundary Conditions

In this paper, we consider direct and inverse problems for the two-dimensional wave equation. The direct problem is an initial boundary value problem for this equation with nonlocal boundary conditions. In the inverse problem, it is required to find the time-variable coefficient at the lower term of the equation. The classical solution of the direct problem is presented in the form of a biorthogonal series in eigenvalues and associated functions, and the uniqueness and stability of this solution are proven. For solution to the inverse problem, theorems of existence in local, uniqueness in global, and an estimate of conditional stability are obtained. The problems of determining the right-hand sides and variable coefficients at the lower terms from initial boundary value problems for second-order linear partial differential equations with local boundary conditions have been studied by many authors. Since the nonlinearity is convolutional, the unique solvability theorems in them are proven in a global sense. In the works, the method of separation of variables is used to find the classical solution of the direct problem in the form of a biorthogonal series in terms of eigenfunctions and associated functions. The nonlocal integral condition is used as the overdetermination condition with respect to the solution of the direct problem. The direct problem reduces to equivalent integral equations of the Fourier method. To establish integral inequalities, the generalized Gronwall-Bellman inequality is used. We obtain an a priori estimate of the solution in terms of an unknown coefficient, that are useful for studying the inverse problem.

Electron microscopy characterization of proton irradiation induced growth in pure Zr

Irradiation induced growth is a constant volume shape change that occurs without externally applied stress that is observed in some materials under irradiation damage. Proton irradiation was carried out on a pure Zr sample to many dpa, to enable investigation of microscale aspects of the irradiation growth phenomenon. Irradiation induced a significant surface morphology change in the irradiated area, which is believed to be the result of the anisotropic growth behavior of the hcp structured Zr. The localized strain that developed was characterized by Electron back scatter diffraction (EBSD), on both the irradiated surface and on a cross sectional through-thickness plane. It was found that there is a correlation between the amount of local deformation and level of misorientation existing between two adjacent grains. The irradiation induced defect microstructure was characterized by transmission electron microscopy (TEM), showing 〈a〉 and 〈c〉 component loops similar to that generated by neutron irradiation in literature. Lastly, site specific focused ion beam (FIB) TEM lift-outs were prepared on local grain boundaries to investigate the origin of the localised deformation.

On territorial border markers of the settlement of Russians of the Middle Tom River region in the beginning of the 18th — mid 20th centuries

The concept of studying of ethnographic and archaeological complexes (EAC) involves the analysis of their individual components: population, villages, communication routes and others, including borders — both external and internal. The analysis of archaeological, historical, and ethnographic literature has shown that borders or borderlands can be traced in almost all populations at any stage of their development. However, while the borders between large associations, like states or ethnic groups with different cultures, have been addressed by experts, almost no attention is being given to local boundaries between smaller collectives, although there are written, cartographic and oral sources that can be used as a basis for such research. After considering the materials of various origins concerning the native villages of the Middle Tom region, it became possible to discuss the bounda-ries between them, and the boundaries of the administrative entities which encompassed them in the 18th century. At this time, residents of villages located 15–30 km north of the Kuznetsk fortress were moving to new unoccupied lands in the upper reaches of the river Inia and its upper tributaries, as well as to the left bank of Tom below the mouth of the Mungat River. According to the drawings of S.U. Remezov, there was a boundary between the Tomsk and Kuznetsk districts. The borderline rivers could be Unga-Promyshlennaya in the north and Osipovo-Mungat in the south. Possibly, there were small settlements of Tulbers. After the middle of the 19th century, an-other process of settlement of the Tom riverbank territories of its both sides began. By the 1930s, all its banks were inhabited, and the reserve of free lands came to end. Indigenous people began developing islands on the river or starting settlements within 15–20 km from the village. In the second third of the 20th century, new villages were developing in the remote territories away from Tom. Almost all of them were abandoned in the second half of the 20th century. The available information suggests that there were borderlands between the villages within single districts. Most often these were represented by watercourses — small rivers and streams, ridges — elon-gated hills located perpendicular to terraces, and sometimes lakes. These borders were well known to locals. It cannot be ruled out that river rapids and shoals could also have been used as borders. The analysis of the corre-lation of locations of the villages, river rifts and stretches suggests that, in the studied area of Tom, villages were located on the river stretches between the shoals. There is also information about the existence of boundaries between minor objects, though they require further research.

