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arXiv 2021年

作者： Gartner, Thomas E. Torquato, Salvatore Car, Roberto Debenedetti, Pablo G. Department of Chemistry Princeton University PrincetonNJ United States Department of Physics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ United States

Much attention has been devoted to water’s metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship between these phenomena remains incompletely understood. Using molecular dynamics simulations of the realistic TIP4P/2005 model, we found a striking signature of the liquid-liquid critical point in the structure of water glasses, manifested as a pronounced increase in long-range density fluctuations at pressures proximate to the critical pressure. By contrast, these signatures were absent in glasses of two model systems that lack a critical point. We also characterized the departure from equilibrium upon vitrification via the non-equilibrium index;water-like systems exhibited a strong pressure dependence in this metric, whereas simple liquids did not. These results reflect a surprising relationship between the metastable equilibrium phenomenon of liquid-liquid criticality and the non-equilibrium structure of glassy water, with implications for our understanding of water phase behavior and glass physics. Our calculations suggest a possible experimental route to probing the existence of the liquid-liquid transition in water and other fluids. © 2021, CC BY.

关键词： Criticality (nuclear fission)

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Charge equilibration of laser-accelerated carbon ions in a porous-structure foam target

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Physical Review A 2024年第4期109卷 042810-042810页

作者： Bubo Ma Jieru Ren Lirong Liu Wenqing Wei Benzheng Chen Shizheng Zhang Hao Xu Zhongmin Hu Fangfang Li Xing Wang Wenxuan Li Qiuyan Li Shuai Yin Jianhua Feng Xianming Zhou Yifang Gao Yuan Li Xiaohua Shi Jianxing Li Xueguang Ren Zhongfeng Xu Zhigang Deng Wei Qi Shaoyi Wang Quanping Fan Bo Cui Weiwu Wang Zongqiang Yuan Jian Teng Yuchi Wu Zhurong Cao Zongqing Zhao Yuqiu Gu Leifeng Cao Shaoping Zhu Rui Cheng Yu Lei Zhao Wang Zexian Zhou Guoqing Xiao Hongwei Zhao Dieter H. H. Hoffmann Weimin Zhou Yongtao Zhao MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter School of Science Xi'an Jiaotong University Xi'an 710049 China Science and Technology on Plasma Physics Laboratory Laser Fusion Research Center China Academy of Engineering Physics Mianyang 621900 China Advanced Materials Testing Technology Research Center Shenzhen University of Technology Shenzhen 518118 China Institute of Applied Physics and Computational Mathematics Beijing 100094 China Graduate School China Academy of Engineering Physics Beijing 100088 China Institute of Modern Physics Chinese Academy of Sciences Lanzhou 710049 China

The equilibrium charge state distribution of laser-accelerated carbon ions traversing a tri-cellulose-acetate (TCA, C9H16O8) foam target was measured experimentally. The ions were generated through the target normal sheath acceleration mechanism. This allowed us to obtain the equilibrium charge state for a wide energy range near the maximum energy loss within a single laser shot. The foam had a porous structure with 2 mg/cm3 volume density, which is between the typical density of gas- and solid-state matter. We found that the measured average equilibrium charge states were significantly underestimated by theoretical models applicable for gas targets, while were in close agreement with both semiempirical formulas and rate equation predictions based on ion-solid interactions. The solid-density fiber filaments in the current foam structure were attributed and demonstrated. The target density effects, which increase the ionization probability through frequent collisions and decrease the electron capture probability, were proven to play an important role in the foam target. Since the foam targets are widely used in laser plasma interaction experiments, our findings are relevant for a broad range of applications.

关键词： Atomic & molecular collisions Beam dynamics Beam injection, extraction & transport Lasers Ions Low- & intermediate-energy accelerators Atomic Properties Ab initio molecular dynamics Bragg spectroscopy Inner-shell processes

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Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order-disorder transitions in LixCoO2

arXiv

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arXiv 2023年

作者： Teichert, G.H. Das, S. Shojaei, M. Faghih Holber, J. Mueller, T. Hung, L. Gavini, V. Garikipati, K. Department of Mechanical Engineering University of Michigan United States Toyota Research Institute Los AltosCA United States Department of Materials Science & Engineering University of Michigan United States Department of Mathematics University of Michigan United States Michigan Institute for Computational Discovery & Engineering University of Michigan United States Applied Physics Program University of Michigan United States Materials Science & Engineering Johns Hopkins University United States

