🍩 Database of Original & Non-Theoretical Uses of Topology

(found 16 matches in 0.015067s)

  1. Unsupervised Topological Learning Approach of Crystal Nucleation in Pure Tantalum (2021)

    Sébastien Becker, Emilie Devijver, Rémi Molinier, Noël Jakse
    Abstract Nucleation phenomena commonly observed in our every day life are of fundamental, technological and societal importance in many areas, but some of their most intimate mechanisms remain however to be unraveled. Crystal nucleation, the early stages where the liquid-to-solid transition occurs upon undercooling, initiates at the atomic level on nanometer length and sub-picoseconds time scales and involves complex multidimensional mechanisms with local symmetry breaking that can hardly be observed experimentally in the very details. To reveal their structural features in simulations without a priori, an unsupervised learning approach founded on topological descriptors loaned from persistent homology concepts is proposed. Applied here to a monatomic metal, namely Tantalum (Ta), it shows that both translational and orientational ordering always come into play simultaneously when homogeneous nucleation starts in regions with low five-fold symmetry.

  2. Statistical Topology of Bond Networks With Applications to Silica (2020)

    B. Schweinhart, D. Rodney, J. K. Mason
    Abstract Whereas knowledge of a crystalline material's unit cell is fundamental to understanding the material's properties and behavior, there are no obvious analogs to unit cells for disordered materials despite the frequent existence of considerable medium-range order. This article views a material's structure as a collection of local atomic environments that are sampled from some underlying probability distribution of such environments, with the advantage of offering a unified description of both ordered and disordered materials. Crystalline materials can then be regarded as special cases where the underlying probability distribution is highly concentrated around the traditional unit cell. The 𝐻1 barcode is proposed as a descriptor of local atomic environments suitable for disordered bond networks and is applied with three other descriptors to molecular dynamics simulations of silica glasses. Each descriptor reliably distinguishes the structure of glasses produced at different cooling rates, with the 𝐻1 barcode and coordination profile providing the best separation. The approach is generally applicable to any system that can be represented as a sparse graph.

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  3. Unsupervised Topological Learning Approach of Crystal Nucleation (2022)

    Sébastien Becker, Emilie Devijver, Rémi Molinier, Noël Jakse
    Abstract Nucleation phenomena commonly observed in our every day life are of fundamental, technological and societal importance in many areas, but some of their most intimate mechanisms remain however to be unravelled. Crystal nucleation, the early stages where the liquid-to-solid transition occurs upon undercooling, initiates at the atomic level on nanometre length and sub-picoseconds time scales and involves complex multidimensional mechanisms with local symmetry breaking that can hardly be observed experimentally in the very details. To reveal their structural features in simulations without a priori, an unsupervised learning approach founded on topological descriptors loaned from persistent homology concepts is proposed. Applied here to monatomic metals, it shows that both translational and orientational ordering always come into play simultaneously as a result of the strong bonding when homogeneous nucleation starts in regions with low five-fold symmetry. It also reveals the specificity of the nucleation pathways depending on the element considered, with features beyond the hypothesis of Classical Nucleation Theory.

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  4. Ultrahigh-Pressure Form of \$\Mathrm\Si\\\mathrm\O\\_\2\\$ Glass With Dense Pyrite-Type Crystalline Homology (2019)

    M. Murakami, S. Kohara, N. Kitamura, J. Akola, H. Inoue, A. Hirata, Y. Hiraoka, Y. Onodera, I. Obayashi, J. Kalikka, N. Hirao, T. Musso, A. S. Foster, Y. Idemoto, O. Sakata, Y. Ohishi
    Abstract High-pressure synthesis of denser glass has been a longstanding interest in condensed-matter physics and materials science because of its potentially broad industrial application. Nevertheless, understanding its nature under extreme pressures has yet to be clarified due to experimental and theoretical challenges. Here we reveal the formation of OSi4 tetraclusters associated with that of SiO7 polyhedra in SiO2 glass under ultrahigh pressures to 200 gigapascal confirmed both experimentally and theoretically. Persistent homology analyses with molecular dynamics simulations found increased packing fraction of atoms whose topological diagram at ultrahigh pressures is similar to a pyrite-type crystalline phase, although the formation of tetraclusters is prohibited in the crystalline phase. This critical difference would be caused by the potential structural tolerance in the glass for distortion of oxygen clusters. Furthermore, an expanded electronic band gap demonstrates that chemical bonds survive at ultrahigh pressure. This opens up the synthesis of topologically disordered dense oxide glasses.

