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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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Multi-body wave function of ground and low-lying excited states using unornamented deep neural networks

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Physical Review Research 2023年第3期5卷 033189-033189页

作者： Tomoya Naito (内藤智也) Hisashi Naito (内藤久資) Koji Hashimoto (橋本幸士) RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) Wako 351-0198 Japan and Department of Physics Graduate School of Science The University of Tokyo Tokyo 113-0033 Japan Graduate School of Mathematics Nagoya University Nagoya 464-8602 Japan Department of Physics Kyoto University Kyoto 606-8502 Japan

We propose a method to calculate wave functions and energies not only of the ground state but also of low-lying excited states using a deep neural network and the unsupervised machine learning technique. For systems composed of identical particles, a simple method to perform symmetrization for bosonic systems and antisymmetrization for fermionic systems is also proposed.

关键词： Few-body systems Quantum many-body systems Deep learning Machine learning Variational approach Variational wave functional methods

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Extraordinary Optical and Transport Properties of Disordered Stealthy Hyperuniform Two-Phase Media

arXiv

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arXiv 2024年

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

Disordered stealthy hyperuniform two-phase media are a special subset of hyperuniform structures with novel physical properties due to their hybrid crystal-liquid nature. We have previously shown that the rapidly converging strong-contrast expansion of a linear fractional form of the effective dynamic dielectric constant Εe(k1,ω) [Phys. Rev. X 11, 296 021002 (2021)] leads to accurate approximations for both hyperuniform and nonhyperuniform two-phase composite media when truncated at the two-point level for distinctly different types of microstructural symmetries in three dimensions. In this paper, we further elucidate the extraordinary optical and transport properties of disordered stealthy hyperuniform media. Among other results, we provide detailed proofs that stealthy hyperuniform layered and transversely isotropic media are perfectly transparent (i.e., no Anderson localization, in principle) within finite wavenumber intervals through the third-order terms. Remarkably, these results imply that there can be no Anderson localization within the predicted perfect transparency interval in stealthy hyperuniform layered and transversely isotropic media in practice because the localization length (associated with only possibly negligibly small higher-order contributions) should be very large compared to any practically large sample size. We further contrast and compare the extraordinary physical properties of stealthy hyperuniform two-phase layered, transversely isotropic media, and fully 3D isotropic media to other model nonstealthy microstructures, including their attenuation characteristics, as measured by the imaginary part of Εe(k1,ω), and transport properties, as measured by the time-dependent diffusion spreadability S(t). We demonstrate that there are cross-property relations between them, namely, we quantify how the imaginary parts of Εe(k1,ω) and the spreadability at long times are positively correlated as the structures span from nonhyperuniform, nonstealthy hy

关键词： Transport properties

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NOMAD: Nonlinear Manifold Decoders for Operator Learning

arXiv

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arXiv 2022年

作者： Seidman, Jacob H. Kissas, Georgios Perdikaris, Paris Pappas, George J. Graduate Program in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania United States Department of Electrical and Systems Engineering University of Pennsylvania United States

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost. © 2022, CC BY-NC-SA.

关键词： Benchmarking

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Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

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Physical Review applied 2022年第3期17卷 034022-034022页

