Non uniform thickness and weighted global radius of curvature of smooth curves

The uniform thickness of knots has been used to investigate knotted polymers and DNA strands. Even though these structures carry great length, it is unusual for them to contain knots. However, when they do, it can cause gene malfunctions. In fact, scientist have demonstrated that knotting may cause a loss of genetic material by blocking DNA replication and also blocking transcription of a gene into its active protein.

Since it is possible for biological structures, such as polymers and DNA strands, to exhibit forces or charges of different strengths the idea of a non uniform thickness of a knot is explored. In his work, O. Durumeric provides a definition for the non uniform thickness. This thesis will provide an alternative characterization for the non uniform thickness of a knot, which is more conducive to computer calculations.