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1. Analytical Approach for Sharp Corner Reconstruction in Kernel Free Boundary Integral Method for Magnetostatic Analysis Toward Inductors Design

   Jin, Z; Cao, Y; Li, S; Ying, W; Krishnamurthy, M (July 2023, Energies)

   Sciubba, Enrico (Ed.)

   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 magnetostatics 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 air gap (C-core) is used to show the effectiveness of the proposed approach 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 from 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. A direct forcing, immersed boundary method for conjugate heat transport

   https://doi.org/10.1016/j.jcp.2025.114135  

   Koponen, Kimmo; Pal_Singh_Bhalla, Amneet; Sprinkle, Brennan; Wu, Ning; Tilton, Nils (October 2025, Journal of Computational Physics)

   Motivated by applications to fluid flows with conjugate heat transfer and electrokinetic effects, we propose a direct forcing immersed boundary method for simulating general, discontinuous, Dirichlet and Robin conditions at the interface between two materials. In comparison to existing methods, our approach uses smaller stencils and accommodates complex geometries with sharp corners. The method is built on the concept of a “forcing pair,” defined as two grid points that are adjacent to each other, but on opposite sides of an interface. For 2D problems this approach can simultaneously enforce discontinuous Dirichlet and Robin conditions using a six-point stencil at one of the forcing points, and a 12-point stencil at the other. In comparison, prior work requires up to 14-point stencils at both points. We also propose two methods of accommodating surfaces with sharp corners. The first locally reduces stencils in sharp corners. The second uses the signed distance function to globally smooth all corners on a surface. The smoothing is defined to recover the actual corners as the grid is refined. We verify second-order spatial accuracy of our proposed methods by comparing to manufactured solutions to the Poisson equation with challenging dis- continuous fields across immersed surfaces. Next, to explore the performance of our method for simulating fluid flows with conjugate heat transport, we couple our method to the incompressible Navier–Stokes and continuity equations using a finite-volume projection method. We verify the spatial-temporal accuracy of the solver using manufactured solutions and an analytical solution for circular Couette flow with conjugate heat transfer. Finally, to demonstrate that our method can model moving surfaces, we simulate fluid flow and conjugate heat transport between a stationary cylinder and a rotating ellipse or square. 

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3. 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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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. 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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