A Topological Approach to Molecular Chirality, Erica Flapan

Self-Assembly of a Chiral Cubic Three-Connected Net from the High Symmetry Molecules C60 and SnI4

10.26434/chemrxiv.12196788 ◽

2020 ◽

Author(s):

Daniel B. Straus ◽

Robert J. Cava

Keyword(s):

Organic Synthesis ◽

Self Assembly ◽

Van Der Waals ◽

Van Der Waals Forces ◽

High Symmetry ◽

Molecular Chirality ◽

Chiral Materials ◽

Self Assembled ◽

Chiral Centers

The design of new chiral materials usually requires stereoselective organic synthesis to create molecules with chiral centers. Less commonly, achiral molecules can self-assemble into chiral materials, despite the absence of intrinsic molecular chirality. Here, we demonstrate the assembly of high-symmetry molecules into a chiral van der Waals structure by synthesizing crystals of C60(SnI4)2 from icosahedral buckminsterfullerene (C60) and tetrahedral SnI4 molecules through spontaneous self-assembly. The SnI4 tetrahedra template the Sn atoms into a chiral cubic three-connected net of the SrSi2 type that is held together by van der Waals forces. Our results represent the remarkable emergence of a self-assembled chiral material from two of the most highly symmetric molecules, demonstrating that almost any molecular, nanocrystalline, or engineered precursor can be considered when designing chiral assemblies.

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A topological approach to the strain-rate pattern of ice sheets

Journal of Glaciology ◽

10.3189/s0022143000015677 ◽

1993 ◽

Vol 39 (131) ◽

pp. 10-14 ◽

Cited By ~ 1

Author(s):

J. F. Nye

Keyword(s):

Strain Rate ◽

Ice Sheets ◽

Ice Sheet ◽

Point Of View ◽

Principal Strain ◽

Topological Approach ◽

Contour Maps ◽

Isotropic Point ◽

Horizontal Strain

AbstractThe pattern of horizontal strain rate in an ice sheet is discussed from a topological point of view. In a circularly symmetric ice sheet, the isotropic point for strain rate at its centre is degenerate and structurally unstable. On perturbation the degenerate point splits into two elementary isotropic points, each of which has the lemon pattern for the trajectories of principal strain rate. Contour maps of principal strain-rate values are presented which show the details of the splitting.

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A TOPOLOGICAL APPROACH IN CORDIAL GRAPHS

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.4.13 ◽

2020 ◽

Vol 9 (4) ◽

pp. 1585-1595

Author(s):

A. Divya ◽

D. Sasikala

Keyword(s):

Topological Approach

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The “Emerging” Reality from “Hidden” Spaces

Universe ◽

10.3390/universe7030075 ◽

2021 ◽

Vol 7 (3) ◽

pp. 75

Author(s):

Richard Pincak ◽

Alexander Pigazzini ◽

Saeid Jafari ◽

Cenap Ozel

Keyword(s):

Dark Matter ◽

String Theory ◽

Topological Approach ◽

New Approach ◽

Topological Interpretation ◽

New Interpretation ◽

M Theory

The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of “emergent space” as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among which the possibility of considering a non-orientable wormhole, but mainly we provide a topological interpretation, using this new approach, to M-Theory and String Theory in 10 dimensions. Further, we present some conclusions which this new interpretation suggests, and also some remarks considering a unifying approach between strings and dark matter. The approach shown in the paper considers that reality, as it appears to us, can be the “emerging” part of a more complex hidden structure. Pacs numbers: 11.25.Yb; 11.25.-w; 02.40.Ky; 02.40.-k; 04.50.-h; 95.35.+d.

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