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Dislocation climb strengthening in systems with immobile obstacles: Three-dimensional level-set simulation study

Physical Review B 2010年第5期81卷 054104-054104页

作者： Zi Chen Kevin T. Chu David J. Srolovitz Jeffrey M. Rickman Mikko P. Haataja Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08540 USA Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08540 USA Vitamin D Inc. Menlo Park California 94025 USA Institute of High Performance Computing Singapore Singapore Department of Materials Science and Engineering Lehigh University Bethlehem Pennsylvania 18015 USA Department of Physics Lehigh University Bethlehem Pennsylvania 18015 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08540 USA

We employ a parallel, three-dimensional level-set code to simulate the dynamics of isolated dislocation lines and loops in an obstacle-rich environment. This system serves as a convenient prototype of those in which extended, one-dimensional objects interact with obstacles and the out-of-plane motion of these objects is key to understanding their pinning-depinning behavior. In contrast to earlier models of dislocation motion, we incorporate long-ranged interactions among dislocation segments and obstacles to study the effect of climb on dislocation dynamics in the presence of misfitting penetrable obstacles/solutes, as embodied in an effective climb mobility. Our main observations are as follows. First, increasing climb mobility leads to more effective pinning by the obstacles, implying increased strengthening. Second, decreasing the range of interactions significantly reduces the effect of climb. The dependence of the critical stress on obstacle concentration and misfit strength is also explored and compared with existing models. In particular, our results are shown to be in reasonable agreement with the Friedel-Suzuki theory. Finally, the limitations inherent in the simplified model employed here, including the neglect of some lattice effects and the use of a coarse-grained climb mobility, are discussed.

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Erratum to: An Incompressible 2D Didactic Model with Singularity and Explicit Solutions of the 2D Boussinesq Equations

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Journal of Mathematical Fluid Mechanics 2014年第3期16卷 481-481页

作者： Dongho Chae Peter Constantin Jiahong Wu Department of Mathematics College of Natural Science Chung-Ang University Seoul South Korea Program in Applied and Computational Mathematics Princeton University Princeton USA Department of Mathematics Oklahoma State University Stillwater USA Department of Mathematics Chung-Ang University Seoul Republic of Korea

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Thermal Conductivity of Water at Extreme Conditions

arXiv

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arXiv 2023年

作者： Zhang, Cunzhi Puligheddu, Marcello Zhang, Linfeng Car, Roberto Galli, Giulia Pritzker School of Molecular Engineering University of Chicago ChicagoIL60637 United States Materials Science Division Center for Molecular Engineering Argonne National Laboratory LemontIL60439 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Chemistry University of Chicago ChicagoIL60637 United States

Measuring the thermal conductivity (κ) of water at extreme conditions is a challenging task and few experimental data are available. We predict κ for temperatures and pressures relevant to the conditions of the Earth mantle, between 1,000 and 2,000 K and up to 22 GPa. We employ close to equilibrium molecular dynamics simulations and a deep neural network potential fitted to density functional theory data. We then interpret our results by computing the equation of state of water on a fine grid of points and using a simple model for κ. We find that the thermal conductivity is weakly dependent on temperature and monotonically increases with pressure with an approximate square-root behavior. In addition we show how the increase of κ at high pressure, relative to ambient conditions, is related to the corresponding increase in the sound velocity. Although the relationships between the thermal conductivity, pressure and sound velocity established here are not rigorous, they are sufficiently accurate to allow for a robust estimate of the thermal conductivity of water in a broad range of temperatures and pressures, where experiments are still difficult to perform. Copyright © 2023, The Authors. All rights reserved.

