1
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Suzuki A, Sasa Y, Kobashi M, Kato M, Segawa M, Shimono Y, Nomoto S. Persistent Homology Analysis of the Microstructure of Laser-Powder-Bed-Fused Al-12Si Alloy. MATERIALS (BASEL, SWITZERLAND) 2023; 16:7228. [PMID: 38005157 PMCID: PMC10673303 DOI: 10.3390/ma16227228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Revised: 10/30/2023] [Accepted: 11/08/2023] [Indexed: 11/26/2023]
Abstract
The laser powder bed fusion (L-PBF) process provides the cellular microstructure (primary α phase surrounded by a eutectic Si network) inside hypo-eutectic Al-Si alloys. The microstructure changes to the particle-dispersed microstructure with heat treatments at around 500 °C. The microstructural change leads to a significant reduction in the tensile strength. However, the microstructural descriptors representing the cellular and particle-dispersed microstructures have not been established, resulting in difficulty in terms of discussion regarding the structure-property relationship. In this study, an attempt was made to analyze the microstructure in L-PBF-built and subsequently heat-treated Al-12Si (mass%) alloys using the persistent homology, which can analyze the spatial distributions and connections of secondary phases. The zero-dimensional persistent homology revealed that the spacing between adjacent Si particles was independent of Si particle size in the as-built alloy, whereas fewer Si particles existed near large Si particles in the heat-treated alloy. Furthermore, the first principal component of a one-dimensional persistent homology diagram would represent the microstructural characteristics from cellular to particle-dispersed morphology. These microstructural descriptors were strongly correlated with the tensile and yield strengths. This study provides a new insight into the microstructural indices describing unique microstructures in L-PBF-built alloys.
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Affiliation(s)
- Asuka Suzuki
- Department of Materials Process Engineering, Graduate School of Engineering, Nagoya University, 1, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan; (Y.S.); (M.K.)
| | - Yusuke Sasa
- Department of Materials Process Engineering, Graduate School of Engineering, Nagoya University, 1, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan; (Y.S.); (M.K.)
| | - Makoto Kobashi
- Department of Materials Process Engineering, Graduate School of Engineering, Nagoya University, 1, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan; (Y.S.); (M.K.)
| | - Masaki Kato
- Aichi Center for Industry and Science Technology, 1267-1 Akiai, Yakusa-cho, Toyota 470-0356, Japan;
| | - Masahito Segawa
- ITOCHU Techno-Solutions Corporation, Toranomon Kamiyacho Trust Tower, Minato-ku, Tokyo 105-6907, Japan; (M.S.); (Y.S.)
| | - Yusuke Shimono
- ITOCHU Techno-Solutions Corporation, Toranomon Kamiyacho Trust Tower, Minato-ku, Tokyo 105-6907, Japan; (M.S.); (Y.S.)
| | - Sukeharu Nomoto
- National Institute for Materials Science, 1-2-1, Sengen, Tsukuba 305-0047, Japan;
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2
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Riley L, Cheng P, Segura T. Identification and analysis of 3D pores in packed particulate materials. NATURE COMPUTATIONAL SCIENCE 2023; 3:975-992. [PMID: 38177603 DOI: 10.1038/s43588-023-00551-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 10/09/2023] [Indexed: 01/06/2024]
Abstract
We took the classic 'guess the number of beans in a jar game' and amplified the research question. Rather than estimate the quantity of particles in the jar, we sought to characterize the spaces between them. Here we present an approach for delineating the pockets of empty space (three-dimensional pores) between packed particles, which are hotspots for activity in applications and natural phenomena that deal with particulate materials. We utilize techniques from graph theory to exploit information about particle configuration that allows us to locate important spatial landmarks within the void space. These landmarks are the basis for our pore segmentation, where we consider both interior pores as well as entrance and exit pores into and out of the structure. Our method is robust for particles of varying size, form, stiffness and configuration, which allows us to study and compare three-dimensional pores across a range of packed particle types. We report striking relationships between particles and pores that are described mathematically, and we offer a visual library of pore types. With a meaningful discretization of void space, we demonstrate that packed particles can be understood not by their solid space, but by their empty space.
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Affiliation(s)
- Lindsay Riley
- Department of Biomedical Engineering, Duke University, Durham, NC, USA
| | | | - Tatiana Segura
- Department of Biomedical Engineering, Duke University, Durham, NC, USA.
- Department of Medicine, Neurology, Dermatology, Duke University, Durham, NC, USA.
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3
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Shipman PD, Sharath T, Bradley RM. Topological measures of order for imperfect two-dimensional Bravais lattices. Phys Rev E 2023; 107:044216. [PMID: 37198833 DOI: 10.1103/physreve.107.044216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2022] [Accepted: 03/20/2023] [Indexed: 05/19/2023]
Abstract
Motivated by patterns with defects in natural and laboratory systems, we develop two quantitative measures of order for imperfect Bravais lattices in the plane. A tool from topological data analysis called persistent homology combined with the sliced Wasserstein distance, a metric on point distributions, are the key components for defining these measures. The measures generalize previous measures of order using persistent homology that were applicable only to imperfect hexagonal lattices in two dimensions. We illustrate the sensitivities of these measures to the degree of perturbation of perfect hexagonal, square, and rhombic Bravais lattices. We also study imperfect hexagonal, square, and rhombic lattices produced by numerical simulations of pattern-forming partial differential equations. These numerical experiments serve to compare the measures of lattice order and reveal differences in the evolution of the patterns in various partial differential equations.
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Affiliation(s)
- Patrick D Shipman
- Department of Mathematics and School of Advanced Materials Discovery, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Tejas Sharath
- Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
| | - R Mark Bradley
- Departments of Physics and Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA
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4
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Schaller FM, Punzmann H, Schröder-Turk GE, Saadatfar M. Mixing properties of bi-disperse ellipsoid assemblies: mean-field behaviour in a granular matter experiment. SOFT MATTER 2023; 19:951-958. [PMID: 36633168 DOI: 10.1039/d2sm00922f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical relationship for mixture distributions to explain the observations of an extensive X-ray computed tomography study of granular ellipsoidal packings. We study a size-bi-disperse mixture of two types of ellipsoids of revolutions that have the same aspect ratio of α ≈ 0.57 and differ in size, by about 10% in linear dimension, and compare these to mono-disperse systems of ellipsoids with the same aspect ratio. Jammed configurations with a range of packing densities are achieved by employing different tapping protocols. We numerically interrogate the final packing configurations by analyses of the local packing fraction distributions calculated from the Voronoi diagrams. Our main finding is that the bi-disperse ellipsoidal packings studied here can be interpreted as a mixture of two uncorrelated mono-disperse packings, insensitive to the compaction protocol. Our results are consolidated by showing that the local packing fraction shows no correlation beyond their first shell of neighbours in the binary mixtures. We propose a model of uncorrelated binary mixture distribution that describes the observed experimental data with high accuracy. This analysis framework will enable future studies to test whether the observed mean-field behaviour is specific to the particular granular system or the specific parameter values studied here or if it is observed more broadly in other bi-disperse non-spherical particle systems.
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Affiliation(s)
- F M Schaller
- Friedrich-Alexander Universität Erlangen-Nürnberg, Institut für Theoretische Physik, Staudtstr. 7B, 91058 Erlangen, Germany.
- Karlsruhe Institute of Technology (KIT), Institut für Stochastik, 76131 Karlsruhe, Germany
| | - H Punzmann
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
| | - G E Schröder-Turk
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
- Murdoch University, College of Science, Technology, Engineering and Mathematics, 90 South St, Murdoch WA 6150, Australia
| | - M Saadatfar
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
- The University of Sydney, School of Civil Engineering, NSW 2006, Australia.
