2008/05/15 by Anthony J. Creaco, ANTHONY J. CREACO, Nikos Kalogeropoulos +1
Materials Science · Mathematics · Physics and Astronomy · #Liquid Crystal Research Advancements #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #hep-ph #hep-th
paper · pdf · doi:10.1142/s0217732308027242
published as Mod.Phys.Lett.A23:2053-2066,2008 · 17 pages, no figures. To be published in Mod. Phys. Lett. A
arxiv created 2008/05/15 · openalex publication_date 2008/08/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We generalize the geodesic rule to the case of formation of higher codimensional global defects. Relying on energetic arguments, we argue that, for such defects, the geometric structures of interest are the totally geodesic submanifolds. On the other hand, stochastic arguments lead to a diffusion equation approach, from which the geodesic rule is deduced. It turns out that the most appropriate geometric structure that one should consider is the convex hull of the values of the order parameter on the causal volumes whose collision gives rise to the defect. We explain why these two approaches lead to similar results when calculating the density of global defects by using a theorem of Cheeger and Gromoll. We present a computation of the probability of formation of strings/vortices in the case of a system, such as nematic liquid crystals, whose vacuum is ℝP 2 .