# 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 self-intersects 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 self-intersects (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.