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5
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Ishihara S, Franks G, Kano J. Effect of particle packing structure on the elastic modulus of wet powder compacts analyzed by persistent homology. ADV POWDER TECHNOL 2023. [DOI: 10.1016/j.apt.2022.103874] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
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6
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Zubov AS, Murygin DA, Gerke KM. Pore-network extraction using discrete Morse theory: Preserving the topology of the pore space. Phys Rev E 2022; 106:055304. [PMID: 36559419 DOI: 10.1103/physreve.106.055304] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2022] [Accepted: 10/17/2022] [Indexed: 11/10/2022]
Abstract
Pore-scale modeling based on the 3D structural information of porous materials has enormous potential in assessing physical properties beyond the capabilities of laboratory methods. Such capabilities are pricey in terms of computational expenses, and this limits the applicability of the direct simulations to a small volume and requires high-performance computational resources, especially for multiphase flow simulations. The only pore-scale technique capable of dealing with large representative volumes of porous samples is pore-network (PNM) based modeling. The problem of the PNM approach is that 3D pore geometry first needs to be simplified into a graph of pores and throats that conserve topological and geometrical properties of the original 3D image. While significant progress has been achieved in terms of geometry representation, no methodology provides full conservation of the topological features of the pore structure. In this paper we present a pore-network extraction algorithm for binary 3D images based on discrete Morse theory and persistent homology that by design targets topology preservation. In addition to methodological developments, we also clarify the relationship between topological characteristics of constructed Morse chain complex and pore-network elements. We show that the Euler numbers calculated for PNMs based on our methodology coincide with those obtained using the direct topological analysis. The characteristics of the extracted pore network are calculated for several 3D porous binary images and compared with the results of maximum inscribed balls-based and watershed-based approaches as well as a hybrid approach to support our methodology.
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Affiliation(s)
- Andrey S Zubov
- Joint Institute for Nuclear Research, 141980 Dubna, Russia
| | - Dmitry A Murygin
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, 107031 Moscow, Russia
| | - Kirill M Gerke
- Schmidt Institute of Physics of the Earth of Russian Academy of Sciences, 107031 Moscow, Russia
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7
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Francois N, Cruikshank R, Herring A, Kingston A, Webster S, Knackstedt M, Saadatfar M. A versatile microtomography system to study in situ the failure and fragmentation in geomaterials. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:083704. [PMID: 36050093 DOI: 10.1063/5.0093650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
This article describes a microtomography experimental platform enabling in situ micro-mechanical study of failure and fragmentation in geomaterials. The system is based on an original high-pressure triaxial flow cell, which is fully integrated into a custom built microtomography scanner equipped with a laboratory x-ray source. The design of the high-precision mechanical apparatus was informed by the concurrent development of advanced tomographic reconstruction methods based on helical scanning and of algorithms correcting for hardware inaccuracies. This experimental system produces very high-quality 3D images of microstructural changes occurring in rocks undergoing mechanical failure and substantial fragmentation. We present the results of two experiments as case studies to demonstrate the capabilities and versatility of this instrumental platform. These experiments tackle various questions related to the onset of rock failure, the hydromechanical coupling and relaxation mechanisms in fractured rocks, or the fragmentation process in geomaterials such as copper ores.
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Affiliation(s)
- N Francois
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - R Cruikshank
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - A Herring
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - A Kingston
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - S Webster
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - M Knackstedt
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - M Saadatfar
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
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8
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Grbić J, Wu J, Xia K, Wei GW. ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE. FOUNDATIONS OF DATA SCIENCE (SPRINGFIELD, MO.) 2022; 4:165-216. [PMID: 36712596 PMCID: PMC9881677 DOI: 10.3934/fods.2022002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.
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Affiliation(s)
- Jelena Grbić
- School of Mathematical Sciences, University of Southampton, Southampton, UK
| | - Jie Wu
- School of Mathematical Sciences, Center of Topology and Geometry based Technology, Hebei Normal University, Yuhua District, Shijiazhuang, Hebei, 050024 China
- Yanqi Lake Beijing Institute of Mathematica Sciences, Yanqihu, Huairou District, Beijing, 101408 China
| | - Kelin Xia
- School of Physical and Mathematical Sciences, Nanyang Technological University, SPMS-MAS-05-18, 21 Nanyang Link, 1, Singapore 63737
| | - Guo-Wei Wei
- Department of Mathematics, Department of Computer Science and Engineering, Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824, USA
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9
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Detecting Carbon Nanotube Orientation with Topological Analysis of Scanning Electron Micrographs. NANOMATERIALS 2022; 12:nano12081251. [PMID: 35457959 PMCID: PMC9029586 DOI: 10.3390/nano12081251] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Revised: 03/25/2022] [Accepted: 03/31/2022] [Indexed: 02/04/2023]
Abstract
As the aerospace industry is increasingly demanding stronger, lightweight materials, ultra-strong carbon nanotube (CNT) composites with highly aligned CNT network structures could be the answer. In this work, a novel methodology applying topological data analysis (TDA) to scanning electron microscope (SEM) images was developed to detect CNT orientation. The CNT bundle extensions in certain directions were summarized algebraically and expressed as visible barcodes. The barcodes were then calculated and converted into the total spread function, V(X, θ), from which the alignment fraction and the preferred direction could be determined. For validation purposes, the random CNT sheets were mechanically stretched at various strain ratios ranging from 0 to 40%, and quantitative TDA was conducted based on the SEM images taken at random positions. The results showed high consistency (R2 = 0.972) compared to Herman’s orientation factors derived from polarized Raman spectroscopy and wide-angle X-ray scattering analysis. Additionally, the TDA method presented great robustness with varying SEM acceleration voltages and magnifications, which might alter the scope of alignment detection. With potential applications in nanofiber systems, this study offers a rapid and simple way to quantify CNT alignment, which plays a crucial role in transferring the CNT properties into engineering products.
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10
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Noshita K, Murata H, Kirie S. Model-based plant phenomics on morphological traits using morphometric descriptors. BREEDING SCIENCE 2022; 72:19-30. [PMID: 36045892 PMCID: PMC8987841 DOI: 10.1270/jsbbs.21078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Accepted: 12/20/2021] [Indexed: 06/15/2023]
Abstract
The morphological traits of plants contribute to many important functional features such as radiation interception, lodging tolerance, gas exchange efficiency, spatial competition between individuals and/or species, and disease resistance. Although the importance of plant phenotyping techniques is increasing with advances in molecular breeding strategies, there are barriers to its advancement, including the gap between measured data and phenotypic values, low quantitativity, and low throughput caused by the lack of models for representing morphological traits. In this review, we introduce morphological descriptors that can be used for phenotyping plant morphological traits. Geometric morphometric approaches pave the way to a general-purpose method applicable to single units. Hierarchical structures composed of an indefinite number of multiple elements, which is often observed in plants, can be quantified in terms of their multi-scale topological characteristics using topological data analysis. Theoretical morphological models capture specific anatomical structures, if recognized. These morphological descriptors provide us with the advantages of model-based plant phenotyping, including robust quantification of limited datasets. Moreover, we discuss the future possibilities that a system of model-based measurement and model refinement would solve the lack of morphological models and the difficulties in scaling out the phenotyping processes.
