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.

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.