Analytic solution for two dimensional beam problems: Pure displacement boundary conditions

The present manuscript delineates the derivation of strong solutions for the linear elasticity problem in a two dimensional rectangular beam. The materials under consideration can exhibit either isotropic or orthotropic properties. Additionally, the analysis is not restricted to slender beams because the ratio between the length and the height of the beam can be arbitrary. The boundary conditions fall into the Dirichlet category, implying that both horizontal and vertical displacements are specified on all four surfaces. The sole requirement is that these surface displacements are continuous functions, although they may not necessarily be smooth. Since the displacements at the surfaces can be arbitrary, there is no need to consider approximations, such as those concerning local (small) boundaries in slender beams. Nonetheless, it is demonstrated that an equivalent principle to the Saint-Venant principle exists for pure displacement boundary conditions. The partial differential equations are solved through the separation of variables method, leading to the identification of two solution types, encompassing both cosine and sine Fourier series. Particular emphasis is placed on evaluating the convergence of these solutions. For two distinct and general examples, it is confirmed that the solutions indeed exist.

Nonlocal Problems with Local Boundary Conditions I: Function Spaces and Variational Principles

Nonlocal Problems with Local Boundary Conditions I: Function Spaces and Variational Principles

Revealing molecular insights into surface charge and local viscosity in electroosmotic flows

The limitations of the continuum theory in predicting osmotic response at the nanoscale stem from its lack of molecular-level insight into local fluid properties and the interfacial structure of fluid and electrolyte solutions. To overcome this challenge, our study integrates molecular dynamics (MD) simulation with the continuum framework to explore how surface charge and various hydrodynamic properties impact electroosmotic flow (EOF). The failure of continuum theories to account for molecular interactions and geometric boundaries leads to significant disparities between MD simulations and continuum predictions, influenced by local fluid properties and the electric field. Emphasizing the importance of incorporating appropriate local hydrodynamic properties and atomic interface boundary conditions, our findings bridge the gap between MD simulations and continuum EOF predictions. Our computational results and theoretical model, considering surface charge, atomic interface boundaries, and dynamic structure-based hydrodynamic properties, provide crucial insights and guidance for EOF investigations.

Complex phases in quantum mechanics

Schrödinger's equation is a local differential equation and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a given Hamiltonian may describe several different physically observable phases, each exhibiting its own characteristic global symmetry.

An aerodynamic digital twin of real-world leading edge erosion: Acquisition, Generation and 3D CFD

Wind turbine blades face extremely challenging environmental conditions over their operating life-time, that can easily exceed 2 decades. Airborne particles (insects, sand, rain, hail, ice, sea spray etc.) strike the blade leading edge (LE) first and erode or attach to it, roughening its surface. Leading edge roughness (LER) can critically alter the aerodynamic performance of blades, as its aerodynamic impact is strongly coupled to its height with respect to the local boundary layer thickness, which is thinnest around the LE. The actual, detailed topographic manifestation of LER on in-service blades—needed to accurately assess its aerodynamic impact—is highly probabilistic, as it depends on the interaction of multiple stochastic parameters, like the environmental conditions, material composition and production process. Yet little high-resolution topographic LER data of this kind is currently available. This paper details how such data is collected from blades of different turbine manufacturers and processed consistently to build digital twins of the measured LER, that can be analysed aerodynamically using 3D CFD or wind tunnels. Here a special focus lies on how to reconstruct the LER topography and build the computational mesh such that the correct aerodynamic response is observed. For this purpose multiresolution signal decomposition is used to process the topographies and a special meshing procedure established.

Exploring circular economy transition pathways: a roadmap analysis of 15 Canadian local governments

Abstract This paper explores how 15 Canadian local governments of various sizes and contexts are transitioning to a circular economy by analysing their roadmap currently in development. It provides qualitative insights into how physical, socioeconomic and institutional factors are influencing the content of roadmaps, along with their similarities and differences. Drawing from the literature on the geography of transitions, we show that while local physical and socioeconomic attributes typically shape the roadmaps by determining likely activities, their actual trajectory varies based on the roadmap instigators and the broader institutional contexts in which they operate. The findings suggest the importance of local governments supporting the roadmap instigators while also recognising that circular economy transition pathways can capitalise on policies and programs not only locally but beyond local boundaries.