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Affiliation(s)
- Koji Noshita
- Department of Biology, Kyushu University, Fukuoka, Fukuoka 819-0395, Japan
- Plant Frontier Research Center, Kyushu University, Fukuoka, Fukuoka 819-0395, Japan
| | - Hidekazu Murata
- Department of Biology, Kyushu University, Fukuoka, Fukuoka 819-0395, Japan
| | - Shiryu Kirie
- metaPhorest (Bioaesthetics Platform), Department of Electrical Engineering and Bioscience, Waseda University, TWIns, Tokyo 162-8480, Japan
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11
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Pun CS, Lee SX, Xia K. Persistent-homology-based machine learning: a survey and a comparative study. Artif Intell Rev 2022. [DOI: 10.1007/s10462-022-10146-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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12
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Zhao SC, Pöschel T. Collective motion of granular matter subjected to swirling excitation. Phys Rev E 2022; 105:L022902. [PMID: 35291099 DOI: 10.1103/physreve.105.l022902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
A two-dimensional granular packing under horizontally circular shaking exhibits various collective motion modes where nonuniform density distribution and correlated dynamics are present. For intermediate packing density and oscillation amplitude, a condensed phase travels around the container's side wall in the clockwise direction, while the oscillation itself is set anticlockwise. Further increasing the packing density towards that of hexagonal packing, the whole packing rotates collectively in the clockwise direction. The core of the packing rotates as a solid and is separated from the boundary by a fluid-like layer. Both motion modes are associated with the asymmetric motion of particles close to the side wall in one oscillation cycle, where the dependence of particle velocity on the local density plays a key role.
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Affiliation(s)
- Song-Chuan Zhao
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China
| | - Thorsten Pöschel
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität, Cauerstraße 3, 91058 Erlangen, Germany
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13
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Pandey K, Bin Masood T, Singh S, Hotz I, Natarajan V, Murthy TG. Morse theory-based segmentation and fabric quantification of granular materials. GRANULAR MATTER 2022; 24:27. [DOI: 10.1007/s10035-021-01182-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 10/12/2021] [Indexed: 09/01/2023]
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14
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Zhai C, Albayrak N, Engqvist J, Hall SA, Wright J, Majkut M, Herbold EB, Hurley RC. Quantifying local rearrangements in three-dimensional granular materials: Rearrangement measures, correlations, and relationship to stresses. Phys Rev E 2022; 105:014904. [PMID: 35193203 DOI: 10.1103/physreve.105.014904] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 01/04/2022] [Indexed: 06/14/2023]
Abstract
Quantifying the ways in which local particle rearrangements contribute to macroscopic plasticity is one of the fundamental pursuits of granular mechanics and soft matter physics. Here we examine local rearrangements that occur naturally during the deformation of three samples of 3D granular materials subjected to distinct boundary conditions by employing in situ x-ray measurements of particle-resolved structure and stress. We focus on five distinct rearrangement measures, their statistics, interrelationships, contributions to macroscopic deformation, repeatability, and dependence on local structure and stress. Our most significant findings are that local rearrangements (1) are correlated on a scale of three to four particle diameters, (2) exhibit volumetric strain-shear strain and nonaffine displacement-rotation coupling, (3) exhibit correlations that suggest either rearrangement repeatability or that rearrangements span multiple steps of incremental sample strain, and (4) show little dependence on local stress but correlate with quantities describing local structure, such as porosity. Our results are presented in the context of relevant plasticity theories and are consistent with recent findings suggesting that local structure may play at least as important of a role as local stress in determining the nature of local rearrangements.
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Affiliation(s)
- Chongpu Zhai
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an, China and Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Nahuel Albayrak
- Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Jonas Engqvist
- Division for Solid Mechanics, Lund University, Lund 22100, Sweden
| | | | | | | | - Eric B Herbold
- Atmospheric, Earth, & Energy Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Ryan C Hurley
- Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA and Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, Maryland 21218, USA
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15
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Yen TC. Construction of simplicial complexes with prescribed degree-size sequences. Phys Rev E 2021; 104:L042303. [PMID: 34781564 DOI: 10.1103/physreve.104.l042303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Accepted: 09/30/2021] [Indexed: 11/07/2022]
Abstract
We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s≥3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)2470-004510.1103/PhysRevE.96.032312], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analyses of higher-order phenomena based on local structures.
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Affiliation(s)
- Tzu-Chi Yen
- Department of Computer Science, University of Colorado, Boulder, Colorado 80309, USA
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16
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Osang G, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. SOFT MATTER 2021; 17:9107-9115. [PMID: 34569592 DOI: 10.1039/d1sm00774b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals.
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Affiliation(s)
- Georg Osang
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Herbert Edelsbrunner
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Mohammad Saadatfar
- School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia.
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17
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Yen PTW, Xia K, Cheong SA. Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1211. [PMID: 34573837 PMCID: PMC8467365 DOI: 10.3390/e23091211] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Revised: 09/05/2021] [Accepted: 09/06/2021] [Indexed: 12/24/2022]
Abstract
In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region.
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Affiliation(s)
- Peter Tsung-Wen Yen
- Center for Crystal Researches, National Sun Yet-Sen University, No. 70, Lien-hai Rd., Kaohsiung 80424, Taiwan;
| | - Kelin Xia
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore;
| | - Siew Ann Cheong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
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18
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Abstract
This work studies how morphology (i.e., the shape of a structure) and topology (i.e., how different structures are connected) influence wall adsorption and capillary condensation under tight confinement. Numerical simulations based on classical density functional theory (cDFT) are run for a wide variety of geometries using both hard-sphere and Lennard-Jones fluids. These cDFT computations are compared to results obtained using the Minkowski functionals. It is found that the Minkowski functionals can provide a good description of the behavior of Lennard-Jones fluids down to small system sizes. In addition, through decomposition of the free energy, the Minkowski functionals provide a good framework to better understand what are the dominant contributions to the phase behavior of a system. Lastly, while studying the phase envelope shift as a function of the Minkowski functionals it is found that topology has a different effect depending on whether the phase transition under consideration is a continuous or a discrete (first-order) transition.
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Classification of apatite structures via topological data analysis: a framework for a 'Materials Barcode' representation of structure maps. Sci Rep 2021; 11:11599. [PMID: 34078920 PMCID: PMC8172868 DOI: 10.1038/s41598-021-90070-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 05/05/2021] [Indexed: 12/03/2022] Open
Abstract
This paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.
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20
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Jiang SQ, Li MZ. Local crystalline order features in disordered packings of monodisperse spheres. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:205401. [PMID: 33770772 DOI: 10.1088/1361-648x/abf271] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 03/26/2021] [Indexed: 06/12/2023]
Abstract
A new tetrahedral structure model was developed for disordered sphere packings, including not only regular tetrahedron (T), but also quartoctahedron (Q) and bcc simplex (B), the tetrahedral building blocks in fcc, hcp and bcc crystal structures, respectively. Both geometric frustrated configurations and local configurations associated with crystalline order in disordered packings can be comprehensively characterized. It is found that with increasing packing fraction, the population of T, Q, and B increases. Moreover, the crystal-type local configurations formed by face-adjacent T, Q and B increases as packing fraction increases, which is more prevalent than the geometric frustrated ones formed by face-adjacent T. In addition, as packing fraction increases, the local density of irregular simplexes is found to increase more quickly than regular ones, playing more important roles in the density increase in disordered packings. These structure features are found to be intrinsic in the jammed random sphere packings with different friction coefficients, which is independent of interparticle friction and only determined by the packing fraction. Our findings provide new understanding for the structural nature of disordered packings and the underlying structural basis of the random close packing.
