🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.001339s)

  1. Topological Echoes of Primordial Physics in the Universe at Large Scales (2020)

    Alex Cole, Matteo Biagetti, Gary Shiu
    Abstract We present a pipeline for characterizing and constraining initial conditions in cosmology via persistent homology. The cosmological observable of interest is the cosmic web of large scale structure, and the initial conditions in question are non-Gaussianities (NG) of primordial density perturbations. We compute persistence diagrams and derived statistics for simulations of dark matter halos with Gaussian and non-Gaussian initial conditions. For computational reasons and to make contact with experimental observations, our pipeline computes persistence in sub-boxes of full simulations and simulations are subsampled to uniform halo number. We use simulations with large NG (\$f_\\rm NL\\textasciicircum\\rm loc\=250\$) as templates for identifying data with mild NG (\$f_\\rm NL\\textasciicircum\\rm loc\=10\$), and running the pipeline on several cubic volumes of size \$40~(\textrm\Gpc/h\)\textasciicircum\3\\$, we detect \$f_\\rm NL\\textasciicircum\\rm loc\=10\$ at \$97.5\%\$ confidence on \$\sim 85\%\$ of the volumes for our best single statistic. Throughout we benefit from the interpretability of topological features as input for statistical inference, which allows us to make contact with previous first-principles calculations and make new predictions.

  2. Topological Feature Extraction for Comparison of Terascale Combustion Simulation Data (2011)

    Ajith Mascarenhas, Ray W. Grout, Peer-Timo Bremer, Evatt R. Hawkes, Valerio Pascucci, Jacqueline H. Chen
    Abstract We describe a combinatorial streaming algorithm to extract features which identify regions of local intense rates of mixing in twoterascale turbulent combustion simulations. Our algorithm allows simulation data comprised of scalar fields represented on 728x896x512 or 2025x1600x400 grids to be processed on a single relatively lightweight machine. The turbulence-induced mixing governs the rate of reaction and hence is of principal interest in these combustion simulations. We use our feature extraction algorithm to compare two very different simulations and find that in both the thickness of the extracted features grows with decreasing turbulence intensity. Simultaneous consideration of results of applying the algorithm to the HO2 mass fraction field indicates that autoignition kernels near the base of a lifted flame tend not to overlap with the high mixing rate regions.

  3. 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.