作者： Haina Wang Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Time-dependent interphase diffusion processes in multiphase heterogeneous media are ubiquitous phenomena in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, foams, and cell aggregates. The recently developed concept of spreadability, S(t), provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)]. To investigate the capacity of S(t) to probe microstructures of real heterogeneous media, we explicitly compute S(t) for well-known two-dimensional and three-dimensional idealized model structures that span across nonhyperuniform and hyperuniform classes. Among the former class, we study fully penetrable spheres and equilibrium hard spheres, and in the latter class, we examine sphere packings derived from “perfect glasses,” uniformly randomized lattices (URLs), disordered stealthy hyperuniform point processes, and Bravais lattices. Hyperuniform media are characterized by an anomalous suppression of volume fraction fluctuations at large length scales compared to that of any nonhyperuniform medium. We further confirm that the small-, intermediate-, and long-time behaviors of S(t) sensitively capture the small-, intermediate-, and large-scale characteristics of the models. In instances in which the spectral density χ~V(k) has a power-law form B|k|α in the limit |k|→0, the long-time spreadability provides a simple means to extract the value of the coefficients α and B that is robust against noise in χ~V(k) at small wave numbers. For typical nonhyperuniform media, the intermediate-time spreadability is slower for models with larger values of the coefficient B=χ~V(0). Interestingly, the excess spreadability S(∞)−S(t) for URL packings has nearly exponential decay at small to intermediate t, but transforms to a power-law decay at large t, and the time for this transition has a logarithmic divergence in th

关键词： Complex systems Diffusion Flows in porous media Rocks Composite materials Glassy systems Porous materials Random & disordered media

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Velocity-gauge Real-time Time-dependent Density Functional Tight-binding for Large-scale Condensed Matter Systems

arXiv

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arXiv 2023年

作者： Xu, Qiang Del Ben, Mauro Okyay, Mahmut Sait Choi, Min Ibrahim, Khaled Z. Wong, Bryan M. Materials Science & Engineering Program Department of Chemistry Department of Physics & Astronomy University of California-Riverside RiversideCA92521 United States Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

We present a new velocity-gauge real-time, time-dependent density functional tight-binding (VG-rtTDDFTB) implementation in the open-source DFTB+ software package (https://***) for probing electronic excitations in large, condensed matter systems. Our VG-rtTDDFTB approach enables real-time electron dynamics simulations of large, periodic, condensed matter systems containing thousands of atoms with a favorable computational scaling as a function of system size. We provide computational details and benchmark calculations to demonstrate its accuracy and computational parallelizability on a variety of large material systems. As a representative example, we calculate laser-induced electron dynamics in a 512-atom amorphous silicon supercell to highlight the large periodic systems that can be examined with our implementation. Taken together, our VG-rtTDDFTB approach enables new electron dynamics simulations of complex systems that require large periodic supercells, such as crystal defects, complex surfaces, nanowires, and amorphous materials. Copyright © 2023, The Authors. All rights reserved.

关键词： Gages

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Regimes of stratified turbulence at low Prandtl number

arXiv

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arXiv 2023年

作者： Shah, Kasturi Chini, Gregory P. Caulfield, Colm-Cille P. Garaud, Pascale Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom Department of Earth Atmospheric and Planetary Sciences Massachusetts Institute of Technology CambridgeMA02139 United States Program in Integrated Applied Mathematics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States Institute for Energy and Environmental Flows University of Cambridge CambridgeCB3 0EZ United Kingdom Department of Applied Mathematics Baskin School of Engineering University of California Santa Cruz Santa CruzCA95064 United States

Quantifying transport by strongly stratified turbulence in low Prandtl number (Pr) fluids is critically important for the development of better models for the structure and evolution of stellar and planetary interiors. Motivated by recent numerical simulations showing strongly anisotropic flows suggestive of scale-separated dynamics, we perform a multiscale asymptotic analysis of the governing equations. We find that, in all cases, the resulting slow-fast systems take a quasilinear form. Our analysis also reveals the existence of several distinct dynamical regimes depending on the emergent buoyancy Reynolds and Péclet numbers, Reb = α2Re and Peb = PrReb, respectively, where α is the aspect ratio of the large-scale turbulent flow structures, and Re is the outer scale Reynolds number. Scaling relationships relating the aspect ratio, the characteristic vertical velocity, and the strength of the stratification (measured by the Froude number Fr) naturally emerge from the analysis. When Peb α, the dynamics at all scales is dominated by buoyancy diffusion, and our results recover the scaling laws empirically obtained from direct numerical simulations by Cope et al. (2020). For Peb ≥ O(1), diffusion is negligible (or at least subdominant) at all scales and our results are consistent with those of Chini et al. (2022) for strongly stratified geophysical turbulence at Pr = O(1). Finally, we have identified a new regime for α Peb 1, in which slow, large scales are diffusive while fast, small scales are not. We conclude by presenting a map of parameter space that clearly indicates the transitions between isotropic turbulence, non-diffusive stratified turbulence, diffusive stratified turbulence and viscously-dominated flows, and by proposing parameterisations of the buoyancy flux, mixing efficiency and turbulent diffusion coefficient for each regime. © 2023, CC BY.