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Affiliation(s)
- S Q Jiang
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
| | - M Z Li
- Department of Physics, Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
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21
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Ormrod Morley D, Salmon PS, Wilson M. Persistent homology in two-dimensional atomic networks. J Chem Phys 2021; 154:124109. [PMID: 33810685 DOI: 10.1063/5.0040393] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The topology of two-dimensional network materials is investigated by persistent homology analysis. The constraint of two dimensions allows for a direct comparison of key persistent homology metrics (persistence diagrams, cycles, and Betti numbers) with more traditional metrics such as the ring-size distributions. Two different types of networks are employed in which the topology is manipulated systematically. In the first, comparatively rigid networks are generated for a triangle-raft model, which are representative of materials such as silica bilayers. In the second, more flexible networks are generated using a bond-switching algorithm, which are representative of materials such as graphene. Bands are identified in the persistence diagrams by reference to the length scales associated with distorted polygons. The triangle-raft models with the largest ordering allow specific bands Bn (n = 1, 2, 3, …) to be allocated to configurations of atoms separated by n bonds. The persistence diagrams for the more disordered network models also display bands albeit less pronounced. The persistent homology method thereby provides information on n-body correlations that is not accessible from structure factors or radial distribution functions. An analysis of the persistent cycles gives the primitive ring statistics, provided the level of disorder is not too large. The method also gives information on the regularity of rings that is unavailable from a ring-statistics analysis. The utility of the persistent homology method is demonstrated by its application to experimentally-obtained configurations of silica bilayers and graphene.
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Affiliation(s)
- David Ormrod Morley
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Philip S Salmon
- Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom
| | - Mark Wilson
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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22
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Krebs J, Hirsch C. Functional central limit theorems for persistent Betti numbers on cylindrical networks. Scand Stat Theory Appl 2021. [DOI: 10.1111/sjos.12524] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Johannes Krebs
- Institute of Applied Mathematics Heidelberg University Heidelberg Germany
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23
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Pore Space and Fluid Phase Characterization in Round and Angular Partially Saturated Sands Using Radiation-Based Tomography and Persistent Homology. Transp Porous Media 2021. [DOI: 10.1007/s11242-021-01554-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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24
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Hong S, Klatt MA, Schröder-Turk G, François N, Saadatfar M. Dynamical arrest of topological defects in 2D hyperuniform disk packings. EPJ WEB OF CONFERENCES 2021. [DOI: 10.1051/epjconf/202124915002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.
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25
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Jin W, O'Hern CS, Radin C, Shattuck MD, Swinney HL. Homogeneous Crystallization in Cyclically Sheared Frictionless Grains. PHYSICAL REVIEW LETTERS 2020; 125:258003. [PMID: 33416399 DOI: 10.1103/physrevlett.125.258003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear via Newtonian dynamics with linear viscous drag at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction ϕ=0.646±0.001. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media. Understanding how crystal formation is initiated within a homogeneous disordered state gives key insights into the old open problem of glass formation in fluids.
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Affiliation(s)
- Weiwei Jin
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Charles Radin
- Department of Mathematics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
| | - Harry L Swinney
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
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Pattern detection in colloidal assembly: A mosaic of analysis techniques. Adv Colloid Interface Sci 2020; 284:102252. [PMID: 32971396 DOI: 10.1016/j.cis.2020.102252] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Revised: 08/27/2020] [Accepted: 08/28/2020] [Indexed: 01/19/2023]
Abstract
Characterization of the morphology, identification of patterns and quantification of order encountered in colloidal assemblies is essential for several reasons. First of all, it is useful to compare different self-assembly methods and assess the influence of different process parameters on the final colloidal pattern. In addition, casting light on the structures formed by colloidal particles can help to get better insight into colloidal interactions and understand phase transitions. Finally, the growing interest in colloidal assemblies in materials science for practical applications going from optoelectronics to biosensing imposes a thorough characterization of the morphology of colloidal assemblies because of the intimate relationship between morphology and physical properties (e.g. optical and mechanical) of a material. Several image analysis techniques developed to investigate images (acquired via scanning electron microscopy, digital video microscopy and other imaging methods) provide variegated and complementary information on the colloidal structures under scrutiny. However, understanding how to use such image analysis tools to get information on the characteristics of the colloidal assemblies may represent a non-trivial task, because it requires the combination of approaches drawn from diverse disciplines such as image processing, computational geometry and computational topology and their application to a primarily physico-chemical process. Moreover, the lack of a systematic description of such analysis tools makes it difficult to select the ones more suitable for the features of the colloidal assembly under examination. In this review we provide a methodical and extensive description of real-space image analysis tools by explaining their principles and their application to the investigation of two-dimensional colloidal assemblies with different morphological characteristics.
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Cramer Pedersen M, Robins V, Mortensen K, Kirkensgaard JJK. Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases. Proc Math Phys Eng Sci 2020; 476:20200170. [PMID: 33071571 PMCID: PMC7544332 DOI: 10.1098/rspa.2020.0170] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Accepted: 08/04/2020] [Indexed: 12/30/2023] Open
Abstract
Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by 'topological proximity', a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.
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Affiliation(s)
| | - Vanessa Robins
- Department of Applied Mathematics, Australian National University, Canberra, Australia
| | - Kell Mortensen
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - Jacob J. K. Kirkensgaard
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
- Department of Food Science, University of Copenhagen, Copenhagen, Denmark
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28
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Parvanian AM, Salimijazi H, Shabaninejad M, Troitzsch U, Kreider P, Lipiński W, Saadatfar M. Thermochemical CO 2 splitting performance of perovskite coated porous ceramics. RSC Adv 2020; 10:23049-23057. [PMID: 35520356 PMCID: PMC9054684 DOI: 10.1039/d0ra02353a] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Accepted: 05/31/2020] [Indexed: 11/28/2022] Open
Abstract
In this paper, we investigate the redox performance of perovskite coated porous ceramics with various architectures. For this purpose, reticulated porous ceramics (RPCs) in three different pore sizes (5, 12, 75 ppi) were fabricated to represent a broad range of structures and pore sizes. The perovskite material is based on lanthanum manganite and was synthesized and doped with Ca and Al through the Pechini method. Using a deep coating method, the surface of RPC substrates was modified by a thin-film coating with a thickness of ∼15 μm. We evaluated the CO2 conversion performance of the developed materials in a gold-image IR furnace. X-ray micro-computed tomography along with SEM/EDX were utilized in different steps of the work for a thorough study of the bulk and surface features. Results reveal that the intermediate pore size of 12 ppi delivers the maximum perovskite loading with a high degree of coating homogeneity and connectivity while CO2 conversion tests showed the highest CO yield for 75 ppi. Our results show that the extreme conditions inside the furnace combined with the flow of gaseous phases cause the RPCs to shrink in length up to 23% resulting in the alteration of the pore phase and elimination of small pores reducing the total specific surface area. Further our results reveal an important mechanism resulting in the inhibition of CO2 conversion where the perovskite coating layer migrates into the matrix of the RPC frame. A representative volume of LCMA coated porous SiC showing a maximum of 23% shrinkage when subject to high-temperature CO2 conversion redox reactions. This results in significant structural changes including a reduction in specific surface area.![]()
