2026-09-19T09:22:23Zhttps://wakespace.lib.wfu.edu/server/oai/requestoai:null:10339/907512026-09-02T08:58:02Zcom_10339_14934col_10339_38132
McConkey, Robert
2018-05-24T08:36:17Z
2018-05-24T08:36:17Z
2018
https://wakespace.lib.wfu.edu/handle/10339/90751
In this thesis we will focus on the topic of helicity. Helicity gives us a way to
measure the coiling of flow lines in a vector field, computed by the formula
[see formula in PDF file]
.
To start our exploration of helicity we begin with the topic of differential forms and
their correspondence with vector fields in
R
3
. Then we use the correspondence of
forms and vector fields to show that Maxwell’s Equations can be reduced to two
equations of differential forms. We continue our exploration of mathematics in physics
with the Biot-Savart operator; this operator calculates the associated magnetic field
on a domain Ω given an electric current on Ω. The Biot-Savart operator gives us a
way to compute vector field helicity.
We will begin our exploration of helicity with its standard definition above, and
where it comes of use in both mathematics and physics. Next we return to differential
forms to show how the correspondence to vector fields allows us to define the helicity
of forms. Then using helicity of forms we can expand on the three-dimensional idea
of helicity to both submanifolds and higher dimension ambient spaces.
en
Wake Forest University
Submanifold Helicity
Thesis
Parsley, Robert J
Moore, William F
Mathematics and Statistics
open.access