关键词： Thermal conductivity

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Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions

arXiv

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arXiv 2023年

作者： Maher, Charles Emmett Jiao, Yang Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The maximally random jammed (MRJ) state is the most random (i.e., disordered) configuration of strictly jammed (mechanically rigid) nonoverlapping objects. MRJ packings are hyperuniform, meaning their long-wavelength density fluctuations are anomalously suppressed compared to typical disordered systems, i.e., their structure factors S(k) tend to zero as the wave number |k| tends to zero. Here, we show that generating high-quality strictly jammed states for Euclidean space dimensions d = 3, 4, and 5 is of paramount importance in ensuring hyperuniformity and extracting precise values of the hyperuniformity exponent α > 0 for MRJ states, defined by the power-law behavior of S(k) ∼ |k|α in the limit |k| → 0. Moreover, we show that for fixed d it is more difficult to ensure jamming as the particle number N increases, which results in packings that are nonhyperuniform. Free-volume theory arguments suggest that the ideal MRJ state does not contain rattlers, which act as defects in numerically generated packings. As d increases, we find that the fraction of rattlers decreases substantially. Our analysis of the largest truly jammed packings suggests that the ideal MRJ packings for all dimensions d ≥ 3 are hyperuniform with α = d − 2, implying the packings become more hyperuniform as d increases. The differences in α between MRJ packings and recently proposed Manna-class random close packed (RCP) states, which were reported to have α = 0.25 in d = 3 and be nonhyperuniform (α = 0) for d = 4 and d = 5, demonstrate the vivid distinctions between the large-scale structure of RCP and MRJ states in these dimensions. Our paper clarifies the importance of the link between true jamming and hyperuniformity and motivates the development of an algorithm to produce rattler-free three-dimensional MRJ packings. © 2023, CC BY.

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Exclusion Volumes of Convex Bodies in High Space Dimensions: Applications to Virial Coefficients and Continuum Percolation

arXiv

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arXiv 2022年

作者： Torquato, Salvatore Jiao, Yang 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 Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States

Using the concepts of mixed volumes and quermassintegrals of convex geometry, we derive an exact formula for the exclusion volume vex(K) for a general convex body K that applies in any space dimension. While our main interests concern the rotationally-averaged exclusion volume of a convex body with respect to another convex body, we also describe some results for the exclusion volumes for convex bodies with the same orientation. We show that the sphere minimizes the dimensionless exclusion volume vex(K)/v(K) among all convex bodies, whether randomly oriented or uniformly oriented, for any d, where v(K) is the volume of K. When the bodies have the same orientation, the simplex maximizes the dimensionless exclusion volume for any d with a large-d asymptotic scaling behavior of 22d/d3/2, which is to be contrasted with the corresponding scaling of 2d for the sphere. We present explicit formulas for quermassintegrals W0(K), . . ., Wd(K) for many different nonspherical convex bodies, including cubes, parallelepipeds, regular simplices, cross-polytopes, cylinders, spherocylinders, ellipsoids as well as lower-dimensional bodies, such as hyperplates and line segments. These results are utilized to determine the rotationally-averaged exclusion volume vex(K) for these convex-body shapes for dimensions 2 through 12. While the sphere is the shape possessing the minimal dimensionless exclusion volume, we show that, among the convex bodies considered that are sufficiently compact, the simplex possesses the maximal vex(K)/v(K) with a scaling behavior of 21.6618...d. Subsequently, we apply these results to determine the corresponding second virial coefficient B2(K) of the aforementioned hard hyperparticles. Our results are also applied to compute estimates of the continuum percolation threshold ηc derived previously by the authors for systems of identical overlapping convex bodies. We conjecture that overlapping spheres possess the maximal value of ηc among all identical nonzero-vol