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  5. Unsupervised Topological Learning for Identification of Atomic Structures (2022)

    Sébastien Becker, Emilie Devijver, Rémi Molinier, Noël Jakse
    Abstract We propose an unsupervised learning methodology with descriptors based on topological data analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a priori knowledge, our method allows for an autonomous identification of clusters of atomic structures through a Gaussian mixture model. We apply successfully this approach to the analysis of elemental Zr in the crystalline and liquid states as well as homogeneous nucleation events under deep undercooling conditions. This opens the way to deeper and autonomous study of complex phenomena in materials at the atomic scale.

  6. Understanding Diffraction Patterns of Glassy, Liquid and Amorphous Materials via Persistent Homology Analyses (2019)

    Yohei Onodera, Shinji Kohara, Shuta Tahara, Atsunobu Masuno, Hiroyuki Inoue, Motoki Shiga, Akihiko Hirata, Koichi Tsuchiya, Yasuaki Hiraoka, Ippei Obayashi, Koji Ohara, Akitoshi Mizuno, Osami Sakata
    Abstract The structure of glassy, liquid, and amorphous materials is still not well understood, due to the insufficient structural information from diffraction data. In this article, attempts are made to understand the origin of diffraction peaks, particularly of the first sharp diffraction peak (FSDP, Q1), the principal peak (PP, Q2), and the third peak (Q3), observed in the measured diffraction patterns of disordered materials whose structure contains tetrahedral motifs. It is confirmed that the FSDP (Q1) is not a signature of the formation of a network, because an FSDP is observed in tetrahedral molecular liquids. It is found that the PP (Q2) reflects orientational correlations of tetrahedra. Q3, that can be observed in all disordered materials, even in common liquid metals, stems from simple pair correlations. Moreover, information on the topology of disordered materials was revealed by utilizing persistent homology analyses. The persistence diagram of silica (SiO2) glass suggests that the shape of rings in the glass is similar not only to those in the crystalline phase with comparable density (α-cristobalite), but also to rings present in crystalline phases with higher density (α-quartz and coesite); this is thought to be the signature of disorder. Furthermore, we have succeeded in revealing the differences, in terms of persistent homology, between tetrahedral networks and tetrahedral molecular liquids, and the difference/similarity between liquid and amorphous (glassy) states. Our series of analyses demonstrated that a combination of diffraction data and persistent homology analyses is a useful tool for allowing us to uncover structural features hidden in halo pattern of disordered materials.

  7. Visualizing Nanoparticle Surface Dynamics and Instabilities Enabled by Deep Denoising (2025)

    Peter A. Crozier, Matan Leibovich, Piyush Haluai, Mai Tan, Andrew M. Thomas, Joshua Vincent, Sreyas Mohan, Adria Marcos Morales, Shreyas A. Kulkarni, David S. Matteson, Yifan Wang, Carlos Fernandez-Granda
    Abstract Materials functionalities may be associated with atomic-level structural dynamics occurring on the millisecond timescale. However, the capability of electron microscopy to image structures with high spatial resolution and millisecond temporal resolution is often limited by poor signal-to-noise ratios. With an unsupervised deep denoising framework, we observed metal nanoparticle surfaces (platinum nanoparticles on cerium oxide) in a gas environment with time resolutions down to 10 milliseconds at a moderate electron dose. On this timescale, many nanoparticle surfaces continuously transition between ordered and disordered configurations. Stress fields can penetrate below the surface, leading to defect formation and destabilization, thus making the nanoparticle fluxional. Combining this unsupervised denoiser with in situ electron microscopy greatly improves spatiotemporal characterization, opening a new window for the exploration of atomic-level structural dynamics in materials.

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  9. Feature Detection and Hypothesis Testing for Extremely Noisy Nanoparticle Images Using Topological Data Analysis (2023)

    Andrew M. Thomas, Peter A. Crozier, Yuchen Xu, David S. Matteson
    Abstract We propose a flexible algorithm for feature detection and hypothesis testing in images with ultra-low signal-to-noise ratio using cubical persistent homology. Our main application is in the identification of atomic columns and other features in Transmission Electron Microscopy (TEM). Cubical persistent homology is used to identify local minima and their size in subregions in the frames of nanoparticle videos, which are hypothesized to correspond to relevant atomic features. We compare the performance of our algorithm to other employed methods for the detection of columns and their intensity. Additionally, Monte Carlo goodness-of-fit testing using real-valued summaries of persistence diagrams derived from smoothed images (generated from pixels residing in the vacuum region of an image) is developed and employed to identify whether or not the proposed atomic features generated by our algorithm are due to noise. Using these summaries derived from the generated persistence diagrams, one can produce univariate time series for the nanoparticle videos, thus, providing a means for assessing fluxional behavior. A guarantee on the false discovery rate for multiple Monte Carlo testing of identical hypotheses is also established.

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  10. Morse Theory and Persistent Homology for Topological Analysis of 3D Images of Complex Materials (2014)

    O. Delgado-Friedrichs, V. Robins, A. Sheppard
    Abstract We develop topologically accurate and compatible definitions for the skeleton and watershed segmentation of a 3D digital object that are computed by a single algorithm. These definitions are based on a discrete gradient vector field derived from a signed distance transform. This gradient vector field is amenable to topological analysis and simplification via For-man's discrete Morse theory and provides a filtration that can be used as input to persistent homology algorithms. Efficient implementations allow us to process large-scale x-ray micro-CT data of rock cores and other materials.

  11. Topology of Force Networks in Granular Media Under Impact (2017)

    M. X. Lim, R. P. Behringer
    Abstract We investigate the evolution of the force network in experimental systems of two-dimensional granular materials under impact. We use the first Betti number, , and persistence diagrams, as measures of the topological properties of the force network. We show that the structure of the network has a complex, hysteretic dependence on both the intruder acceleration and the total force response of the granular material. can also distinguish between the nonlinear formation and relaxation of the force network. In addition, using the persistence diagram of the force network, we show that the size of the loops in the force network has a Poisson-like distribution, the characteristic size of which changes over the course of the impact.

  12. Four-Dimensional Observation of Ductile Fracture in Sintered Iron Using Synchrotron X-Ray Laminography (2019)

    Y. Ozaki, Y. Mugita, M. Aramaki, O. Furukimi, S. Oue, F. Jiang, T. Tsuji, A. Takeuchi, M. Uesugi, K. Ashizuka
    Abstract Synchrotron X-ray laminography was used to examine the time-dependent evolution of the three-dimensional (3D) morphology of micropores in sintered iron during the tensile test. 3D snapshots showed that the networked open pores grow wider than 20 µm along the tensile direction, resulting in the internal necking of the specimen. Subsequently, these pores initiated the cracks perpendicular to the tensile direction by coalescing with the surrounding pre-existing microvoids or with the secondary-generated voids immediately before fracture. Topological analysis of the barycentric positions of these microvoids showed that they form the two-dimensional networks within the ∼20 µm of radius area. These observations strongly indicate that the microvoid coalescence could occur on shear planes formed close to the enlarged open pores or between closed pores by strain accumulation and play an important role in the crack initiation.

  13. Pore Geometry Characterization by Persistent Homology Theory (2018)

    Fei Jiang, Takeshi Tsuji, Tomoyuki Shirai
    Abstract Rock pore geometry has heterogeneous characteristics and is scale dependent. This feature in a geological formation differs significantly from artificial materials and makes it difficult to predict hydrologic and elastic properties. To characterize pore heterogeneity, we propose an evaluation method that exploits the recently developed persistent homology theory. In the proposed method, complex pore geometry is first represented as sphere cloud data using a pore-network extraction method. Then, a persistence diagram (PD) is calculated from the point cloud, which represents the spatial distribution of pore bodies. A new parameter (distance index H) derived from the PD is proposed to characterize the degree of rock heterogeneity. Low H value indicates high heterogeneity. A new empirical equation using this index H is proposed to predict the effective elastic modulus of porous media. The results indicate that the proposed PD analysis is very efficient for extracting topological feature of pore geometry.

  14. Tenfold Topology of Crystals (2020)

    Eyal Cornfeld, Shachar Carmeli
    Abstract The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of non-spatial symmetries. It lays at the core of the periodic table of topological insulators and superconductors which provided a complete classification of weakly-interacting electrons' non-crystalline topological phases for all symmetry classes. Over recent years, a plethora of topological phenomena with diverse surface states has been discovered in crystalline materials. In this paper, we obtain an exhaustive classification of topologically distinct groundstates as well as topological phases with anomalous surface states of crystalline topological insulators and superconductors for key space-groups, layer-groups, and rod-groups. This is done in a unified manner for the full tenfold-way of Altland-Zirnbauer non-spatial symmetry classes. We establish a comprehensive paradigm that harnesses the modern mathematical framework of equivariant spectra; it allows us to obtain results applicable to generic topological classification problems. In particular, this paradigm provides efficient computational tools that enable an inherently unified treatment of the full tenfold-way.

  15. Topological Electronic Structure and Weyl Points in Nonsymmorphic Hexagonal Materials (2020)

    Rafael González-Hernández, Erick Tuiran, Bernardo Uribe
    Abstract Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and connectivity group theory show that Weyl points are generated by band crossings in accordion-like and hourglass-like dispersion relations. These Weyl points are stable against weak perturbations and are protected by the screw rotation symmetry. Based on first-principles calculations we found a complete agreement between the topological predicted energy dispersion relations and real hexagonal materials. Topological charge (chirality) and Berry curvature calculations show the simultaneous formation of Weyl points and nodal-lines in 4d transition-metal trifluorides such as AgF3 and AuF3. Furthermore, a large intrinsic spin-Hall conductivity was found due to the combined strong spin-orbit coupling and multiple Weyl-point crossings in the electronic structure. These materials could be used to the spin/charge conversion in more energy-efficient spintronic devices.

  16. Tuning Cavitation and Crazing in Polymer Nanocomposite Glasses Containing Bimodal Grafted Nanoparticles at the Nanoparticle/Polymer Interface (2019)

    Rui Shi, Hu-Jun Qian, Zhong-Yuan Lu
    Abstract It is widely accepted that adding nanoparticles (NPs) into polymer matrices can dramatically alter the mechanical properties of the material, and that the properties at the NP/polymer interface play a vital role. By performing coarse-grained molecular dynamics simulations, we study the stress–strain behaviour of polymer/NP composites (PNCs) in a glassy state under a triaxial tensile deformation, in which the NPs are well dispersed in the system via bimodal grafting. A ‘HOMO’ system, in which the short grafted chains are chemically identical to the matrix polymer, and a ‘HETERO’ system, in which the short grafted chains interact weakly with the matrix, are investigated. Our simulations demonstrate that the HOMO system behaves very similarly to the pure polymer system, with quick cavitation and a drop in stress after the yielding point, corresponding to a craze deformation process. While in the HETERO system, weak interactions between the short grafts and the matrix polymer induce a low local modulus, therefore, rather homogeneous void formation and consequently a slower cavitation process are observed at the surface of the well dispersed NPs during the tensile deformation. As a result, the depletion effect at the NP surface eventually leads to NP re-assembly at large strains. Moreover, the HETERO system undergoes a shear-deformation-tended tensile process rather than the craze deformation found in the HOMO system. At the same time, the HETERO system is more ductile, with a much slower drop in stress after yielding than the HOMO system. In addition, the homogeneous generation of voids at small strain in the HETERO system can be utilized in the fabrication of polymer films with desirable separation abilities for gases or small molecules. We hope that these simulation results will be helpful for the property regulation of PNC materials containing polymer grafted NPs.