254 citations · 3k across the 56 of their papers we have counts for
9 papers · 1 filter
Constructing a polynomial whose nodal set is any prescribed knot or link
Benjamin Bode, Mark R. Dennis
We describe an algorithm that for every given braid explicitly constructs a function such that is a polynomial in , and $\ove…
A ray-optical Poincaré sphere for structured Gaussian beams
Miguel A Alonso, Mark R Dennis
A general family of structured Gaussian beams naturally emerges from a consideration of families of rays. These ray families, with the property that their transverse profile is inv…
Constructing a polynomial whose nodal set is the three-twist knot
Mark R Dennis, Benjamin Bode
We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot . The construction g…
A random wave model for the Aharonov-Bohm effect
Alexander J H Houston, Martin Gradhand, Mark R Dennis
We study an ensemble of random waves subject to the Aharonov-Bohm effect. The introduction of a point with a magnetic flux of arbitrary strength into a random wave ensemble gives a…
Swings and roundabouts: Optical Poincaré spheres for polarization and Gaussian beams
Mark R Dennis, Miguel A Alonso
The connection between Poincaré spheres for polariz-ation and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic 2-dimens…
Proteins analysed as virtual knots
Keith Alexander, Alexander J Taylor, Mark R Dennis
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects…