🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.001011s)

  1. 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.

  2. 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.

  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.