Mapping hyperbolic order in curved materials

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Standard

Mapping hyperbolic order in curved materials. / Pedersen, Martin Cramer; Hyde, Stephen T.; Ramsden, Stuart; Kirkensgaard, Jacob J. K.

I: Soft Matter, Bind 2023, Nr. 19, 2023, s. 1586-1595.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Pedersen, MC, Hyde, ST, Ramsden, S & Kirkensgaard, JJK 2023, 'Mapping hyperbolic order in curved materials', Soft Matter, bind 2023, nr. 19, s. 1586-1595. https://doi.org/10.1039/d2sm01403c

APA

Pedersen, M. C., Hyde, S. T., Ramsden, S., & Kirkensgaard, J. J. K. (2023). Mapping hyperbolic order in curved materials. Soft Matter, 2023(19), 1586-1595. https://doi.org/10.1039/d2sm01403c

Vancouver

Pedersen MC, Hyde ST, Ramsden S, Kirkensgaard JJK. Mapping hyperbolic order in curved materials. Soft Matter. 2023;2023(19):1586-1595. https://doi.org/10.1039/d2sm01403c

Author

Pedersen, Martin Cramer ; Hyde, Stephen T. ; Ramsden, Stuart ; Kirkensgaard, Jacob J. K. / Mapping hyperbolic order in curved materials. I: Soft Matter. 2023 ; Bind 2023, Nr. 19. s. 1586-1595.

Bibtex

@article{9f26b704844140688e226eb60f74c39c,
title = "Mapping hyperbolic order in curved materials",
abstract = "Nature employs an impressive range of topologically complex ordered nanostructures that occur in various forms in both natural and synthetic materials. A particular class of these exhibits negative curvature and forms periodic saddle-shaped surfaces in three dimensions. Unlike pattern formation on flat or positively curved surfaces like spherical systems, the understanding of patterning on such surfaces is highly complicated due to the structures being intrinsically intertwined in three dimensions. We present a new method for visualisation and analysis of patterns on triply periodic negatively curved surfaces by mapping to two-dimensional hyperbolic space analogous to spherical projections in cartography thus effectively creating a more accessible {"}hyperbolic map{"} of the pattern. Specifically, we exemplify the method via the simplest triply periodic minimal surfaces: the Primitive, Diamond, and Gyroid in their universal cover along with decorations from a soft materials, whose structures involve decorations of soft matter on negatively curved surfaces, not necessarily minimal.",
keywords = "PERIODIC MINIMAL-SURFACES, MOLECULAR-DYNAMICS SIMULATIONS, CRYSTALS, CRYSTALLOGRAPHY, PARAMETRIZATION, NETWORKS, PATTERNS, DIAMOND, SYSTEMS, TILINGS",
author = "Pedersen, {Martin Cramer} and Hyde, {Stephen T.} and Stuart Ramsden and Kirkensgaard, {Jacob J. K.}",
year = "2023",
doi = "10.1039/d2sm01403c",
language = "English",
volume = "2023",
pages = "1586--1595",
journal = "Soft Matter",
issn = "1744-683X",
publisher = "Royal Society of Chemistry",
number = "19",

}

RIS

TY - JOUR

T1 - Mapping hyperbolic order in curved materials

AU - Pedersen, Martin Cramer

AU - Hyde, Stephen T.

AU - Ramsden, Stuart

AU - Kirkensgaard, Jacob J. K.

PY - 2023

Y1 - 2023

N2 - Nature employs an impressive range of topologically complex ordered nanostructures that occur in various forms in both natural and synthetic materials. A particular class of these exhibits negative curvature and forms periodic saddle-shaped surfaces in three dimensions. Unlike pattern formation on flat or positively curved surfaces like spherical systems, the understanding of patterning on such surfaces is highly complicated due to the structures being intrinsically intertwined in three dimensions. We present a new method for visualisation and analysis of patterns on triply periodic negatively curved surfaces by mapping to two-dimensional hyperbolic space analogous to spherical projections in cartography thus effectively creating a more accessible "hyperbolic map" of the pattern. Specifically, we exemplify the method via the simplest triply periodic minimal surfaces: the Primitive, Diamond, and Gyroid in their universal cover along with decorations from a soft materials, whose structures involve decorations of soft matter on negatively curved surfaces, not necessarily minimal.

AB - Nature employs an impressive range of topologically complex ordered nanostructures that occur in various forms in both natural and synthetic materials. A particular class of these exhibits negative curvature and forms periodic saddle-shaped surfaces in three dimensions. Unlike pattern formation on flat or positively curved surfaces like spherical systems, the understanding of patterning on such surfaces is highly complicated due to the structures being intrinsically intertwined in three dimensions. We present a new method for visualisation and analysis of patterns on triply periodic negatively curved surfaces by mapping to two-dimensional hyperbolic space analogous to spherical projections in cartography thus effectively creating a more accessible "hyperbolic map" of the pattern. Specifically, we exemplify the method via the simplest triply periodic minimal surfaces: the Primitive, Diamond, and Gyroid in their universal cover along with decorations from a soft materials, whose structures involve decorations of soft matter on negatively curved surfaces, not necessarily minimal.

KW - PERIODIC MINIMAL-SURFACES

KW - MOLECULAR-DYNAMICS SIMULATIONS

KW - CRYSTALS

KW - CRYSTALLOGRAPHY

KW - PARAMETRIZATION

KW - NETWORKS

KW - PATTERNS

KW - DIAMOND

KW - SYSTEMS

KW - TILINGS

U2 - 10.1039/d2sm01403c

DO - 10.1039/d2sm01403c

M3 - Journal article

C2 - 36749349

VL - 2023

SP - 1586

EP - 1595

JO - Soft Matter

JF - Soft Matter

SN - 1744-683X

IS - 19

ER -

ID: 338425856