Beyond local boundaries: Unraveling the spatiality of entrepreneurial ecosystems

The underlying rationale of Entrepreneurial Ecosystems (EE) interactions is essentially attached to geographical space. So far, literature remains largely focused on a shortsighted notion of EE as ‘insular’ systems. In this article we address the spatial dynamics of two ecosystems based on the inflow of venture capital over the last three decades. Drawing from the cases of Tokyo and Bangalore, our key insight is that the EE configurations cannot be properly understood without a clear assessment of its spatial features. i.e., the geographical scope of connections that compose EE. As it turns out, EE present heterogeneous spatialities – and these evolve along different trajectories. This, we believe, is a key missing piece of the EE theoretical puzzle.

Robust detection and refinement of saliency identification

Salient object detection is an increasingly popular topic in the computer vision field, particularly for images with complex backgrounds and diverse object parts. Background information is an essential factor in detecting salient objects. This paper suggests a robust and effective methodology for salient object detection. This method involves two main stages. The first stage is to produce a saliency detection map based on the dense and sparse reconstruction of image regions using a refined background dictionary. The refined background dictionary uses a boundary conductivity measurement to exclude salient object regions near the image's boundary from a background dictionary. In the second stage, the CascadePSP network is integrated to refine and correct the local boundaries of the saliency mask to highlight saliency objects more uniformly. Using six evaluation indexes, experimental outcomes conducted on three datasets show that the proposed approach performs effectively compared to the state-of-the-art methods in salient object detection, particularly in identifying the challenging salient objects located near the image's boundary. These results demonstrate the potential of the proposed framework for various computer vision applications.

YOLOv8-MU: An Improved YOLOv8 Underwater Detector Based on a Large Kernel Block and a Multi-Branch Reparameterization Module.

Underwater visual detection technology is crucial for marine exploration and monitoring. Given the growing demand for accurate underwater target recognition, this study introduces an innovative architecture, YOLOv8-MU, which significantly enhances the detection accuracy. This model incorporates the large kernel block (LarK block) from UniRepLKNet to optimize the backbone network, achieving a broader receptive field without increasing the model's depth. Additionally, the integration of C2fSTR, which combines the Swin transformer with the C2f module, and the SPPFCSPC_EMA module, which blends Cross-Stage Partial Fast Spatial Pyramid Pooling (SPPFCSPC) with attention mechanisms, notably improves the detection accuracy and robustness for various biological targets. A fusion block from DAMO-YOLO further enhances the multi-scale feature extraction capabilities in the model's neck. Moreover, the adoption of the MPDIoU loss function, designed around the vertex distance, effectively addresses the challenges of localization accuracy and boundary clarity in underwater organism detection. The experimental results on the URPC2019 dataset indicate that YOLOv8-MU achieves an mAP@0.5 of 78.4%, showing an improvement of 4.0% over the original YOLOv8 model. Additionally, on the URPC2020 dataset, it achieves 80.9%, and, on the Aquarium dataset, it reaches 75.5%, surpassing other models, including YOLOv5 and YOLOv8n, thus confirming the wide applicability and generalization capabilities of our proposed improved model architecture. Furthermore, an evaluation on the improved URPC2019 dataset demonstrates leading performance (SOTA), with an mAP@0.5 of 88.1%, further verifying its superiority on this dataset. These results highlight the model's broad applicability and generalization capabilities across various underwater datasets.

Unsteady cylinder wakes from arbitrary bodies with differentiable physics-assisted neural network.

This work describes a hybrid predictive framework configured as a coarse-grained surrogate for reconstructing unsteady fluid flows around multiple cylinders of diverse configurations. The presence of cylinders of arbitrary nature causes abrupt changes in the local flow profile while globally exhibiting a wide spectrum of dynamical wakes fluctuating in either a periodic or chaotic manner. Consequently, the focal point of the present study is to establish predictive frameworks that accurately reconstruct the overall fluid velocity flowfield such that the local boundary layer profile, as well as the wake dynamics, are both preserved for long time horizons. The hybrid framework is realized using a base differentiable flow solver combined with a neural network, yielding a differentiable physics-assisted neural network (DPNN). The framework is trained using bodies with arbitrary shapes, and then it is tested and further assessed on out-of-distribution samples. Our results indicate that the neural network acts as a forcing function to correct the local boundary layer profile while also remarkably improving the dissipative nature of the flowfields. It is found that the DPNN framework clearly outperforms the supervised learning approach while respecting the reduced feature space dynamics. The model predictions for arbitrary bodies indicate that the Strouhal number distribution with respect to spacing ratio exhibits similar patterns with existing literature. In addition, our model predictions also enable us to discover similar wake categories for flow past arbitrary bodies. For the chaotic wakes, the present approach predicts the chaotic switch in gap flows up to the mid-time range.

