By C.J.A.P. Martins
This booklet sheds new mild on topological defects in generally differing structures, utilizing the Velocity-Dependent One-Scale version to raised comprehend their evolution. Topological defects – cosmic strings, monopoles, area partitions or others - unavoidably shape at cosmological (and condensed subject) section transitions. in the event that they are reliable and long-lived they are going to be fossil relics of higher-energy physics. figuring out their behaviour and results is a key a part of any critical try and comprehend the universe, and this calls for modelling their evolution. The velocity-dependent one-scale version is the single totally quantitative version of illness community evolution, and the canonical version within the box. This e-book presents a evaluation of the version, explaining its actual content material and describing its vast diversity of applicability.
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Additional resources for Defect Evolution in Cosmology and Condensed Matter: Quantitative Analysis with the Velocity-Dependent One-Scale Model
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If the function is smooth, it is possible to parametrize the wall surface such that two tangential vectors will be orthogonal μ ∂σ1 x μ ∂σ2 xμ ≡ x,1 xμ,2 = 0. 1) We can also require that the velocity of the wall ∂τ x μ ≡ x˙ μ is normal to the tangent surface. P. 1007/978-3-319-44553-3_3 29 30 3 Domain Walls μ ν where σw is a constant mass per unit area, γab = gμν x,a x,b is the induced metric, μ 1 ab cd ∂x μ ab γ = 3! ε ε γac γbd is its determinant, x,a = ∂σ a , ε is the Levi-Civita symbol, and L is the Lagrangian density.
3 The Ideal Model The availability of a large number of models (of which the two studied above are but examples), all different but to some extent related, begs the question of which features are fundamental and which are irrelevant details. More to the point, one might ask what is the best possible model for domain walls, at least from the point of view of its potential to produce frustrated networks. In an ideal model, the probability that two domains in the same vacuum state are close to each other should be as small as possible, since that will minimize the probability of coarse-graining.
Defect Evolution in Cosmology and Condensed Matter: Quantitative Analysis with the Velocity-Dependent One-Scale Model by C.J.A.P. Martins