🍩 Database of Original & Non-Theoretical Uses of Topology

(found 5 matches in 0.001416s)

  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. Crystallographic Interacting Topological Phases and Equvariant Cohomology: To Assume or Not to Assume (2020)

    Daniel Sheinbaum, Omar Antolín Camarena
    Abstract For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case we discuss some invariants given by equivariant characteristic classes. We do not assume an emergent relativistic field theory nor that phases form a topological spectrum. We also do not assume short-range entanglement nor the existence of quasi-particles as is done in SPT and SET classifications respectively. Using a slightly generalized Bloch decomposition and Grassmanians made out of ground state spaces, we show that the \$P\$-equivariant cohomology of a \$d\$-dimensional torus gives rise to different interacting phases. We compare our results to bosonic symmorphic crystallographic SPT phases and to non-interacting fermionic crystallographic phases in class A. Finally we discuss the relation of our assumptions to those made for crystallographic SPT and SET phases.

  4. 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.

  5. Revealing Key Structural Features Hidden in Liquids and Glasses (2019)

    Hajime Tanaka, Hua Tong, Rui Shi, John Russo
    Abstract A great success of solid state physics comes from the characterization of crystal structures in the reciprocal (wave vector) space. The power of structural characterization in Fourier space originates from the breakdown of translational and rotational symmetries. However, unlike crystals, liquids and amorphous solids possess continuous translational and rotational symmetries on a macroscopic scale, which makes Fourier space analysis much less effective. Lately, several studies have revealed local breakdown of translational and rotational symmetries even for liquids and glasses. Here, we review several mathematical methods used to characterize local structural features of apparently disordered liquids and glasses in real space. We distinguish two types of local ordering in liquids and glasses: energy-driven and entropy-driven. The former, which is favoured energetically by symmetry-selective directional bonding, is responsible for anomalous behaviours commonly observed in water-type liquids such as water, silicon, germanium and silica. The latter, which is often favoured entropically, shows connections with the heterogeneous, slow dynamics found in hard-sphere-like glass-forming liquids. We also discuss the relationship between such local ordering and crystalline structures and its impact on glass-forming ability.