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Results for “non-Euclidean geometry”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2021

Computational optimal transport for molecular spectra: The fully discrete case

In this study, the use of computational optimal transport is investigated as a tool for comparing two molecular spectra. Unlike other techniques for comparing molecular spectra in a pattern-recognition framework, transport distances simultaneously encode information about line positions and intensities. In addition, it is shown that transport distances are a useful alternative to Euclidean distances as Euclidean distances are based on line-by-line comparisons, while transport distances reflect broader features of molecular spectra and adequately compare spectra with different resolutions. This paper includes a tutorial on the use of optimal transport and investigates several well-chosen examples to illustrate the utility of computational optimal transport for comparing molecular spectra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Crystallography of hyperbolic lattices

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes the straightforward application of the often indispensable energy band theory to study model Hamiltonians on hyperbolic lattices. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. Here we show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. This dramatically simplifies the computation of energy spectra of tight-binding Hamiltonians on hyperbolic lattices, from exact diagonalization on the graph to solving a finite set of equations in terms of irreducible representations. The significance of this achievement needs to be compared to the all-important role played by conventional Euclidean crystallography in the study of solids. We exemplify the high potential of this approach by constructing and diagonalizing finite-dimensional Bloch wave Hamiltonians.

2-dimensional systems↗
DOE OSTI2020

Supertwisted spirals of layered materials enabled by growth on non-Euclidean surfaces

Using curves to make twists The growth of layered materials on flat substrates usually occurs in stacked layers, although defects or a lattice mismatch can induce strains that distort the shape of subsequent layers. However, these effects are usually small and can be uncontrolled. Zhao et al. now demonstrate the possibility of synthesizing multilayers of two-dimensional materials with certain twists between the layers induced by the presence of screw dislocations in combination with curved substrate surfaces. Different twist angles are achieved by varying the amount of nonplanarity and the character (conical or hyperbolic) of the surface. Science , this issue p. 442

Science & Technology - Other Topics↗