Level set method for the evolution of defect and brane networks

Hindmarsh, Mark (2003) Level set method for the evolution of defect and brane networks. Physical Review D, 68 (4). 043510. ISSN 0556-2821

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A theory for studying the dynamic scaling properties of branes and relativistic topological defect networks is presented. The theory, based on a relativistic version of the level set method, well known in other contexts, possesses self-similar “scaling” solutions, for which one can calculate many quantities of interest. Here, the length and area densities of cosmic strings and domain walls are calculated in Minkowski space, and radiation, matter, and curvature-dominated Friedmann-Robertson-Walker cosmologies with two and three space dimensions. The scaling exponents agree with the naive ones based on dimensional analysis, except for cosmic strings in three-dimensional Minkowski space, which are predicted to have a logarithmic correction to the naive scaling form. The scaling amplitudes of the length and area densities are a factor of approximately 2 lower than the results from numerical simulations of classical field theories. An expression for the length density of strings in the condensed matter literature is corrected.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QC Physics
Depositing User: Mark Hindmarsh
Date Deposited: 06 Feb 2012 21:17
Last Modified: 07 Mar 2017 09:23
URI: http://srodev.sussex.ac.uk/id/eprint/30616

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