Knotting and Linking in Macromolecules

Intrinsic Linking and Knotting of Graphs

An analog to intrinsic linking, intrinsic even linking, is explored in the first half of this paper. Four graphs are established to be minor minimal intrinsically even linked, and it is conjectured that they form a complete minor minimal set. Some characterizations are given, using the simplest of the four graphs as an integral part of the arguments, that may be useful in proving the conjecture...

Reconfigurable knots and links in chiral nematic colloids.

Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid-crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six...

Intrinsic Linking and Knotting in Virtual Spatial Graphs

We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that these filtrations are descending and non-terminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, ...

Intrinsic Linking and Knotting of Graphs in Arbitrary 3â•fimanifolds

A comparative study of knotting decorations and knot tools Used in Ghaffarieh and Kabud domes of Maragheh city

Knotting is one of the most regular geometric decorations that spread with the spread of Islam. Among the different Islamic governments, the Ilkhani era is one of the most brilliant periods of prosperity and flourishing of art and architecture with the use of knot-making in Iran. Among the magnificent buildings of this period are Kabud Dome and Ghaffarieh Dome, located in Maragheh city, the ext...