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Effective Transport and Mechanical Properties of Two-Phase Materials Across the Order-Disorder Spectrum

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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

An Algorithm for Illuminating n Nonoverlapping Circular Discs’ Boundaries on the Plane with Application to Tree Stem Illumination Problem

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arXiv 2025年

作者： Sukkasem, Phapaengmuang Chaidee, Supanut Khokthong, Watit Program in Applied Mathematics Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai50200 Thailand Department of Mathematics Faculty of Science Chiang Mai University Thailand Forest Restoration Research Unit Department of Biology Faculty of Science Chiang Mai University Chiang Mai50200 Thailand Environmental Science Research Centre Faculty of Science Chiang Mai University Chiang Mai50200 Thailand

Given a set of n nonoverlapping circular discs on a plane, we aim to determine possible positions of points (referred to as cameras) that could fully illuminate all the circular discs’ boundaries. This work presents a geometric approach for determining feasible camera positions that would provide total illumination of all circular discs. The Laguerre Delaunay triangulation, coupled with the intersection of slabs formed by the boundaries of circular discs, is employed to form the region that satisfies the given conditions. The experiment is conducted using a set of randomly positioned circular discs on a plane. This study has the potential to address the issue of illumination in forests by utilizing a LiDAR camera to determine the possible number and placement of cameras that can effectively illuminate trees within a forest. © 2025, CC BY.

关键词： Laser recording

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

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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

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

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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

Odd-even mass differences of well and rigidly deformed nuclei in the rare earth region:Test of a newly proposed fit for average pairing matrix elements

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Chinese Physics C 2025年第3期49卷 64-71页

作者： T.V.Nhan Hao N.N.Bao Nguyen D.Quang Tam P.Quentin L.Bonneau Meng-Hock Koh Faculty of Physics University of EducationHue University34 Le Loi StreetHue CityVietnam Center for Theoretical and Computational Physics University of EducationHue University34 Le Loi StreetHue CityVietnam Faculty of Basic Sciences University of Medicine and PharmacyHue University06 Ngo Quyen StreetHue CityVietnam LP2I UMR 5797Universitéde BordeauxCNRSF-33170GradignanFrance Department of Physics Faculty of ScienceUniversiti Teknologi Malaysia81310 Johor BahruJohorMalaysia UTM Centre for Industrial and Applied Mathematics 81310 Johor BahruJohorMalaysia

We present an analysis of a recent approach for determining the average pairing matrix elements within a specified interval of single-particle(sp)states around the Fermi level,denoted asλ.This method,known as the uniform gap method(UGM),highlights the critical importance of the averaged sp level *** pairing matrix elements within the UGM approach are deduced from microscopically calculated values of and gaps obtained from analytical formulae of a semi-classical *** effects generally ignored in similar fits are addressed:(a)a correction for a systematic bias introduced by fitting pairing gaps corresponding to equilibrium deformation solutions,as discussed by Möller and Nix[***.A 476,1(1992)],and(b)a correction for a systematic spurious enhancement of for protons in the vicinity ofλ,caused by the local Slater approximation commonly employed in treating Coulomb exchange terms(e.g.,[***.C 84,014310(2011)]).This approach has demonstrated significant efficiency when applied to Hartree-Fock+Bardeen-Cooper-Schrieffer(BCS)calculations(including the seniority force and self-consistent blocking for odd nuclei)of a large sample of well and rigidly deformed even-even rare-earth *** experimental moments of inertia for these nuclei were reproduced with an accuracy comparable to that achieved through direct fitting of the data[***.C 99,064306(2019)].In this study,we extended the evaluation of our method to the reproduction of three-point odd-even mass differences centered on odd-N or odd-Z nuclei in the same *** agreement with experimental data was found to be comparable to that obtained through direct fitting,as reported in[***.C 99,064306(2019)].

关键词： level density pairing strength odd-even staggering constant pairing matrix element meanfield BCS pairing Skyrme single-particle

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

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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

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

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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

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

No Imputation Without Representation 35th

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No Imputation Without Representation

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