LixTMO2 (TM=Ni, Co, Mn) forms an important family of cathode materials for Li-ion batteries, whose performance is strongly governed by Li composition-dependent crystal structure and phase stability. Here, we use LixCoO2 (LCO) as a model system to benchmark a machine learning-enabled framework for bridging scales in materials physics. We focus on two scales: (a) assemblies of thousands of atoms described by density functional theory-informed statistical mechanics, and (b) continuum phase field models to study the dynamics of order-disorder transitions in LCO. Central to the scale bridging is the rigorous, quantitatively accurate, representation of the free energy density and chemical potentials of this material system by coarsegraining formation energies for specific atomic configurations. We develop active learning workflows to train recently developed integrable deep neural networks for such high-dimensional free energy density and chemical potential functions. The resulting, first principles-informed, machine learning-enabled, phase-field computations allow us to study LCO cathodes’ phase evolution in terms of temperature, morphology, charge cycling and particle size. © 2023, CC BY-NC-SA.

关键词： Cathodes

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Interactions leading to disordered ground states and unusual low-temperature behavior

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Physical Review E 2009年第3期80卷 031105-031105页

作者： Robert D. Batten Frank H. Stillinger Salvatore Torquato Department of Chemical Engineering Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Materials Institute Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

We have shown that any pair potential function v(r) possessing a Fourier transform V(k) that is positive and has compact support at some finite wave number K yields classical disordered ground states for a broad density range [R. D. Batten, F. H. Stillinger, and S. Torquato, J. Appl. Phys. 104, 033504 (2008)]. By tuning a constraint parameter χ (defined in the text), the ground states can traverse varying degrees of local order from fully disordered to crystalline ground states. Here, we show that in two dimensions, the “k-space overlap potential,” where V(k) is proportional to the intersection area between two disks of diameter K whose centers are separated by k, yields anomalous low-temperature behavior, which we attribute to the topography of the underlying energy landscape. At T=0, for the range of densities considered, we show that there is continuous energy degeneracy among Bravais-lattice configurations. The shear elastic constant of ground-state Bravais-lattice configurations vanishes. In the harmonic regime, a significant fraction of the normal modes for both amorphous and Bravais-lattice ground states have vanishing frequencies, indicating the lack of an internal restoring force. Using molecular-dynamics simulations, we observe negative thermal-expansion behavior at low temperatures, where upon heating at constant pressure, the system goes through a density maximum. For all temperatures, isothermal compression reduces the local structure of the system unlike typical single-component systems.

关键词： Ground state

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A First-Principles and Calphad-Assisted Phase-Field Model for Microstructure Evolution: Application to Mo-V Binary Alloy Systems

SSRN

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SSRN 2023年

作者： Thakur, Abhishek Kumar Kovacevic, Sasa Manga, Venkateswara Rao Deymier, Pierre Alix Muralidharan, Krishna Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Department of Civil and Environmental Engineering Imperial College London LondonSW7 2AZ United Kingdom Lunar and Planetary Laboratory University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics India

A multiscale computational framework combining the first-principles calculations and the CALPHAD approach with the phase-field method is presented to simulate the microstructure evolution in multicomponent steel alloys. We demonstrate the potential of the framework by predicting the microstructural evolution in elastically periodic arrays of the Mo-V binary sub-system. The framework utilizes the first-principles calculations using special quasi-random structures. Hitherto unavailable thermodynamic and material properties of the alloy are obtained by employing the first-principles calculations and the CALPHAD approach and fed into the phase-field model to predict the microstructure evolution at different temperatures within the miscibility gap region. In addition to the temperature and cooling rates, the model incorporates the role of mechanical fields in decomposition kinetics in the Mo-V binary alloy system. Regimes for temperatures and cooling rates at which spinodal decomposition occurs are identified. Applying external loading leads to directional phase separation in the Mo-V binary system. The elastic inhomogeneity in terms of material properties between the two phases initiates the directional alignment while eigenstrains and applied external loading control the degree of alignment. The framework developed is general and extendable to higher multicomponent sub-systems in steel alloys. © 2023, The Authors. All rights reserved.