关键词： Buoyancy

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Correlations between student connectivity and academic performance: A pandemic follow-up

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Physical Review Physics Education Research 2023年第1期19卷 010106-010106页

作者： Nathan Crossette Lincoln D. Carr Bethany R. Wilcox Department of Physics University of Colorado Boulder Boulder Colorado 80309 USA Quantum Engineering Program Colorado School of Mines Golden Colorado 80401 USA Department of Physics Colorado School of Mines Golden Colorado 80401 USA Department of Applied Mathematics and Statistics Colorado School of Mines Golden Colorado 80401 USA

Social network analysis (SNA) has been gaining traction as a technique for quantitatively studying student collaboration. We analyze networks, constructed from student self-reports of collaboration on homework assignments, in two courses from the University of Colorado Boulder and one course from the Colorado School of Mines. All three courses occurred during the COVID-19 pandemic, which allows for a comparison between the course at the Colorado School of Mines (in a fully remote format) with results from a previous pre-pandemic study of student collaboration at the Colorado School of Mines (in an in-person format), as well as comparison between the Mines results with the two University of Colorado courses (in a hybrid format). We compute nodal centrality measures and calculate the correlation between student centrality and performance. Results varied widely between each of the courses studied. The course at the Colorado School of Mines had strong correlations between many centrality measures and performance which matched the patterns seen in the pre-pandemic study. The courses at the University of Colorado Boulder showed weaker correlations, and one course showed nearly no correlations at all between students’ connectivity to their classmates and their performance. Taken together, the results from the trio of courses indicate that the context and environment in which the course is situated play a more important role in fostering a correlation between student collaboration and course performance than the format (remote, hybrid, in-person) of the course, a finding which has implications for the broader use of SNA within physics education research. Additionally, we conducted a short study on the effect that missing nodes may have on the correlations calculated from the measured networks, an analysis largely missing from the SNA literature within PER. This investigation showed that missing nodes tend to shift correlations towards zero, providing evidence that the stati

关键词： Learning environment Research methodology Upper undergraduate students

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A new class of distances on complex projective spaces

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Linear Algebra and Its Applications 2024年 721卷 577-611页

作者： Bistroń, Rafal Eckstein, Michal Friedland, Shmuel Miller, Tomasz Życzkowski, Karol Institute of Theoretical Physics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. prof. Stanislawa Lojasiewicza 11 Krakow30-348 Poland Doctoral School of Exact and Natural Sciences Jagiellonian University ul. prof. Stanislawa Lojasiewicza 11 Krakow30-348 Poland Department of Mathematics Statistics and Computer Science University of Illinois at Chicago 851 S. Morgan Street ChicagoIL60607-7045 United States Copernicus Center for Interdisciplinary Studies Jagiellonian University ul. Mikolaja Kopernika 27 Krakow31-501 Poland Center for Theoretical Physics Polish Academy of Science aleja Lotników 32/46 Warsaw02-668 Poland

The complex projective space P(Cn) can be interpreted as the space of all quantum pure states of size n. A distance on this space, interesting from the perspective of quantum physics, can be induced from a classical distance defined on the n-point probability simplex by the ‘earth mover problem’. We show that this construction leads to a quantity satisfying the triangle inequality, which yields a true distance on complex projective space belonging to the family of quantum 2-Wasserstein distances. © 2024 Elsevier Inc.

关键词： State space methods

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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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