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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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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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Publisher's Note: “Reacting and non-reacting, three-dimensional shear layers with spanwise stretching” [Phys. Fluids 34, 123602 (2022)]

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Physics of Fluids 2023年第1期35卷

作者： Jonathan L. Palafoutas William A. Sirignano 1Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA 2Department of Mechanical and Aerospace Engineering University of California Irvine Irvine California 92697 USA

This article was published online on 2 December 2022 with errors throughout the paper. All the derivative terms had the wrong denominator; the denominators were

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Lithospheric foundering and underthrusting imaged beneath Tibet

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Nature Communications 2017年第1期8卷 15659-15659页

作者： Chen, Min Niu, Fenglin Tromp, Jeroen Lenardic, Adrian Lee, Cin-Ty A. Cao, Wenrong Ribeiro, Julia 318 Keith-Wiess Geology Lab Department of Earth Science Rice University 6100 Main Street Houston 77005 TX United States State Key Laboratory of Petroleum Resource Prospecting and Unconventional Natural Gas Institute China University of Petroleum Beijing 102249 China Department of Geosciences Princeton University Princeton 08544 NJ United States Program in Applied and Computational Mathematics Princeton University Princeton 08544 NJ United States

Long-standing debates exist over the timing and mechanism of uplift of the Tibetan Plateau and, more specifically, over the connection between lithospheric evolution and surface expressions of plateau uplift and volcanism. Here we show a T-shaped high wave speed structure in our new tomographic model beneath South-Central Tibet, interpreted as an upper-mantle remnant from earlier lithospheric foundering. Its spatial correlation with ultrapotassic and adakitic magmatism supports the hypothesis of convective removal of thickened Tibetan lithosphere causing major uplift of Southern Tibet during the Oligocene. Lithospheric foundering induces an asthenospheric drag force, which drives continued underthrusting of the Indian continental lithosphere and shortening and thickening of the Northern Tibetan lithosphere. Surface uplift of Northern Tibet is subject to more recent asthenospheric upwelling and thermal erosion of thickened lithosphere, which is spatially consistent with recent potassic volcanism and an imaged narrow low wave speed zone in the uppermost mantle. © 2017 The Author(s).

关键词： Seismology

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Corrigendum:‘‘Reconnection of two vortex rings’’ [Phys. Fluids A 1, 630 (1989)]

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Physics of Fluids A: Fluid Dynamics 1990年第4期2卷 638-638页

作者： S. Kida M. Takaoka F. Hussain Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 Department of Physics Faculty of Science Kyoto University Kyoto 606 Japan Department of Mechanical Engineering University of Houston Houston Texas 77004

S. Kida, M. Takaoka, F. Hussain; Corrigendum:‘‘Reconnection of two vortex rings’’ [Phys. Fluids A 1, 630 (1989)]Comments, Physics of Fluids A: Fluid Dynamics, V

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A Model of Fluid-Structure and Biochemical Interactions for Applications to Subclinical Leaflet Thrombosis

arXiv

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arXiv 2022年

作者： Barrett, Aaron Brown, Jordan A. Smith, Margaret Anne Woodward, Andrew Vavalle, John P. Kheradvar, Arash Griffith, Boyce E. Fogelson, Aaron L. Department of Mathematics University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Advanced Medical Imaging Lab University of North Carolina Medical Center Chapel HillNC United States University of North Carolina School of Medicine Chapel HillNC United States Division of Cardiology Department of Medicine University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of California Irvine IrvineCA United States Department of Mathematics Applied Physical Sciences and 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 Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States Department of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis in which they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction. © 2022, CC BY-SA.

关键词： Deposition

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Ergodic directional switching in mobile insect groups

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Physical Review E 2010年第1期82卷 011926-011926页

作者： Carlos Escudero Christian A. Yates Jerome Buhl Iain D. Couzin Radek Erban Ioannis G. Kevrekidis Philip K. Maini ICMAT (CSIC-UAM-UC3M-UCM) Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid Ciudad Universitaria de Cantoblanco 28049 Madrid Spain Centre for Mathematical Biology Mathematical Institute University of Oxford 24-29 St. Giles’ Oxford OX1 3LB United Kingdom School of Biological Sciences and Centre for Mathematical Biology Heydon-Laurence Building A08 The University of Sydney Sydney New South Wales Australia Department of Ecology and Evolutionary Biology Princeton University Princeton New Jersey 08544 USA Oxford Centre for Collaborative Applied Mathematics Mathematical Institute University of Oxford 24-29 St. Giles’ Oxford OX1 3LB United Kingdom Department of Chemical Engineering Program in Applied and Computational Mathematics and Mathematics Princeton University Princeton New Jersey 08544 USA Department of Biochemistry Oxford Centre for Integrative Systems Biology University of Oxford South Parks Road Oxford OX1 3QU United Kingdom

We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of constituents of the swarm. The stationary probability distribution shows a rich phenomenology including nonmonotonic behavior of several order and disorder transition indicators in noise intensity. This complex behavior arises naturally as a result of the randomness in the system. Its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models. Our results suggest that the collective switches of the group’s direction of motion might be due to a random ergodic effect and, as such, they are inherent to group formation.

关键词： Fokker Planck equation

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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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