Boundary Data Research Articles

Efficient thermodynamic model optimization and uncertainty quantification via integration of combinatorial materials chip and Bayesian approach

Combinatorial materials chips (CMC) are composition spread thin-films deposited on a substrate that can rapidly determine the compositional-temperature information of ternary phase diagrams by high-throughput characterization. In this study, phase boundary information determined by CMC from the recent studies was used as input to optimize the thermodynamic model parameters by ESPEI based on Bayesian approach. The uncertainties in the model were also quantified. Fe–Cr–Ni and Fe–Co–Ni systems were chosen as examples to demonstrate the effectiveness of process. The newly optimized phase diagrams are in good agreement with the experimental results. It is also verified that the model can be effectively optimized by the dense CMC phase boundary data only without including the scattered experimental data. Moreover, the uncertainty in the model is reduced with the addition of CMC data. Finally, probability distributions of various phase combinations in the phase diagram were calculated, providing confidence intervals for material design.

The p–Laplace “Signature” for Quasilinear Inverse Problems with Large Boundary Data

The <i>p</i>–Laplace “Signature” for Quasilinear Inverse Problems with Large Boundary Data

Continuous curvature wayline generation using quadratic optimisation for agricultural machine guidance

Navigation systems are widely used in precision agriculture to improve efficiencies and yields. These systems guide agricultural machines to follow waylines calculated based on specific traffic patterns, including straight and curved waylines. While generating straight waylines is relatively straightforward, generating curved waylines presents challenges due to the variation in their shape and curvature during propagation, which can lead to skips and overlaps between adjacent waylines.In this paper, we present a novel method to curved wayline generation by formulating the problem as a non-linear optimisation problem, as opposed to using geometry operations like existing methods. With the designed objective function and constraints, the problem is reduced to a quadratic optimisation problem that can be efficiently solved, and the generated waylines satisfy the curvature constraint, while minimising skips and overlaps. The functionality and applicability of the method were demonstrated with a simulation experiment, the comparison tests with geometric methods, and a field test. Our algorithm achieved coverage over 97%, with overlap and skip rates lower than 0.8% and 2.3%, respectively. The results indicate that our algorithm can generate smooth, continuous curvature waylines with high coverage and low skip/overlap. Furthermore, our algorithm can also generate straight waylines when the input reference line is a straight AB line. This algorithm can be used as a wayline planning component of navigation system for agricultural machines and robots. The code and boundary data utilised in the "Results and Discussion" section are accessible online at https://github.com/prefect-of-gryffindor/curve-wayline-generation.

Finite Element Analysis Of a Real Man-made Disaster

Many software is used to analyse the effects of an explosion and its impact on other objects. ANSYS Autodyn is one such software. In this study, a real chemical weapons attack event that took place in Khan Sheikhoun, Syria on 4 April 2017 was simulated using ANSYS Autodyn software using the finite element method. The software was used to analyse whether the crater formed after the bombing event, whose boundary conditions (type and properties of the munition, properties of the ground, velocity of the munition and height of fall) and data are known, will be formed as a result of this collision and explosion. Looking at the results of the study, it can be seen that at the end of 6 different simulations, and especially as a result of the sixth simulation, the crater diameter converged to the real values by 97% and the crater depth by 92.4%. This strengthens the assumption that the ammunition in question was used in this incident.

Systems involving mean value formulas on trees

Abstract In this paper, we study the Dirichlet problem for systems of mean value equations on a regular tree. We deal both with the directed case (the equations verified by the components of the system at a node in the tree only involve values of the unknowns at the successors of the node in the tree) and the undirected case (now the equations also involve the predecessor in the tree). We find necessary and sufficient conditions on the coefficients in order to have existence and uniqueness of solutions for continuous boundary data. In a particular case, we also include an interpretation of such solutions as a limit of value functions of suitable two-players zero-sum games.

Estimating two time-varying reaction coefficients in a water quality model from inexact initial and boundary data

Estimating two time-varying reaction coefficients in a water quality model from inexact initial and boundary data

Local and global regularity for the Stokes and Navier-Stokes equations with boundary data in the half-space

Local and global regularity for the Stokes and Navier-Stokes equations with boundary data in the half-space

Data-driven approaches for electrical impedance tomography image segmentation from partial boundary data

Data-driven approaches for electrical impedance tomography image segmentation from partial boundary data

Weak limit of homeomorphisms in W1,n−1: Invertibility and lower semicontinuity of energy

Let Ω, Ω′ ⊂ ℝn be bounded domains and let fm: Ω → Ω′ be a sequence of homeomorphisms with positive Jacobians Jfm &gt; 0 a.e. and prescribed Dirichlet boundary data. Let all fm satisfy the Lusin (N) condition and supm ∫Ω( |D fm|n - 1 + A( |cof D fm|) + φ(Jf)) &lt; ∞, where A and φ are positive convex functions. Let f be a weak limit of fm in W1,n−1. Provided certain growth behaviour of A and φ, we show that f satisfies the (INV) condition of Conti and De Lellis, the Lusin (N) condition, and polyconvex energies are lower semicontinuous.

