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SSRN 2025年

作者： Skolnick, Murray Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Two-phase heterogeneous materials arise in a plethora of natural and synthetic situations, such as alloys, composites, geological media, complex fluids, and biological media, exhibit a wide-variety of microstructures, and thus display a broad-spectrum of effective physical properties. Elucidating how microstructural details (e.g., specific surface, phase volume fractions, geometries, and topologies) influence two-phase materials’ effective transport and mechanical properties enhances our fundamental understanding of microstructure-property relationships, and is of great practical use in the design of structural and functional materials. Here, we compute the three-point microstructural parameters ζ2 and η2 for phase 2 to evaluate bounds and accurate approximation formulas on the effective thermal/electrical conductivities σe as well as the bulk Ke and shear Ge moduli of a wide class of disordered 2D and 3D material microstructures;including various dispersions of hard and penetrable particles, certain amorphous dispersions, and networks. These parameters are determined using a Monte Carlo integration scheme that incorporates certain algorithmic enhancements that improve upon the accuracy and performance of previous methods. Our results reveal that ζ2 and η2 are sensitive to the phase-connectedness properties of microstructures. Using numerical simulations and rigorous approximations that incorporate ζ2 and η2, we show that certain disordered microstructures nearly realize the Hashin-Shtrikman lower and upper bounds on σe, Ke, and Ge across volume-fractions. We also describe how our algorithm can be used in inverse methodologies to realize ordered and disordered materials with desirable effective physical properties by targeting specific values of ζ2 and η2, and hence aid in materials by design. © 2025, The Authors. All rights reserved.

关键词： Inverse problems

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Nonlinear bubble behaviours of compressible Rayleigh–Taylor instability with isothermal stratification in cylindrical geometry

arXiv

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arXiv 2025年

作者： Yuan, Ming Zhao, Zhiye Liu, Luoqin Wang, Pei Liu, Nan-Sheng Lu, Xi-Yun Department of Modern Mechanics University of Science and Technology of China Anhui Hefei230026 China Department of Mechanical and Aerospace Engineering The Hong Kong University of Science and Technology Hong Kong Institute of Applied Physics and Computational Mathematics Beijing100094 China

Nonlinear evolutions of two-dimensional single-mode compressible Rayleigh–Taylor instability (RTI) with isothermal stratification are investigated in cylindrical geometry via direct numerical simulation for different Atwood numbers (AT = 0.1 − 0.9) and Mach numbers (Ma = 0.1 − 0.9). It is found that the nonlinear bubble growth involves the effects of density stratification, vorticity accumulation and flow compressibility and shows considerable differences between convergent (acceleration acting radially inward) and divergent (acceleration acting radially outward) cases. Specifically, the density stratification leads to non-acceleration at low AT and high Ma. The accelerations in convergent cases are dominated by vorticity accumulation at low AT and low Ma and by flow compressibility at high AT and high Ma whereas the accelerations in divergent cases are purely induced by flow compressibility at high AT and high Ma. Based on the nonlinear theory of incompressible cylindrical RTI with uniform-density background (Zhao et al., J. Fluid Mech., vol. 900, 2020, A24), an improved model is proposed by taking the density variation, vorticity accumulation and flow compressibility into consideration. This model is verified by numerical results and well reproduces the bubble evolution for different AT and Ma from linear to highly nonlinear regimes. © 2025, CC BY.

关键词： Vorticity

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Q-Pop-Imt: An Open-Source Phase-Field Software for Simulating Insulator-Metal Transition Processes in Quantum Materials

SSRN

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SSRN 2025年

作者： Shi, Yin Xu, Xiaofeng Cheng, Xiaoxing Shenoy, Saurav Xu, Jinchao Chen, Long-Qing Department of Materials Science and Metallurgical Engineering United States Department of Materials Science and Engineering The Pennsylvania State University University Park PA16802 United States Department of Mathematics The Pennsylvania State University University Park PA16802 United States Department of Applied Mathematics and Computational Science King Abdullah University of Science and Technology Mecca Thuwal23955-6900 Saudi Arabia

Insulator-metal transitions in quantum materials have important potential applications in areas such as field-effect transistors and neuromorphic computing. Here we present an initial release of the Q-POP-IMT module, an open-source phase-field software for simulating mesoscopic, nonequilibrium processes of insulator-metal transitions in quantum materials. Q-POP-IMT solves the phase-field equations of evolution that describe insulator-metal transitions at the mesoscale using the finite element method. It currently utilizes the powerful FEniCS library to define and solve finite element problems. Thanks to the finite element method, the code can address general boundary conditions such as a complex integral boundary condition corresponding to one of the most common setups in experiments and applications. We demonstrate the usage of the code through simulating the neuron-like voltage self-oscillation phenomenon in a prototypical correlated material, vanadium dioxide. © 2025, The Authors. All rights reserved.

