Knot-detection algorithm to measure viscosity in three-dimensional MHD plasmas

TL;DR

This paper introduces a computational knot-detection algorithm called LINKAGE that measures the linking of magnetic field lines in 3D plasmas, aiding in understanding plasma viscosity and topological evolution.

Contribution

The study presents a novel algorithm that quantifies linking in 3D space and applies it to analyze evolving magnetic field topologies in plasma physics.

Findings

Successfully distinguishes between different knot types.

Tracks topological changes over time in plasma systems.

Demonstrates versatility in analyzing dynamic topological systems.

Abstract

This project explores the mathematical study of knots and links in topology, focusing on differentiating between the two-component Unlink and the Hopf Link using a computational tool named LINKAGE. LINKAGE employs the linking number, calculated through Barycentric Equations, Matrix Algebra, and basic topological principles, to quantify the degree of linking between two closed curves in three-dimensional space. This approach not only distinguishes between different knot structures but also has applications in understanding complex systems such as magnetic field lines in plasma physics. Additionally, this project includes an example where multiple interlinked loops were analyzed over different time stamps using the LINKAGE algorithm. By observing how these links break and evolve, the algorithm demonstrates its ability to track changes in the topological properties of the system. This dynamic analysis shows the versatility of the tool in studying evolving systems, where the topology of the components can change, providing valuable information about the underlying physical processes driving these changes.