Scaling in Numerical Simulations of Domain Walls

We study the evolution of domain wall networks appearing after phase transitions in the early Universe. They exhibit interesting dynamical scaling behaviour which is not yet well understood, and are also simple models for the more phenomenologically acceptable string networks. We have run numerical simulations in two- and three-dimensional lattices of sizes up to 4096^3. The theoretically predicted scaling solution for the wall area density A ~ 1/t is supported by the simulation results, while no evidence of a logarithmic correction reported in previous studies could be found. The energy loss mechanism appears to be direct radiation, rather than the formation and collapse of closed loops or spheres. We discuss the implications for the evolution of string networks.Comment: 7pp RevTeX, 9 eps files (including six 220kB ones

The Shapes of Dirichlet Defects

If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher dimension. The shapes of such defects are analyzed numerically, with special attention paid to the intersection regions. Walls (co-dimension 1 branes) terminating on other walls, global strings (co-dimension 2 branes) and local strings (including gauge fields) terminating on walls are all considered. Connections to supersymmetric field theories, string theory and condensed matter systems are pointed out.Comment: 24 pages, RevTeX, 21 eps figure

Level Set Method for the Evolution of Defect and Brane Networks

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 FRW cosmologies with 2 and 3 space dimensions. The scaling exponents agree the naive ones based on dimensional analysis, except for cosmic strings in 3-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 results from numerical simulations of classical field theories. An expression for the length density of strings in the condensed matter literature is corrected.Comment: 46pp LaTeX, revtex4(preprint), 1 eps figure, revised for publication. Note title chang

Sorção de fósforo em função do teor inicial e de sistemas de manejo de solos

A relação entre o P sorvido/P solução do solo pode ser influenciada pelo teor de P previamente sorvido e pelos sistemas de manejo. Este trabalho teve o objetivo de avaliar as modificações na capacidade de sorção máxima (Pmax) e na constante relacionada com a energia de ligação de P com os colóides (k) da isoterma de Langmuir, provocadas (a) pela inclusão do teor de P previamente sorvido (Ppre) e (b) por sistemas de manejo de solos. Coletaram-se, em maio de 1997, amostras de solo (Latossolo Vermelho distroférrico típico, Latossolo Vermelho distrófico típico e Argissolo Vermelho distrófico típico), em três camadas (0-2,5, 2,5-7,5 e 7,5-17,5 cm), de três experimentos instalados a partir de 1979, envolvendo os sistemas plantio direto e cultivo convencional com diferentes sucessões de cultura. O solo foi equilibrado com oito concentrações de P em solução de CaCl2 0,001 mol L-1. Após a agitação por 16 h, avaliou-se a concentração de P no sobrenadante. Os dados de P-sorvido e P-solução foram ajustados à equação de Langmuir, obtendo-se a Pmax e a k, considerando ou não o Ppre. A inclusão do Ppre no modelo de Langmuir aumenta, em média, 2,9 vezes o valor da k e não afeta a Pmax, no LVdf, e aumenta em todas as camadas, no LVd, e na camada superficial, no PVd. A Pmax é pouco influenciada pelos métodos de preparo do solo, sucessões de culturas e camadas amostradas