关键词： Temperature

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DIFFUSION CURVATURE FOR ESTIMATING LOCAL CURVATURE IN HIGH DIMENSIONAL DATA

arXiv

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arXiv 2022年

作者： Bhaskar, Dhananjay MacDonald, Kincaid Fasina, Oluwadamilola Thomas, Dawson Rieck, Bastian Adelstein, Ian Krishnaswamy, Smita Department of Genetics Yale School of Medicine New HavenCT United States Department of Mathematics Yale University New HavenCT United States Program for Applied Mathematics Yale University New HavenCT United States Department of Physics Yale University New HavenCT United States Institute of AI for Health Helmholtz Pioneer Campus Munich Germany Department of Computer Science Yale University New HavenCT United States Program for Computational Biology and Bioinformatics Yale University New HavenCT United States

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes. © 2022, CC BY.

关键词： Geometry

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Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem

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Physical Review E 2014年第2期89卷 022721-022721页

作者： Yang Jiao Timothy Lau Haralampos Hatzikirou Michael Meyer-Hermann Joseph C. Corbo Salvatore Torquato Princeton Institute of the Science and Technology of Materials Princeton University Princeton New Jersey 08540 USA Materials Science and Engineering Arizona State University Tempe Arizona 85287 USA Department of Pathology and Immunology Washington University School of Medicine St. Louis Missouri 63110 USA Department of Systems Immunology Helmholtz Centre for Infection Research Braunschweig Germany Center for Advancing Electronics Dresden TU Dresden 01062 Dresden Germany Department of Chemistry Department of Physics Program in Computational and Applied Mathematics Princeton University Princeton New Jersey 08544 USA

Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are “hyperuniform” (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns “multihyperuniform” because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multihyperuniformity. These findings suggest that a disordered hyperuniform pattern may represent the most uniform sampling arrangement attainable in the avian system, given intrinsic packing constraints within the photoreceptor epithelium. In addition, they show how fundamental physical constraints can change the course of a biological optimization process. Our results suggest that multihyperuniform disordered structures have implications for the design of materials with novel physical properties and therefore may represent a fruitful area for future research

关键词： PHOTORECEPTORS ARRAY processing BIRDS MULTISCALE modeling SAMPLING (Signal processing) EPITHELIUM

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Exact constructions of a family of dense periodic packings of tetrahedra

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Physical Review E 2010年第4期81卷 041310-041310页

作者： S. Torquato Y. Jiao Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered “dimer” packings of tetrahedra, including the densest known packings with density ϕ=40004671=0.856347…. This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.

关键词： constructions family tetrahedra tetrahedrons family Dense Platonic solid

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A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

arXiv

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arXiv 2022年

作者： Kolahdouz, Ebrahim M. Wells, David R. Rossi, Simone Aycock, Kenneth I. Craven, Brent A. Griffith, Boyce E. Center for Computational Biology Flatiron Institute Simons Foundation New YorkNY United States Department of Mathematics University of North Carolina Chapel HillNC United States Division of Applied Mechanics Office of Science and Engineering Laboratories Center for Devices and Radiological Health United States Food and Drug Administration Silver SpringMD United States Departments of Mathematics 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

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressibl

关键词： Fluid structure interaction

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Local and global measures of the shear moduli of jammed disk packings

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Physical Review E 2023年第5期107卷 054903-054903页

作者： Shiyun Zhang Weiwei Jin Dong Wang Ding Xu Jerry Zhang Mark D. Shattuck Corey S. O'Hern Department of Physics University of Science and Technology of China Hefei Anhui 230026 China Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut 06520 USA Benjamin Levich Institute and Physics Department The City College of New York New York New York 10031 USA Department of Physics Yale University New Haven Connecticut 06520 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1−F−)〈G+〉+F−〈G−〉, where F− is the fraction of jammed packings with negative shear moduli and 〈G+〉 and 〈G−〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G+〉 and 〈|G−|〉 obey different power-law scaling relations above and below pN2∼1. For pN2>1, both 〈G+〉N and 〈|G−|〉N∼(pN2)β, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN2)β′ with β′≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN2 and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN2≪1 limit. As pN2 increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN2≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r⃗) displays weak correlations for pnsub2<10−2, where nsub is the number of particles within each subsystem. However, C(r⃗) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pnsub2≳10−2.

关键词： Jamming Packing & jamming problems Granular materials

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