关键词： Spheres

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An Immersed Interface Method for Incompressible Flows and Geometries with Sharp Features

arXiv

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arXiv 2024年

作者： Facci, Michael J. Kolahdouz, Ebrahim M. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Flatiron Institute Simons Foundation New YorkNY United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work using the IIM for fluid dynamic applications has focused on smooth interfaces, but boundaries with sharp features such as corners and edges can appear in practical analyses, particularly on engineered structures. The present study builds on our work to integrate finite element-type representations of interface geometries with the IIM. Initial realizations of this approach used a continuous Galerkin (CG) finite element discretization for the boundary, but as we show herein, these approaches generate large errors near sharp geometrical features. To overcome this difficulty, this study introduces an IIM approach using discontinuous Galerkin (DG) representation of the jump conditions. Numerical examples explore the impacts of different interface representations on accuracy for both smooth and sharp boundaries, particularly flows interacting with fixed interface configurations. We demonstrate that using a DG approach provides accuracy that is comparable to the CG method for smooth cases. Further, we identify a time step size restriction for the CG representation that is directly related to the sharpness of the geometry. In contrast, time step size restrictions imposed by DG representations are demonstrated to be insensitive to the presence of sharp *** Codes 76-10 (Primary) 76D05 (Secondary) © 2024, CC BY-NC-ND.

关键词： Incompressible flow

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Localization transition in three-dimensional stealthy hyperuniform disordered systems

arXiv

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arXiv 2021年

作者： Sgrignuoli, F. Torquato, S. Dal Negro, L. Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary’s Street BostonMA02215 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Division of Material Science and Engineering Boston University 15 Saint Mary’s Street BrooklineMA02446 United States Department of Physics Boston University 590 Commonwealth Avenue BostonMA02215 United States

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems (3D-SHDS) are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green’s matrix spectral method, we establish a transport phase diagram that demonstrates a clear delocalization-localization transition beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed sub-radiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and localization properties of light in stealthy hyperuniform structures and motivates the engineering of novel photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices. Copyright © 2021, The Authors. All rights reserved.

关键词： Phase diagrams

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Critical pore radius and transport properties of disordered hard- And overlapping-sphere models

arXiv

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arXiv 2021年

作者： Klatt, Michael A. Ziff, Robert M. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 Erlangen91058 Germany Center for the Study of Complex Systems Department of Chemical Engineering University of Michigan Ann ArborMI48109 United States Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δc. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, "quantizer" sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δc is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato. Adv. Wat. Resour. 140,103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size hδ2i, which is easier to determine than δc. Here, we compare δc to the second moment of the pore size hδ2i, and indeed confirm that, for all porosities and all models considered, δc2 is to a good approximation proportional to hδ2i. However, unlike hδ2i, the permeability estimate based on δc2 does not predict the correct ranking of k for our models. Thus, we confirm hδ2i to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via target

关键词： Porous materials

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The Disordered Heterogeneous Universe: Galaxy Distribution and Clustering Across Length Scales

arXiv

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arXiv 2022年

作者： Philcox, Oliver H.E. Torquato, Salvatore Department of Astrophysical Sciences Princeton University PrincetonNJ08540 United States School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Center for Theoretical Physics Department of Physics Columbia University New YorkNY10027 United States Simons Foundation New YorkNY10010 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at ‘microscales’ to predict physical properties of the medium at ‘macroscales’, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, ‘void’ and ‘particle’ nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears ‘hyperuniform’, as a result of primordial density fluctuations, whilst on the smallest scales, the system becomes almost ‘antihyperuniform’, as evidenced by its number variance. Additionally, via a finite scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc = 0.25 in our fiducial analysis compared to ηc = 0.34), with strong dependence on the mean density;this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension

关键词： Galaxies

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Fast principal component analysis for cryo-electron microscopy images

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Biological imaging 2023年 3卷 e2-e2页

作者： Nicholas F Marshall Oscar Mickelin Yunpeng Shi Amit Singer Department of Mathematics Oregon State University Corvallis Oregon 97331 USA. Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA. Department of Mathematics Princeton University Princeton New Jersey 08544 USA.

Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-EM projection images affected by radial point spread functions that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For images of size × , our method has time complexity ( + ) and space complexity ( + ). In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude.

关键词： Covariance estimation Fourier–Bessel cryo-EM denoising principal component analysis single particle reconstruction

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