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1. Analytical Approach for Sharp Corner Reconstruction in the Kernel Free Boundary Integral Method during Magnetostatic Analysis for Inductor Design

   https://doi.org/10.3390/en16145420  

   Jin, Zichao ; Cao, Yue ; Li, Shuwang ; Ying, Wenjun ; Krishnamurthy, Mahesh ( July 2023 , Energies)

   It is very important to perform magnetostatic analysis accurately and efficiently when it comes to multi-objective optimization of designs of electromagnetic devices, particularly for inductors, transformers, and electric motors. A kernel free boundary integral method (KFBIM) was studied for analyzing 2D magnetostatic problems. Although KFBIM is accurate and computationally efficient, sharp corners can be a major problem for KFBIM. In this paper, an inverse discrete Fourier transform (DFT) based geometry reconstruction is explored to overcome this challenge for smoothening sharp corners. A toroidal inductor core with an airgap (C-core) is used to show the effectiveness of the proposed approach for addressing the sharp corner problem. A numerical example demonstrates that the method works for the variable coefficient PDE. In addition, magnetostatic analysis for homogeneous and nonhomogeneous material is presented for the reconstructed geometry, and results carried out using KFBIM are compared with the results of FEM analysis for the original geometry to show the differences and the potential of the proposed method. 

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2. Capillary rise in sharp corners: not quite universal

   https://doi.org/10.1017/jfm.2023.1040  

   Wu, Katie ; Duprat, C ; Stone, HA ( January 2024 , Journal of Fluid Mechanics)

   We study the capillary rise of viscous liquids into sharp corners formed by two surfaces whose geometry is described by power laws, $h_i(x) = c_i x^n$, $i = 1,2$, where $c_2 > c_1$ for $n \geq 1$. Prior investigations of capillary rise in sharp corners have shown that the meniscus altitude increases with time as $t^{1/3}$, a result which is universal, i.e., applies to all corner geometries. The universality of the phenomenon of capillary rise in sharp corners is revisited in this work through the analysis of a partial differential equation for the evolution of a liquid column rising into power-law-shaped corners, which is derived using lubrication theory. Despite the lack of geometric similarity of the liquid column cross-section for $n>1$, there exists a scaling and a similarity transformation that are independent of $c_i$ and $n$, which gives rise to the universal $t^{1/3}$ power-law for capillary rise. However, the prefactor, which corresponds to the tip altitude of the self-similar solution, is a function of $n$, and it is shown to be bounded and monotonically decreasing as $n\to \infty$. Accordingly, the profile of the interface radius as a function of altitude is also independent of $c_i$ and exhibits slight variations with $n$. Theoretical results are compared against experimental measurements of the time evolution of the tip altitude and of profiles of the interface radius as a function of altitude. 

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3. HoORaYs: High-order Optimization of Rating Distance for Recommender Systems

   https://doi.org/10.1145/3097983.3098019  

   Xu, Jingwei ; Yao, Yuan ; Tong, Hanghang ; Tao, Xianping ; Lu, Jian ( August 2017 , KDD)

   Latent factor models have become a prevalent method in recommender systems, to predict users' preference on items based on the historical user feedback. Most of the existing methods, explicitly or implicitly, are built upon the first-order rating distance principle, which aims to minimize the difference between the estimated and real ratings. In this paper, we generalize such first-order rating distance principle and propose a new latent factor model (HoORaYs) for recommender systems. The core idea of the proposed method is to explore high-order rating distance, which aims to minimize not only (i) the difference between the estimated and real ratings of the same (user, item) pair (i.e., the first-order rating distance), but also (ii) the difference between the estimated and real rating difference of the same user across different items (i.e., the second-order rating distance). We formulate it as a regularized optimization problem, and propose an effective and scalable algorithm to solve it. Our analysis from the geometry and Bayesian perspectives indicate that by exploring the high-order rating distance, it helps to reduce the variance of the estimator, which in turns leads to better generalization performance (e.g., smaller prediction error). We evaluate the proposed method on four real-world data sets, two with explicit user feedback and the other two with implicit user feedback. Experimental results show that the proposed method consistently outperforms the state-of-the-art methods in terms of the prediction accuracy. 

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4. Oxidation Induced Stresses in High-Temperature Oxidation of Steel: A Multiphase Field Study

   https://doi.org/10.3390/met10060801  

   Toghraee, Alireza ; Asle Zaeem, Mohsen ( June 2020 , Metals)

   null (Ed.)

   Oxide growth and the induced stresses in the high-temperature oxidation of steel were studied by a multiphase field model. The model incorporates both chemical and elastic energy to capture the coupled oxide kinetics and generated stresses. Oxidation of a flat surface and a sharp corner are considered at two high temperatures of 850 °C and 1180 °C to investigate the effects of geometry and temperature elevation on the shape evolution of oxides and the induced stresses. Results show that the model is capable of capturing the oxide thickness and its outward growth, comparable to the experiments. In addition, it was shown that there is an interaction between the evolution of oxide and the generated stresses, and the oxide layer evolves to reduce stress concentrations by rounding the sharp corners in the geometry. Increasing the temperature may increase or decrease the stress levels depending on the contribution of eigen strain in the generated elastic strain energy during oxidation. 

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5. Deep Geometric Prior for Surface Reconstruction

   https://doi.org/10.1109/CVPR.2019.01037  

   Williams, Francis ; Silva, Claudio ; Zorin, Denis ; Bruna, Joan ; Panozzo, Daniele ( January 2019 , IEEE Computer Society Conference on Computer Vision and Pattern Recognition)

   The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to part of an input point cloud using the Wasserstein distance as a measure of approximation. By jointly fitting many such networks to overlapping parts of the point cloud, while enforcing a consistency condition, we compute a manifold atlas. By sampling this atlas, we can produce a dense reconstruction of the surface approximating the input cloud. The entire procedure does not require any training data or explicit regularization, yet, we show that it is able to perform remarkably well: not introducing typical overfitting artifacts, and approximating sharp features closely at the same time. We experimentally show that this geometric prior produces good results for both man-made objects containing sharp features and smoother organic objects, as well as noisy inputs. We compare our method with a number of well-known reconstruction methods on a standard surface reconstruction benchmark. 

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