Introduction
This site contains information about cosmic strings simulations
performed by C.J. Copi and T. Vachaspati.
Contained here are publications, movies, and code
associated with our cosmic string simulations. All materials
here are copyrighted by the authors (unless explicitly noted
otherwise). The information here is free for use as long as proper
credit is given to the authors.
Publications based on this work
 Paper 1

"The Shape of Cosmic String Loops" is available on the arxiv. Accepted by Phys. Rev. D.
Movies of strings
Flat Space
Movies of loops evolving in flat space. This is based on version 1.0
of the code as used in paper
1.
In the movies the thickness of the loop segments signifies the
distance of the segment from the observer, thicker being closer.
Unstable loops (those that will intersect) are shown in a gray
scale. Stable loops are shown in a blue scale. When a loop
selfintersects it flashes red.
 N=10,000; M=10 loops

 N=10,000; M=50 loop

 Perturbed degenerate kinky loop
 A movie of the numerical evolution of the example given in
paper 1 :
\[
\vec{p}=\cos(\alpha)\hat z \quad \vec{q}=\cos(\beta)\hat x +
\sin(\beta)\hat y,
\]
where
\[
\alpha = \pi \lfloor 2\sigma_\rfloor, \quad \beta =
2\pi\epsilon\sigma_+ + (1\epsilon)\pi\lfloor 2\sigma_+\rfloor,
\]
$\epsilon=0.05$, and $\sigma_\pm\in [0,1]$.
View Movie. Notice that the loop does
not self intersect.
 Perturbed degenerate kinky loop with cusps

A movie of the numerical evolution based on an example given in
paper 1 :
\[
\vec{p}=\sin(\beta_)\hat x +\cos(\beta_)\hat z, \quad
\]
\[
\vec{q}=\sin(\beta_+)\sin(\phi_+)\hat x +
\sin(\beta_+)\cos(\phi_+)\hat y  \cos(\beta_+)\hat z,
\]
where
\[
\beta_\pm = 2\pi\epsilon_\pm\sigma_\pm + (1\epsilon_\pm)\pi\lfloor
2\sigma_\pm\rfloor,
\]
For the numerical simulation we chose
$\epsilon_ = 1/\sqrt{58}$, $\epsilon_+=1/\sqrt{95}$, and
$\phi_+=\pi/\sqrt{67}$.
View Movie. The loop has
been made very thin in the movie. Even with this it is hard to
tell from the movie alone that the loop never selfintersects (it
doesn't!). The cusp occurs at $t=0$ and $t=500$. A small red
sphere is placed on the cusp in one frame at these times.
Downloadable Code
Complete source code with documentation and notes.
 Version 1.0

 Version 1.0
download. This is the code used in paper
1. This code will not be updated after the
paper is published. It will survive for posterity as a record of
the algorithm used for the published results despite its warts and
any errors subsequently discovered.
 Loop documentation
is included with the source code but can also be viewed separately.
Site Info
The webpage design is based on the Gila
design made freely available by haran on the
open source web design
site. The elegance of the layout should be attributed to
haran, the flaws to me.