Coefficient inverse problem for anisotropic time-domain wave equation

In this paper, we investigate an inverse problem of determining coefficient via partial boundary data in anisotropic media. More precisely, we study a scheme for asymptotic reconstruction on coefficient inverse problem for anisotropic time-domain wave equation by a geometric control method. As an initial attempt, it seems natural to treat the case of two dimensional Euclidean space in analogy with many other well-known inverse boundary problems.

Uniqueness and numerical resolution via iterated sensitivity equation of an inverse electromagnetic coefficient problem with partial boundary data

Uniqueness and numerical resolution via iterated sensitivity equation of an inverse electromagnetic coefficient problem with partial boundary data

A Feature-Oriented Reconstruction Method for Surface-Defect Detection on Aluminum Profiles

The number of defect samples on the surface of aluminum profiles is small, and the distribution of abnormal visual features is dispersed, such that the existing supervised detection methods cannot effectively detect undefined defects. At the same time, the normal texture of the aluminum profile surface presents non-uniform and non-periodic features, and this irregular distribution makes it difficult for classical reconstruction networks to accurately reconstruct the normal features, resulting in low performance of related unsupervised detection methods. Aiming at such problems, a feature-oriented reconstruction method of unsupervised surface-defect detection method for aluminum profiles is proposed. The aluminum profile image preprocessing stage uses techniques such as boundary extraction, background removal, and data normalization to process the original image and extract the image of the main part of the aluminum profile, which reduces the influence of irrelevant data features on the algorithm. The essential features learning stage precedes the feature-optimization module to eliminate the texture interference of the irregular distribution of the aluminum profile surface, and image blocks of the area images are reconstructed one by one to extract the features through the mask. The defect-detection stage compares the structural similarity of the feature images before and after the reconstruction, and comprehensively determines the detection results. The experimental results improve detection precision by 1.4% and the F1 value by 1.2% over the existing unsupervised methods, proving the effectiveness and superiority of the proposed method.

Boundary regularity results for minimisers of convex functionals with (p, q)-growth

Abstract We prove improved differentiability results for relaxed minimisers of vectorial convex functionals with ( p , q ) \left(p,q) -growth, satisfying a Hölder-growth condition in x x . We consider both Dirichlet and Neumann boundary data. In addition, we obtain a characterisation of regular boundary points for such minimisers. In particular, in case of homogeneous boundary conditions, this allows us to deduce partial boundary regularity of relaxed minimisers on smooth domains for radial integrands. We also obtain some partial boundary regularity results for non-homogeneous Neumann boundary conditions.

On the convergence of the Willmore flow with Dirichlet boundary conditions

Very little is yet known regarding the Willmore flow of surfaces with Dirichlet boundary conditions. We consider surfaces with a rotational symmetry as initial data and prove a global existence and convergence result for solutions of the Willmore flow with initial data below an explicit, sharp energy threshold. Strikingly, this threshold depends on the prescribed boundary conditions — it can even be made to be 0. We show sharpness for some critical boundary data by constructing surfaces above this energy threshold so that the corresponding Willmore flow develops a singularity. Finally, a Li–Yau inequality for open curves in H2 is proved.

Long‐time asymptotics and the radiation condition with time‐periodic boundary conditions for linear evolution equations on the half‐line and experiment

AbstractThe asymptotic Dirichlet‐to‐Neumann (D‐N) map is constructed for a class of scalar, constant coefficient, linear, third‐order, dispersive equations with asymptotically time/periodic Dirichlet boundary data and zero initial data on the half‐line, modeling a wavemaker acting upon an initially quiescent medium. The large time asymptotics for the special cases of the linear Korteweg‐de Vries and linear Benjamin–Bona–Mahony (BBM) equations are obtained. The D‐N map is proven to be unique if and only if the radiation condition that selects the unique wave number branch of the dispersion relation for a sinusoidal, time‐dependent boundary condition holds: (i) for frequencies in a finite interval, the wave number is real and corresponds to positive group velocity, and (ii) for frequencies outside the interval, the wave number is complex with positive imaginary part. For fixed spatial location , the corresponding asymptotic solution is (i) a traveling wave or (ii) a spatially decaying, time‐periodic wave. The linearized BBM asymptotics are found to quantitatively agree with viscous core‐annular fluid experiments.

