1,721,024 research outputs found
Asymptotic behavior of energy-bounded local minimizers of the Ginzburg-Landau functionals.
No full textIn this paper we describe the asymptotic behavior of an energy-bounded sequence of local minimizers of the Ginzburg-Landau functionals. The main results is that energies of these minimizers concentrate around a singular set which is itself a local minimizer of the area functional
Time-like minimal surfaces in Minkowski space
No full textWe discuss some properties of timelike minimal surfaces in flat Minkowski spacetime, reviewing some recent results concerning the definition of suitable notions of weak or generalized solutions in both the parametric and non parametric case, and the approximation by semilinear wave equations of Allen-Cahn or Ginzburg-Landau type. We mainly focus on the case of relativistic strings
Asymptotic behavior of the Ginzburg-Landau functional on complex line bundles over compact Riemann surfaces.
No full textAlcuni problemi variazionali geometrici suggeriti dalla Fisica
No full textStudiamo alcuni problemi variazionali in cui sono rilevanti alcuni aspetti geometrici (vincoli omotopici/omologici, ambientazione in spazi fibrati). Tali problemi modellizzano svariati fenomeni fisici, come le transizioni di fase negli stati condensati alle basse temperature (modelli di Allen-Cahn o Ginzburg-Landau), ovvero i modelli di Higgs ableiani in Fisica delle particelle. Caratterizziamo il comportamento asintotico delle configurazioni di equilibrio dei sistemi, ossia dei minimi globali dei funzionali coinvolti, che presentano fenomeni di concentrazione su superfici di codimensione uno o due di area minima.We deal with some variational problems with geometrical constraints of homological or homotopical type, or in fiber bundle ambients. These models arise in condensed matter Physics to describe phase transitions at low temperature (Allen-Cahn or Ginzburg-Landau models), and also in particle Physics (abelian Higgs models). We characterize the asymptotic behavior of equilibrium configurations, corresponding to global minimizers of the involved functionals, whose energy concentrate on codimension one or two minimal surfaces
Fiber bundles and regular approximation of codimension-one cycles.
No full textWe derive an approximation of codimension-one integral cycles (and cycles modulo p) in a compact riemannian manifolds by means of piecewise regular cycles: we obtain both flat convergence, and convergence of the masses. The theorem is proved by using suitable principal bundles with discrete group. As a byproduct, we give an alternative proof of the main results in [BO1], [BO2], which does not use the regularity theory for homology minimizers in a riemannian manifold. This gives also a result of G-convergenc
Uniform estimates for the parabolic Ginzburg-Landau equation. A tribute to J. L. Lions.
No full textWe consider complex-valued solutions ue of the Ginzburg-Landau equation on a smooth bounded simply connected domain W of RN, N 3 2, where e > 0 is a small parameter. We assume that the Ginzburg-Landau energy Ee(ue) verifies the bound (natural in the context) Ee(ue) M|log e|, where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of ue, as e® 0, is to establish uniform Lp bounds for the gradient, for some p > 1. We review some recent techniques developed in the elliptic case in [7], discuss some variants, and extend the methods to the associated parabolic equatio
Lifting for manifold-valued maps of bounded variation
No full textLet N be a smooth, compact, connected Riemannian manifold without boundary. Let E be the Riemannian universal covering of N. For any bounded, smooth domain Omega and any u in BV(Omega, N), we show that u has a lifting v in BV(Omega, E). Our result proves a conjecture by Bethuel and Chiron
- …
