## Abstract

We describe an algorithm and a C++ implementation that we have written and made available for calculating the fully nonlinear evolution of 5D braneworld models with scalar fields. Bulk fields allow for the stabilization of the extra dimension. However, they complicate the dynamics of the system, so that analytic calculations (performed within an effective 4D theory) are usually only reliable for static bulk configurations or when the evolution of the extra dimension is negligible. In the general case, the nonlinear 5D dynamics can be studied numerically, and the algorithm and code we describe are the first ones of that type designed for this task. The program and its full documentation are available on the Web at http://www.cita.utoronto.ca/~jmartin/BRANECODE/. ^{1} In this paper we provide a brief overview of what the program does and how to use it. Title of program: BRANECODE Catalogue identifier: ADVX Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVX Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Operating systems under which the program has been tested: Linux Programming language used: C++ Memory required to execute with typical data: less than 1 MB Has the code been vectorized?: no Peripherals used: none No. of lines in distributed program, including test data, etc.: 8277 No. of bytes in distributed program, including test data, etc.: 74 939 CPC Program Library subprograms used: none Nature of physical problem: Dynamics of two co-dimension one branes in a five-dimensional spacetime with a bulk scalar field and arbitrary potentials. The dynamics is governed by the five dimensional Einstein equations of gravity and the junction conditions at the position of the branes. Method of solution: Leapfrog algorithm to solve system of (1+1)-dimensional partial differential equations; Initial and boundary value problem. Restrictions on the complexity of the problem: Assumption of homogeneity along three spatial dimensions parallel to the branes. Typical running time: Depending on the grid size and length of the time evolution: from ∼1 s to ∼1 h or longer. Unusual features of the program:none

Original language | English (US) |
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Pages (from-to) | 69-78 |

Number of pages | 10 |

Journal | Computer Physics Communications |

Volume | 171 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 2005 |

Externally published | Yes |

## Keywords

- Brane collision
- Brane cosmology
- Braneworld dynamics
- Nonlinear evolution
- Numerical String theory