Spatiotemporal Evolution and Rank–Size Pattern of Chinese Urban Settlements

Accurate and timely urban boundaries can effectively quantify the spatial characteristics of urban evolution and are essential for understanding the impacts of urbanization processes and land-use changes on the environment and biodiversity. Currently, there is a lack of long time-series, high-resolution, nationally consistent Chinese urban boundary data for urban research. In this study, the city clustering algorithm was used to generate urban settlement boundaries in China based on the local density, size, and spatial relationships of impervious surfaces. The results showed that both the area and the number of urban settlements in China revealed an upward trend from 1985 to 2020, with East China (EC) being much higher than other regions and South China showing the most significant growth rate. The average area ratio of urban green space in China was 41.68%, with the average area ratio in EC being higher than in other regions. Meanwhile, Zipf’s law was used to verify the universality of urban settlement rank–size; the changes in the Zipf index from 1985 to 2020 also revealed that China’s urban size tended to be concentrated, and the development of large urban settlements was relatively prominent. The urban definition method we propose in this study can divide urban boundaries efficiently and accurately, identify urban expansion hotspots, and promote research on farmland loss and ecological land degradation, further exploring the impacts of urbanization on food security, biodiversity, and carbon sequestration. By coupling big data such as economy, energy, and population with urban evolution patterns, urban managers can analyze current and future problems in urban development, thereby providing scientific decision-making for urban sustainability.

A weak solution to a Kirkoff type problem with discontinuous nonlinearities

This paper is devoted to the study of a class of Kirchhoff-type problems with discontinuous nonlinearities with Neumann boundary data. Here,&#x0D; by employing the topological degree methods for the abstract Hammerstein equation, we establish the existence of at least one solution.

Line Laser Scanning Combined with Machine Learning for Fish Head Cutting Position Identification.

Fish head cutting is one of the most important processes during fish pre-processing. At present, the identification of cutting positions mainly depends on manual experience, which cannot meet the requirements of large-scale production lines. In this paper, a fast and contactless identification method of cutting position was carried out by using a constructed line laser data acquisition system. The fish surface data were collected by a linear laser scanning sensor, and Principal Component Analysis (PCA) was used to reduce the dimensions of the dorsal and abdominal boundary data. Based on the dimension data, Least Squares Support Vector Machines (LS-SVMs), Particle Swarm Optimization-Back Propagation (PSO-BP) networks, and Long and Short Term Memory (LSTM) neural networks were applied for fish head cutting position identification model establishment. According to the results, the LSTM model was considered to be the best prediction model with a determination coefficient (R2) value, root mean square error (RMSE), mean absolute error (MAE), and residual predictive deviation (RPD) of 0.9480, 0.2957, 0.1933, and 3.1426, respectively. This study demonstrated the reliability of combining line laser scanning techniques with machine learning using LSTM to identify the fish head cutting position accurately and quickly. It can provide a theoretical reference for the development of intelligent processing and intelligent cutting equipment for fish.

Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Machine learning (ML) provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils. Traditional pure data-driven methods (e.g. deep neural network, DNN) can provide rapid predictions, but they do require sufficient on-site data for accurate training, and lack interpretability to the physical processes within the data. In this paper, we provide a physics and equality-constrained artificial neural network (PECANN), to derive unsaturated infiltration solutions with a small amount of initial and boundary data. PECANN takes the physics-informed neural network (PINN) as a foundation, encodes the unsaturated infiltration physical laws (i.e. Richards equation, RE) into the loss function, and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions. Four unsaturated infiltration cases are designed to test the training performance of PECANN, i.e. one-dimensional (1D) steady-state unsaturated infiltration, 1D transient-state infiltration, two-dimensional (2D) transient-state infiltration, and 1D coupled unsaturated infiltration and deformation. The predicted results of PECANN are compared with the finite difference solutions or analytical solutions. The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration, and present higher precision and robustness than DNN and PINN. It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data. Additionally, we investigate the effect of the hyperparameters of PECANN on solving RE problem. PECANN provides an effective tool for simulating unsaturated infiltration.

Flat from anti de Sitter

Ricci-flat solutions to Einstein’s equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy-momentum tensor is expanded in Laurent series in powers of the cosmological constant, endowing the system with the infinite number of boundary data, characteristic of an asymptotically flat solution space. The governing flat Einstein dynamics is recovered as the limit of the original energy-momentum conservation law and from the additional requirement of the line-element finiteness, providing at each order the necessary set of flux-balance equations for the boundary data. This analysis is conducted using a covariant version of the Newman-Unti gauge designed for taking advantage of the boundary Carrollian structure emerging at vanishing cosmological constant and its Carrollian attributes such as the Cotton tensor.