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Affiliation(s)
- Amir Masoud Parvanian
- Department of Materials Engineering, Isfahan University of Technology Isfahan 84156-83111 Iran
| | - Hamidreza Salimijazi
- Department of Materials Engineering, Isfahan University of Technology Isfahan 84156-83111 Iran
| | - Mehdi Shabaninejad
- Department of Applied Mathematics, Research School of Physics and Engineering, The Australian National University Canberra ACT 2601 Australia
| | - Ulrike Troitzsch
- Research School of Earth Sciences, The Australian National University Canberra ACT 2601 Australia
| | - Peter Kreider
- Research School of Engineering, The Australian National University Canberra ACT 2601 Australia
| | - Wojciech Lipiński
- Research School of Engineering, The Australian National University Canberra ACT 2601 Australia
| | - Mohammad Saadatfar
- Department of Applied Mathematics, Research School of Physics and Engineering, The Australian National University Canberra ACT 2601 Australia
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29
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Weighted persistent homology for osmolyte molecular aggregation and hydrogen-bonding network analysis. Sci Rep 2020; 10:9685. [PMID: 32546801 PMCID: PMC7297731 DOI: 10.1038/s41598-020-66710-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2019] [Accepted: 05/20/2020] [Indexed: 12/24/2022] Open
Abstract
It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate dramatically different properties in a protein folding process. Even with the enormous theoretical and experimental research work on these two osmolytes, various aspects of their underlying mechanisms still remain largely elusive. In this paper, we propose to use the weighted persistent homology to systematically study the osmolytes molecular aggregation and their hydrogen-bonding network from a local topological perspective. We consider two weighted models, i.e., localized persistent homology (LPH) and interactive persistent homology (IPH). Boltzmann persistent entropy (BPE) is proposed to quantitatively characterize the topological features from LPH and IPH, together with persistent Betti number (PBN). More specifically, from the localized persistent homology models, we have found that TMAO and urea have very different local topology. TMAO is found to exhibit a local network structure. With the concentration increase, the circle elements in these networks show a clear increase in their total numbers and a decrease in their relative sizes. In contrast, urea shows two types of local topological patterns, i.e., local clusters around 6 Å and a few global circle elements at around 12 Å. From the interactive persistent homology models, it has been found that our persistent radial distribution function (PRDF) from the global-scale IPH has same physical properties as the traditional radial distribution function. Moreover, PRDFs from the local-scale IPH can also be generated and used to characterize the local interaction information. Other than the clear difference of the first peak value of PRDFs at filtration size 4 Å, TMAO and urea also shows very different behaviors at the second peak region from filtration size 5 Å to 10 Å. These differences are also reflected in the PBNs and BPEs of the local-scale IPH. These localized topological information has never been revealed before. Since graphs can be transferred into simplicial complexes by the clique complex, our weighted persistent homology models can be used in the analysis of various networks and graphs from any molecular structures and aggregation systems.
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30
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Jaquette J, Schweinhart B. FRACTAL DIMENSION ESTIMATION WITH PERSISTENT HOMOLOGY: A COMPARATIVE STUDY. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION 2020; 84:105163. [PMID: 32256012 PMCID: PMC7117095 DOI: 10.1016/j.cnsns.2019.105163] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance to classical methods to compute the correlation and box-counting dimensions in examples of self-similar fractals, chaotic attractors, and an empirical dataset. The performance of the 0-dimensional persistent homology dimension is comparable to that of the correlation dimension, and better than box-counting.
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31
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Moosavi SM, Xu H, Chen L, Cooper AI, Smit B. Geometric landscapes for material discovery within energy-structure-function maps. Chem Sci 2020; 11:5423-5433. [PMID: 34094069 PMCID: PMC8159328 DOI: 10.1039/d0sc00049c] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2020] [Accepted: 04/28/2020] [Indexed: 01/12/2023] Open
Abstract
Porous molecular crystals are an emerging class of porous materials formed by crystallisation of molecules with weak intermolecular interactions, which distinguishes them from extended nanoporous materials like metal-organic frameworks (MOFs). To aid discovery of porous molecular crystals for desired applications, energy-structure-function (ESF) maps were developed that combine a priori prediction of both the crystal structure and its functional properties. However, it is a challenge to represent the high-dimensional structural and functional landscapes of an ESF map and to identify energetically favourable and functionally interesting polymorphs among the 1000s to 10 000s of structures typically on a single ESF map. Here, we introduce geometric landscapes, a representation for ESF maps based on geometric similarity, quantified by persistent homology. We show that this representation allows the exploration of complex ESF maps, automatically pinpointing interesting crystalline phases available to the molecule. Furthermore, we show that geometric landscapes can serve as an accountable descriptor for porous materials to predict their performance for gas adsorption applications. A machine learning model trained using this geometric similarity could reach a remarkable accuracy in predicting the materials' performance for methane storage applications.
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Affiliation(s)
- Seyed Mohamad Moosavi
- Laboratory of Molecular Simulation (LSMO), Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL) Rue de l'Industrie 17 CH-1951 Sion Valais Switzerland
| | - Henglu Xu
- Laboratory of Molecular Simulation (LSMO), Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL) Rue de l'Industrie 17 CH-1951 Sion Valais Switzerland
| | - Linjiang Chen
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, Department of Chemistry, University of Liverpool 51 Oxford Street Liverpool L7 3NY UK
| | - Andrew I Cooper
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, Department of Chemistry, University of Liverpool 51 Oxford Street Liverpool L7 3NY UK
| | - Berend Smit
- Laboratory of Molecular Simulation (LSMO), Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL) Rue de l'Industrie 17 CH-1951 Sion Valais Switzerland
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32
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Weighted persistent homology for biomolecular data analysis. Sci Rep 2020; 10:2079. [PMID: 32034168 PMCID: PMC7005716 DOI: 10.1038/s41598-019-55660-3] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Accepted: 11/29/2019] [Indexed: 11/08/2022] Open
Abstract
In this paper, we systematically review weighted persistent homology (WPH) models and their applications in biomolecular data analysis. Essentially, the weight value, which reflects physical, chemical and biological properties, can be assigned to vertices (atom centers), edges (bonds), or higher order simplexes (cluster of atoms), depending on the biomolecular structure, function, and dynamics properties. Further, we propose the first localized weighted persistent homology (LWPH). Inspired by the great success of element specific persistent homology (ESPH), we do not treat biomolecules as an inseparable system like all previous weighted models, instead we decompose them into a series of local domains, which may be overlapped with each other. The general persistent homology or weighted persistent homology analysis is then applied on each of these local domains. In this way, functional properties, that are embedded in local structures, can be revealed. Our model has been applied to systematically study DNA structures. It has been found that our LWPH based features can be used to successfully discriminate the A-, B-, and Z-types of DNA. More importantly, our LWPH based principal component analysis (PCA) model can identify two configurational states of DNA structures in ion liquid environment, which can be revealed only by the complicated helical coordinate system. The great consistence with the helical-coordinate model demonstrates that our model captures local structure variations so well that it is comparable with geometric models. Moreover, geometric measurements are usually defined in local regions. For instance, the helical-coordinate system is limited to one or two basepairs. However, our LWPH can quantitatively characterize structure information in regions or domains with arbitrary sizes and shapes, where traditional geometrical measurements fail.