A large-scale graph clustering method for cell conditions spatio-temporal localization in aluminum electrolysis

Sensor nodes (industrial nodes) clustering is an efficacious method for gaining local working conditions real-timely in the production process. The existing deep graph neural networks-based industrial nodes clustering studies construct static graphs to describe the potential spatial correlation among industrial nodes, but the temporal correlation among industrial nodes is ignored, resulting in inferior real-time performance. Meanwhile, these deep learning models fail to obtain good clustering results due to the large-scale and noise-containing characteristics of industrial nodes. In this paper, a large-scale graph clustering method (LsGCM) is proposed for cell conditions spatio-temporal localization in aluminum electrolysis to address the above issues. Specifically, a spatio-temporal graph construction method based on industrial process mechanism knowledge and local working condition boundary types statistical feature fusion is proposed for capturing effective spatio-temporal correlations between industrial nodes. Then, hysteresis knowledge of industrial production system is used to guide the nodes merging, thereby avoiding the incorrect merging of time-asynchronous nodes when performing the spatio-temporal region detection of local working conditions. Finally, combined with the actual spatio-temporal location information of industrial nodes, a novel spatio-temporal information expansion method (StIEM) of the sub-spatio-temporal graph describing local working condition is proposed for obtaining spatio-temporal feature information of the neighborhood, which is beneficial to improve the performance of industrial node clustering. Validation studies on a numerical simulation example and multiple real aluminum electrolysis industrial datasets certificate the effectiveness and superiority of the proposed method. In particular, compared with existing graph clustering methods, our method improves the clustering accuracy by 7.79%.

MDER-Net: A Multi-Scale Detail-Enhanced Reverse Attention Network for Semantic Segmentation of Bladder Tumors in Cystoscopy Images

White light cystoscopy is the gold standard for the diagnosis of bladder cancer. Automatic and accurate tumor detection is essential to improve the surgical resection of bladder cancer and reduce tumor recurrence. At present, Transformer-based medical image segmentation algorithms face challenges in restoring fine-grained detail information and local boundary information of features and have limited adaptability to multi-scale features of lesions. To address these issues, we propose a new multi-scale detail-enhanced reverse attention network, MDER-Net, for accurate and robust bladder tumor segmentation. Firstly, we propose a new multi-scale efficient channel attention module (MECA) to process four different levels of features extracted by the PVT v2 encoder to adapt to the multi-scale changes in bladder tumors; secondly, we use the dense aggregation module (DA) to aggregate multi-scale advanced semantic feature information; then, the similarity aggregation module (SAM) is used to fuse multi-scale high-level and low-level features, complementing each other in position and detail information; finally, we propose a new detail-enhanced reverse attention module (DERA) to capture non-salient boundary features and gradually explore supplementing tumor boundary feature information and fine-grained detail information; in addition, we propose a new efficient channel space attention module (ECSA) that enhances local context and improves segmentation performance by suppressing redundant information in low-level features. Extensive experiments on the bladder tumor dataset BtAMU, established in this article, and five publicly available polyp datasets show that MDER-Net outperforms eight state-of-the-art (SOTA) methods in terms of effectiveness, robustness, and generalization ability.