关键词： Vanadium dioxide

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Multiphysics simulations of microstructure influence on hysteresis and eddy current losses of electrical steel

arXiv

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arXiv 2025年

作者： Kühn, Patrick Yang, Yangyiwei Chen, Guanyu Foster, Shanelle N. Egger, Herbert Xu, Bai-Xiang Mechanics of Functional Materials Division Institute of Materials Science Technische Universität Darmstadt Darmstadt64287 Germany Department of Electrical and Computer Engineering Michigan State University MI48824 United States Johann Radon Institute for Computational and Applied Mathematics Linz Austria Institute for Numerical Mathematics Johannes Kepler University Linz Austria

Improving efficiency of electrical machines requires fundamental knowledge on the mechanisms behind magnetic and eddy current losses of the magnetic core materials, with Fe-Si alloy as a prototype. These losses are intrinsically influenced by the microstructure of the materials. This necessitates physics-based, microstructure-informed multiscale simulations. In the present paper, we utilised micromagnetic simulations and computational homogenization methods to calculate the effective hysteresis and effective conductivities of Fe-Si electrical steels. To demonstrate the methodology, binder-jet printed electrical steel material samples with different microstructure were investigated. The microstructure samples were digitized based on both the descriptor-based synthetic reconstruction and SEM-image-based digitization. More samples were generated with varying microstructure features such as grain size and grain boundary phases. The micromagnetic simulations were then performed to investigate the magnetic hysteresis and hysteresis loss. The eddy current loss was also evaluated by using the effective conductivity through computational homogenization. By performing parameter research on a series of synthetic microstructures, effects of average grain size and grain boundary (GB) phase thickness on the hysteresis loss and eddy current loss were unveiled. An average grain size around 120 µm has the lowest hysteresis loss, although the eddy current loss increases with the grain size. Increasing GB-phase thickness helps reduce both losses. Results indicate the potential to decrease loss of magnetic core materials by microstructure optimization. © 2025, CC BY.

关键词： Silicon alloys

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A Two-Step Formulation of Maxwell’s Equations Using Generalized Tree-Cotree Gauges for Low-Frequency-Stability

arXiv

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arXiv 2025年

作者： Herles, Leon Mally, Mario Ostrowski, Jörg Schöps, Sebastian Merkel, Melina Computational Electromagnetics Group Technische Universität Darmstadt Darmstadt64289 Germany Department of Applied Mathematics Universidade de Santiago de Compostela Santiago de Compostela15782 Spain Siemens Digital Industries Software Switzerland

This paper presents a new low-frequency stabilization for a two-step formulation solving the full set of Maxwell’s equations. The formulation is based on a electric scalar and magnetic vector potential equation using the electroquasistatic problem as gauge condition. The proposed stabilization technique consists of an adequate frequency scaling for the electroquasistatic problem, and a tree-cotree decomposition of the magnetic vector potential such that its divergence remains consistent with the partial decoupling of the magnetic and electric potentials. The paper discusses two variants and demonstrates the effectiveness by a few computational examples. Copyright © 2025, The Authors. All rights reserved.

关键词： Maxwell equations

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Three-dimensional construction of hyperuniform, nonhyperuniform, and antihyperuniform disordered heterogeneous materials and their transport properties via spectral density functions

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Physical Review E 2025年第3期111卷 035310-035310页

作者： Wenlong Shi Yang Jiao Salvatore Torquato Materials Science and Engineering Arizona State University Tempe Arizona 85287 USA Department of Physics Arizona State University Tempe Arizona 85287 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. The spectral density function χ̃V(k), which can be obtained experimentally from scattering data, enables accurate determination of various transport and wave propagation characteristics, including the time-dependent diffusion spreadability S(t) and effective dynamic dielectric constant εe for electromagnetic wave propagation. Moreover, χ̃V(k) determines rigorous upper bounds on the fluid permeability K. Given the importance of χ̃V(k), we present here an efficient Fourier-space based computational framework to construct three-dimensional (3D) statistically isotropic two-phase heterogeneous materials corresponding to targeted spectral density functions. In particular, we employ a variety of analytical functional forms for χ̃V(k) that satisfy all known necessary conditions to construct disordered stealthy hyperuniform, standard hyperuniform, nonhyperuniform, and antihyperuniform two-phase heterogeneous material systems at varying phase volume fractions. We show that by tuning the correlations in the system across length scales via the targeted functions, one can generate a rich spectrum of distinct structures within each of the above classes of materials. Importantly, we present the first realization of antihyperuniform two-phase heterogeneous materials in 3D, which are characterized by autocovariance function χV(r) with a power-law tail, resulting in microstructures that contain clusters of dramatically different sizes and morphologies. We also determine the diffusion spreadability S(t) and estimate the fluid permeability K associated with all of the constructed materials directly from the corresponding spectral densities. Although it is well established that the long-time asymptotic scaling behavior of S(t) only depends on the functional form of χ̃V(k), with the stealthy hyperuniform a