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33
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Wang Z, Ogawa T, Adachi Y. Property Predictions for Dual‐Phase Steels Using Persistent Homology and Machine Learning. ADVANCED THEORY AND SIMULATIONS 2020. [DOI: 10.1002/adts.201900227] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Zhi‐Lei Wang
- Department of Materials Science and EngineeringNagoya University Furo‐cho Chikusa‐ku Nagoya 464‐8601 Japan
| | - Toshio Ogawa
- Department of Materials Science and EngineeringNagoya University Furo‐cho Chikusa‐ku Nagoya 464‐8601 Japan
| | - Yoshitaka Adachi
- Department of Materials Science and EngineeringNagoya University Furo‐cho Chikusa‐ku Nagoya 464‐8601 Japan
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34
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Hong S, Kim D. Medium-range order in amorphous ices revealed by persistent homology. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:455403. [PMID: 31374556 DOI: 10.1088/1361-648x/ab3820] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Despite the amorphous nature of glassy water, x-ray or neutron scattering experiments reveal sharp peaks in the structure factor, indicating the existence of medium-range order (MRO) in the system. However the real space origin of the peaks has yet to be disclosed. Herein, we use a combined approach of molecular dynamics simulations and persistent homology (PH) to investigate two types of glassy water, low-density amorphous (LDA) and high-density amorphous (HDA) ices. We present prominent MRO ring structures in each type of the ices, distinguished by their size and shape as well as the number of their components: MRO rings in HDA are observed smaller, less planar and more membered, compared to those in LDA. The PH-extracted MRO rings successfully reproduce the quantitative features, including the position and width, of the first sharp diffraction peaks in the structure factor, hence suitably serving as the origin of experimental MRO signatures in the amorphous ices. Our study supports that PH is an effective tool to identify hidden MRO in amorphous configurations.
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Affiliation(s)
- Sungyeon Hong
- Computational Science Research Center, Korea Institute of Science and Technology (KIST), Seoul 02792, Republic of Korea
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35
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Wu Q, Cui C, Bertrand T, Shattuck MD, O'Hern CS. Active acoustic switches using two-dimensional granular crystals. Phys Rev E 2019; 99:062901. [PMID: 31330653 DOI: 10.1103/physreve.99.062901] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2019] [Indexed: 11/07/2022]
Abstract
We employ numerical simulations to study active transistor-like switches made from two-dimensional (2D) granular crystals containing two types of grains with the same size but different masses. We tune the mass contrast and arrangement of the grains to maximize the width of the frequency band gap in the device. The input signal is applied to a single grain on one side of the device, and the output signal is measured from another grain on the other side of the device. Changing the size of one or many grains tunes the pressure, which controls the vibrational response of the device. Switching between the on and off states is achieved using two mechanisms: (1) pressure-induced switching where the interparticle contact network is the same in the on and off states and (2) switching through contact breaking. In general, the performance of the acoustic switch, as captured by the gain ratio and switching time between the on and off states, is better for pressure-induced switching. We show that in these acoustic switches the gain ratio between the on and off states can be larger than 10^{4} and the switching time (multiplied by the driving frequency) is comparable to that obtained recently for sonic crystals and less than that for photonic transistor-like switches. Since the self-assembly of grains with different masses into 2D granular crystals is challenging, we describe simulations of circular grains with small circular knobs placed symmetrically around the perimeter mixed with circular grains without knobs. Using umbrella sampling techniques, we show that grains with six knobs most efficiently form the hexagonal crystals that yield the largest frequency band gap. Using the simulation results, we estimate the time required for vibration experiments to generate granular crystals of millimeter-sized steel beads with maximal band gaps.
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Affiliation(s)
- Qikai Wu
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Chunyang Cui
- State Key Laboratory of Hydroscience and Engineering, Tsinghua University, 100084 Beijing, China
| | - Thibault Bertrand
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA.,Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, England, United Kingdom
| | - Mark D Shattuck
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA.,Department of Physics and Benjamin Levich Institute, The City College of the City University of New York, New York, 10031, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA.,Department of Physics, Yale University, New Haven, Connecticut 06520, USA.,Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
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Gutierrez A, Buchet M, Clair S. Persistent Homology to Quantify the Quality of Surface‐Supported Covalent Networks. Chemphyschem 2019; 20:2286-2291. [DOI: 10.1002/cphc.201900257] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Revised: 04/29/2019] [Indexed: 11/10/2022]
Affiliation(s)
- Abraham Gutierrez
- Institute of Discrete MathematicsGraz University of Technology Steyrergasse 30 8010 Graz Austria
| | - Mickaël Buchet
- Institute of Discrete MathematicsGraz University of Technology Steyrergasse 30 8010 Graz Austria
| | - Sylvain Clair
- Aix Marseille Univ, Univ ToulonCNRS, IM2NP Marseille France
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Steinberg L, Russo J, Frey J. A new topological descriptor for water network structure. J Cheminform 2019; 11:48. [PMID: 31292766 PMCID: PMC6617667 DOI: 10.1186/s13321-019-0369-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2018] [Accepted: 07/02/2019] [Indexed: 11/10/2022] Open
Abstract
Bulk water molecular dynamics simulations based on a series of atomistic water potentials (TIP3P, TIP4P/Ew, SPC/E and OPC) are compared using new techniques from the field of topological data analysis. The topological invariants (the different degrees of homology) derived from each simulation frame are used to create a series of persistence diagrams from the atomic positions. These are averaged over the simulation time using the persistence image formalism, before being normalised by their total magnitude (the L1 norm) to ensure a size independent descriptor (L1NPI). We demonstrate that the L1NPI formalism is suitable for the analysis of systems where the number of molecules varies by at least a factor of 10. Using standard machine learning techniques, a basic linear SVM, it is shown that differences in water models are able to be isolated to different degrees of homology. In particular, whereas first degree homology is able to distinguish between all atomistic potentials studied, OPC is the only potential that differs in its second degree homology. The L1 normalised persistence images are then used in the comparison of a series of Stillinger-Weber potential simulations to the atomistic potentials and the effects of changing the strength of three-body interactions on the structures is easily evident in L1NPI space, with a reduction in variance of structures as interaction strength increases being the most obvious result. Furthermore, there is a clear tracking in L1NPI space of the λ parameter. The L1NPI formalism presents a useful new technique for the analysis of water and other materials. It is approximately size-independent, and has been shown to contain information as to real structures in the system. We finally present a perspective on the use of L1NPIs and other persistent homology techniques as a descriptor for water solubility.
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Affiliation(s)
- Lee Steinberg
- School of Chemistry, University of Southampton, Southampton, SO17 1BJ UK
| | - John Russo
- School of Mathematics, University of Bristol, Bristol, UK
| | - Jeremy Frey
- School of Chemistry, University of Southampton, Southampton, SO17 1BJ UK
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Lotito V, Zambelli T. A Journey Through the Landscapes of Small Particles in Binary Colloidal Assemblies: Unveiling Structural Transitions from Isolated Particles to Clusters upon Variation in Composition. NANOMATERIALS (BASEL, SWITZERLAND) 2019; 9:E921. [PMID: 31248053 PMCID: PMC6669769 DOI: 10.3390/nano9070921] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2019] [Revised: 06/21/2019] [Accepted: 06/22/2019] [Indexed: 01/11/2023]
Abstract
Two-dimensional (2D) amorphous binary colloidal assemblies composed of particles of two different sizes are characterized by the loss of hexagonal close-packing for larger particles, occurring when the size ratio between small (S) and large (L) particles dSdL exceeds a certain threshold value. For moderately low particle number ratios NSNL large particles still retain a denser arrangement with transitions from hexagonal symmetry to the coexistence of different types of symmetries as NSNL progressively departs from 0 to higher values. On the other hand, small particles reveal sparser arrangements: shape identification and quantification of structural transitions in small particle arrangements appear particularly challenging. In this article, we investigate their shapes and transitions for amorphous binary colloidal particles assembled at the air/water interface. For the quantitative characterization of the evolution in particle arrangements for NSNL variable between 0.5 and 2, we develop an innovative procedure for morphological analysis, combining Minkowski functionals, Voronoi diagrams and ad hoc techniques to recognize and classify specific features. Such a powerful approach has revealed a wide variety of landscapes featuring isolated particles, dimers, chains, small clusters evolving with the colloidal suspension composition. Our method can be applied to the analysis of spatial configurations of sparse colloidal patterns obtained in different conditions.