Stress-Equivalent Spalart–Allmaras Wall Model with Local Boundary Conditions for Reynolds-Averaged Navier–Stokes

In this paper, we present a wall model based on a modified version of the Spalart–Allmaras turbulence model. Unlike typical wall models, this method avoids the need to query the interior solution by utilizing solution information solely at the boundary, making it well-suited for unstructured grids and mesh adaptation. Furthermore, this wall-modeling method is formulated to lessen the near-wall grid resolution requirements by, below the log layer, making the eddy viscosity approach a constant, nonzero value and the velocity varying approximately linearly with distance from the wall. Using output-based mesh adaptation, this new wall-modeling method is compared to standard Reynolds-Averaged Navier-Stokes (RANS-SA). It is shown that this wall model results in accurate predictions of quantities of interest such as aerodynamic coefficients, surface pressure and temperature, skin friction, and heat transfer compared with RANS-SA, while requiring substantially less near-wall grid.

Investigating the Interaction Between Transboundary Haze and Planetary Boundary Layer in Singapore

AbstractTransboundary air pollution is one of the critical environmental problems in Southeast Asia; nevertheless the interaction between transboundary haze and local planetary boundary layer (PBL) remains unclear due to a lack of sufficient observations and sophisticated simulations. This study applied LiDAR observations and model simulations to comprehensively evaluate the interaction between transboundary haze and local PBL during a recent transboundary haze episode in Singapore in October 2023. Results show that upper‐level southeasterly wind, especially the nocturnal low‐level jet, created favorable conditions for aerosol transport when fire hotspot numbers increased in Indonesia. The rapid diurnal increase in PBL height facilitated the entrainment of upper‐level haze into the PBL, interacting with ground‐level aerosols through turbulent mixing. Model simulations further show the significant contributions of fire emissions to the transboundary haze episode in maritime Southeast Asia. The impacts extended toward the southern region of Peninsular Malaysia, driven by the persistent prevailing southeasterly wind.

BMB-LIME: LIME with modeling local nonlinearity and uncertainty in explainability

The majority of eXplainable Artificial Intelligence (XAI) methods assume the local linearity of the decision boundary, leading to significant errors when dealing with non-linear local decision boundaries. Moreover, explanation methods relying on perturbation samples yield only a constant value for feature contributions. This study aims to overcome these limitations by introducing a novel explanation method that accurately captures non-linear local classification boundaries or regression splines while also quantifying the uncertainty associated with each feature contribution. Expanding upon the state-of-the-art XAI method, Local Interpretable Model-agnostic Explanations (LIME), we propose a nonlinear local explainer called BMB-LIME (Bootstrap aggregating Multivariate adaptive regression splines Bayesian LIME). BMB-LIME is constructed using weighted multivariate adaptive regression splines (MARS) with bootstrap aggregating and models the uncertainty of feature contributions within a Bayesian framework. Through a series of experiments, we demonstrate the superior performance of the BMB-LIME local explainer over baseline methods in terms of local fidelity and stability. Its adjusted r-squared is statistically significant by at least 80.5 percent, and it consistently demonstrates over 89.1 percent consistency in feature contribution and Jaccard similarity across diverse real-world and simulated datasets. The proposed method not only enhances fidelity and stability but also improves the measurement of uncertainty in explanations, thereby significantly contributing to the trustworthiness and transparency of XAI.

Unfolding rotational tectonics and topographic evolution from localized verses diffuse plate boundary counterparts

We present a kinematic model developed from geodetic observations, topography analysis and analogue tectonic modelling results, which reveals a striking similarity between the rotational tectonic settings of the Gakkel Ridge-Chersky Range system in the Arctic, and the Central Indian Tectonic Zone within the Indian subcontinent. A crucial aspect of large-scale extensional rift systems is the gradual variation of extension along the rift axis, due to plate rotation about a Euler pole, which may lead to contraction on the opposite side of the Euler pole to form a rotational tectonic system. Our geodetic and topographic analysis, combined with the reanalysis of analogue tectonic modelling results demonstrates such rotational tectonic plate motion in both the Arctic and Indian case. However, the plate boundary between the North American and Eurasian Plates as represented by the Arctic Gakkel Ridge-Chersky Range system is strongly localized, whereas the Central Indian Tectonic Zone that separates the North and South India Plates involves diffuse deformation instead. Furthermore, in both the Arctic and Central Indian we find that the relative Euler rotation pole is located near an indenter-like feature, which possibly controls the present-day rotational tectonics and contrasting topography on opposite sides of the Euler pole.

Sensitivity of simulation of rapidly intensified tropical cyclones to local planetary boundary layer scheme

Sensitivity of simulation of rapidly intensified tropical cyclones to local planetary boundary layer scheme