关键词： Spectral density

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No Imputation Without Representation 35th

No Imputation Without Representation

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35th Benelux Conference on Artificial Intelligence and Machine Learning, BNAIC/Benelearn 2023

作者： Lenz, Oliver Urs Peralta, Daniel Cornelis, Chris Leiden Institute of Advanced Computer Science Leiden University Leiden Netherlands Research Group for Computational Web Intelligence Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium Department of Information Technology Ghent University Ghent Belgium

ISBN: (纸本)9783031746499

By filling in missing values in datasets, imputation allows these datasets to be used with algorithms that cannot handle missing values by themselves. However, missing values may in principle contribute useful information that is lost through imputation. The missing-indicator approach can be used in combination with imputation to instead represent this information as a part of the dataset. There are several theoretical considerations why missing-indicators may or may not be beneficial, but there has not been any large-scale practical experiment on real-life datasets to test this question for machine learning predictions. We perform this experiment for three imputation strategies and a range of different classification algorithms, on the basis of twenty real-life datasets. In a follow-up experiment, we determine attribute-specific missingness thresholds for each classifier above which missing-indicators are more likely than not to increase classification performance. And in a second follow-up experiment, we evaluate numerical imputation of one-hot encoded categorical attributes. We reach the following conclusions. Firstly, missing-indicators generally increase classification performance. Secondly, with missing-indicators, nearest neighbour and iterative imputation do not lead to better performance than simple mean/mode imputation. Thirdly, for decision trees, pruning is necessary to prevent overfitting. Fourthly, the thresholds above which missing-indicators are more likely than not to improve performance are lower for categorical attributes than for numerical attributes. Lastly, mean imputation of numerical attributes preserves some of the information from missing values. Consequently, when not using missing-indicators it can be advantageous to apply mean imputation to one-hot encoded categorical attributes instead of mode imputation. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Adversarial machine learning

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Developing and analyzing a DG method for modeling of metasurfaces

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Journal of computational Physics 2025年 534卷

作者： Li, Chanjie Huang, Yunqing Li, Jichun School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China Department of Mathematical Sciences University of Nevada Las Vegas Las VegasNV89154-4020 United States

Metasurfaces, with their unique ability to manipulate electromagnetic waves at subwavelength scales, have garnered significant attention for their applications in various areas such as wavefront shaping, beam steering, and cloaking. Accurately modeling these structures presents a complex challenge due to the intricate interactions between electromagnetic waves and the metasurface's subwavelength geometry. In this work, we present a discontinuous Galerkin time-domain (DGTD) method for the efficient and accurate modeling of metasurfaces by coupling with the generalized sheet transition conditions (GSTCs). Numerical stability is proved for two types of metasurfaces. Through a series of benchmark numerical simulations, we demonstrate the accuracy and computational efficiency of the DGTD method in modeling metasurfaces, especially those with irregular geometries. This work opens new avenues for the accurate simulation and design of metasurfaces in a wide range of electromagnetic applications. © 2025 Elsevier Inc.

关键词： Maxwell equations

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ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS

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applied mathematics and Mechanics(English Edition) 2003年第10期24卷 1168-1183页

作者：尚亚东郭柏灵 Department of Mathematics Guangzhou University Institute of Applied Physics and Computational Mathematics

The Chebyshev pseudospectral approximation of the homogeneous initial boundary value problem for a class of multi-dimensional generalized symmetric regularized long wave (SRLW) equations is considered. The fully discrete Chebyshev pseudospectral scheme is constructed. The convergence of the approximation solution and the optimum error of approximation solution are obtained.

关键词： multi-dimensional generalized SRLW equation initial and boundary value problem Chebyshev pseudospectral method error estimate

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Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system

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Science China mathematics 2015年第1期58卷 61-76页

作者： JIANG Song LI FuCai Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Department of Mathematics Nanjing University

We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell *** justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic compressi... 详细信息

关键词： non-isentropic compressible Euler-Maxwell system non-isentropic compressible magnetohydro-dynamic equations zero dielectric constant limit

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