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Affiliation(s)
- Valeria Lotito
- Laboratory of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zurich, Gloriastrasse 35, 8092 Zurich, Switzerland.
| | - Tomaso Zambelli
- Laboratory of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zurich, Gloriastrasse 35, 8092 Zurich, Switzerland.
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39
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Xia K, Anand DV, Shikhar S, Mu Y. Persistent homology analysis of osmolyte molecular aggregation and their hydrogen-bonding networks. Phys Chem Chem Phys 2019; 21:21038-21048. [DOI: 10.1039/c9cp03009c] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Dramatically different patterns can be observed in the topological fingerprints for hydrogen-bonding networks from two types of osmolyte systems.
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Affiliation(s)
- Kelin Xia
- Division of Mathematical Sciences
- School of Physical and Mathematical Sciences
- School of Biological Sciences
- Nanyang Technological University
- Singapore
| | - D. Vijay Anand
- Division of Mathematical Sciences
- School of Physical and Mathematical Sciences
- School of Biological Sciences
- Nanyang Technological University
- Singapore
| | - Saxena Shikhar
- School of Biological Sciences
- Nanyang Technological University
- Singapore
| | - Yuguang Mu
- School of Biological Sciences
- Nanyang Technological University
- Singapore
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40
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Dhiman I, Kimber SAJ, Mehta A, Chatterji T. A neutron tomography study: probing the spontaneous crystallization of randomly packed granular assemblies. Sci Rep 2018; 8:17637. [PMID: 30518966 PMCID: PMC6281579 DOI: 10.1038/s41598-018-36331-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Accepted: 11/20/2018] [Indexed: 11/09/2022] Open
Abstract
We study the spontaneous crystallization of an assembly of highly monodisperse steel spheres under shaking, as it evolves from localized icosahedral ordering towards a packing reaching crystalline ordering. Towards this end, real space neutron tomography measurements on the granular assembly are carried out, as it is systematically subjected to a variation of frequency and amplitude. As expected, we see a presence of localized icosahedral ordering in the disordered initial state (packing fraction ≈ 0.62). As the frequency is increased for both the shaking amplitudes (0.2 and 0.6 mm) studied here, there is a rise in packing fraction, accompanied by an evolution to crystallinity. The extent of crystallinity is found to depend on both the amplitude and frequency of shaking. We find that the icosahedral ordering remains localized and its extent does not grow significantly, while the crystalline ordering grows rapidly as an ordering transition point is approached. In the ordered state, crystalline clusters of both face centered cubic (FCC) and hexagonal close packed (HCP) types are identified, the latter of which grows from stacking faults. Our study shows that an earlier domination of FCC gives way to HCP ordering at higher shaking frequencies, suggesting that despite their coexistence, there is a subtle dynamical competition at play. This competition depends on both shaking amplitude and frequency, as our results as well as those of earlier theoretical simulations demonstrate. It is likely that this involves the very small free energy difference between the two structures.
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Affiliation(s)
- Indu Dhiman
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA.
| | - Simon A J Kimber
- Université Bourgogne-Franche Comté, Université de Bourgogne, ICB-Laboratoire Interdisciplinaire Carnot de Bourgogne, Bâtiment Sciences Mirande, 9 Avenue Alain Savary, B-P. 47870, 21078, Dijon Cedex, France
| | - Anita Mehta
- Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany
| | - Tapan Chatterji
- Institut Laue-Langevin, 71 Avenue des Martyrs, 38000, Grenoble, France.
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41
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Armstrong RT, McClure JE, Robins V, Liu Z, Arns CH, Schlüter S, Berg S. Porous Media Characterization Using Minkowski Functionals: Theories, Applications and Future Directions. Transp Porous Media 2018. [DOI: 10.1007/s11242-018-1201-4] [Citation(s) in RCA: 55] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Abstract
We derive more than 80 embeddings of 2D hyperbolic honeycombs in Euclidean 3 space, forming 3-periodic infinite polyhedra with cubic symmetry. All embeddings are "minimally frustrated," formed by removing just enough isometries of the (regular, but unphysical) 2D hyperbolic honeycombs [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] to allow embeddings in Euclidean 3 space. Nearly all of these triangulated "simplicial polyhedra" have symmetrically identical vertices, and most are chiral. The most symmetric examples include 10 infinite "deltahedra," with equilateral triangular faces, 6 of which were previously unknown and some of which can be described as packings of Platonic deltahedra. We describe also related cubic crystalline packings of equal hyperbolic discs in 3 space that are frustrated analogues of optimally dense hyperbolic disc packings. The 10-coordinated packings are the least "loosened" Euclidean embeddings, although frustration swells all of the hyperbolic disc packings to give less dense arrays than the flat penny-packing even though their unfrustrated analogues in [Formula: see text] are denser.
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Lotito V, Zambelli T. Pattern Formation in Binary Colloidal Assemblies: Hidden Symmetries in a Kaleidoscope of Structures. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:7827-7843. [PMID: 29886749 DOI: 10.1021/acs.langmuir.8b01411] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In this study, we present a detailed investigation of the morphology of binary colloidal structures formed by self-assembly at air/water interface of particles of two different sizes, with a size ratio such that the larger particles do not retain a hexagonal arrangement in the binary assembly. While the structure and symmetry of binary mixtures in which such hexagonal order is preserved has been thoroughly scrutinized, binary colloids in the regime of nonpreservation of the hexagonal order have not been examined with the same level of detail due also to the difficulty in finding analysis tools suitable to recognize hidden symmetries in seemingly amorphous and disordered arrangements. For this purpose, we resorted to a combination of different analysis tools based on computational geometry and computational topology to get a comprehensive picture of the morphology of the assemblies. By carrying out an extensive investigation of binary assemblies in this regime with variable concentration of smaller particles with respect to larger particles, we identify the main patterns that coexist in the apparently disordered assemblies and detect transitions in the symmetries upon increase in the number of small particles. As the concentration of small particles increases, large particle arrangements become more dilute and a transition from hexagonal to rhombic and square symmetries occurs, accompanied also by an increase in clusters of small particles; the relative weight of each specific symmetry can be controlled by varying the composition of the assemblies. The demonstration of the possibility to control the morphology of apparently disordered binary colloidal assemblies by varying experimental conditions and the definition of a route for the investigation of disordered assemblies are important for future studies of complex colloidal patterns to understand self-assembly mechanisms and to tailor the physical properties of colloidal assemblies.
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Affiliation(s)
- Valeria Lotito
- Laboratory of Biosensors and Bioelectronics , Institute for Biomedical Engineering, ETH Zurich , Gloriastrasse 35 , 8092 Zurich , Switzerland
| | - Tomaso Zambelli
- Laboratory of Biosensors and Bioelectronics , Institute for Biomedical Engineering, ETH Zurich , Gloriastrasse 35 , 8092 Zurich , Switzerland
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45
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Xia K. Persistent homology analysis of ion aggregations and hydrogen-bonding networks. Phys Chem Chem Phys 2018; 20:13448-13460. [PMID: 29722784 DOI: 10.1039/c8cp01552j] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Despite the great advancement of experimental tools and theoretical models, a quantitative characterization of the microscopic structures of ion aggregates and their associated water hydrogen-bonding networks still remains a challenging problem. In this paper, a newly-invented mathematical method called persistent homology is introduced, for the first time, to quantitatively analyze the intrinsic topological properties of ion aggregation systems and hydrogen-bonding networks. The two most distinguishable properties of persistent homology analysis of assembly systems are as follows. First, it does not require a predefined bond length to construct the ion or hydrogen-bonding network. Persistent homology results are determined by the morphological structure of the data only. Second, it can directly measure the size of circles or holes in ion aggregates and hydrogen-bonding networks. To validate our model, we consider two well-studied systems, i.e., NaCl and KSCN solutions, generated from molecular dynamics simulations. They are believed to represent two morphological types of aggregation, i.e., local clusters and extended ion networks. It has been found that the two aggregation types have distinguishable topological features and can be characterized by our topological model very well. Further, we construct two types of networks, i.e., O-networks and H2O-networks, for analyzing the topological properties of hydrogen-bonding networks. It is found that for both models, KSCN systems demonstrate much more dramatic variations in their local circle structures with a concentration increase. A consistent increase of large-sized local circle structures is observed and the sizes of these circles become more and more diverse. In contrast, NaCl systems show no obvious increase of large-sized circles. Instead a consistent decline of the average size of the circle structures is observed and the sizes of these circles become more and more uniform with a concentration increase. As far as we know, these unique intrinsic topological features in ion aggregation systems have never been pointed out before. More importantly, our models can be directly used to quantitatively analyze the intrinsic topological invariants, including circles, loops, holes, and cavities, of any network-like structures, such as nanomaterials, colloidal systems, biomolecular assemblies, among others. These topological invariants cannot be described by traditional graph and network models.
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Affiliation(s)
- Kelin Xia
- Division of Mathematical Sciences, School of Physical and Mathematical Sciences, School of Biological Sciences, Nanyang Technological University, 637371, Singapore.
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46
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47
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48
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Kimura M, Obayashi I, Takeichi Y, Murao R, Hiraoka Y. Non-empirical identification of trigger sites in heterogeneous processes using persistent homology. Sci Rep 2018; 8:3553. [PMID: 29476108 PMCID: PMC5824834 DOI: 10.1038/s41598-018-21867-z] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Accepted: 02/12/2018] [Indexed: 11/09/2022] Open
Abstract
Macroscopic phenomena, such as fracture, corrosion, and degradation of materials, are associated with various reactions which progress heterogeneously. Thus, material properties are generally determined not by their averaged characteristics but by specific features in heterogeneity (or 'trigger sites') of phases, chemical states, etc., where the key reactions that dictate macroscopic properties initiate and propagate. Therefore, the identification of trigger sites is crucial for controlling macroscopic properties. However, this is a challenging task. Previous studies have attempted to identify trigger sites based on the knowledge of materials science derived from experimental data ('empirical approach'). However, this approach becomes impractical when little is known about the reaction or when large multi-dimensional datasets, such as those with multiscale heterogeneities in time and/or space, are considered. Here, we introduce a new persistent homology approach for identifying trigger sites and apply it to the heterogeneous reduction of iron ore sinters. Four types of trigger sites, 'hourglass'-shaped calcium ferrites and 'island'- shaped iron oxides, were determined to initiate crack formation using only mapping data depicting the heterogeneities of phases and cracks without prior mechanistic information. The identification of these trigger sites can provide a design rule for reducing mechanical degradation during reduction.
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Affiliation(s)
- Masao Kimura
- Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, 305-0801, Japan. .,Department of Materials Structure Science, School of High Energy Accelerator Science, SOKENDAI (The Graduate University for Advanced Studies), Tsukuba, Ibaraki, 305-0801, Japan.
| | - Ippei Obayashi
- Advanced Institute for Materials Research (AIMR), Tohoku University, Sendai, Miyagi, 980-8577, Japan
| | - Yasuo Takeichi
- Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, 305-0801, Japan.,Department of Materials Structure Science, School of High Energy Accelerator Science, SOKENDAI (The Graduate University for Advanced Studies), Tsukuba, Ibaraki, 305-0801, Japan
| | - Reiko Murao
- Advanced Technology Research Laboratories, Nippon Steel & Sumitomo Metal Co., Futtsu, Chiba, 293-8511, Japan
| | - Yasuaki Hiraoka
- Advanced Institute for Materials Research (AIMR), Tohoku University, Sendai, Miyagi, 980-8577, Japan.,Center for Materials research by Information Integration (CMI2), Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science (NIMS), Tsukuba, Ibaraki, 305-0047, Japan.,Center for Advanced Intelligence Project, RIKEN, Tokyo, 103-0027, Japan
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49
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Rietz F, Radin C, Swinney HL, Schröter M. Nucleation in Sheared Granular Matter. PHYSICAL REVIEW LETTERS 2018; 120:055701. [PMID: 29481202 DOI: 10.1103/physrevlett.120.055701] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Revised: 12/11/2017] [Indexed: 06/08/2023]
Abstract
We present an experiment on crystallization of packings of macroscopic granular spheres. This system is often considered to be a model for thermally driven atomic or colloidal systems. Cyclically shearing a packing of frictional spheres, we observe a first order phase transition from a disordered to an ordered state. The ordered state consists of crystallites of mixed fcc and hcp symmetry that coexist with the amorphous bulk. The transition, initiated by homogeneous nucleation, overcomes a barrier at 64.5% volume fraction. Nucleation consists predominantly of the dissolving of small nuclei and the growth of nuclei that have reached a critical size of about ten spheres.
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Affiliation(s)
- Frank Rietz
- Max-Planck-Institute for Dynamics and Self-Organization Göttingen, 37077 Göttingen, Germany
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91052 Erlangen, Germany
- Department of Nonlinear Phenomena, University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
- Department of Pattern Formation, University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - Charles Radin
- Department of Mathematics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Harry L Swinney
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Matthias Schröter
- Max-Planck-Institute for Dynamics and Self-Organization Göttingen, 37077 Göttingen, Germany
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91052 Erlangen, Germany
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50
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Takahashi K, Charles C, Boswell R, Ando A. Adiabatic Expansion of Electron Gas in a Magnetic Nozzle. PHYSICAL REVIEW LETTERS 2018; 120:045001. [PMID: 29437412 DOI: 10.1103/physrevlett.120.045001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Revised: 12/08/2017] [Indexed: 06/08/2023]
Abstract
A specially constructed experiment shows the near perfect adiabatic expansion of an ideal electron gas resulting in a polytropic index greater than 1.4, approaching the adiabatic value of 5/3, when removing electric fields from the system, while the polytropic index close to unity is observed when the electrons are trapped by the electric fields. The measurements were made on collisionless electrons in an argon plasma expanding in a magnetic nozzle. The collision lengths of all electron collision processes are greater than the scale length of the expansion, meaning the system cannot be in thermodynamic equilibrium, yet thermodynamic concepts can be used, with caution, in explaining the results. In particular, a Lorentz force, created by inhomogeneities in the radial plasma density, does work on the expanding magnetic field, reducing the internal energy of the electron gas that behaves as an adiabatically expanding ideal gas.
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Affiliation(s)
- Kazunori Takahashi
- Department of Electrical Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Christine Charles
- Space Plasma, Power and Propulsion Laboratory, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Rod Boswell
- Space Plasma, Power and Propulsion Laboratory, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Akira Ando
- Department of Electrical Engineering, Tohoku University, Sendai 980-8579, Japan
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