5 papers · 1 filter
Dimensional Reduction and emergence of defects in the Oseen-Frank model for nematic liquid crystals
Giacomo Canevari, Antonio Segatti
In this paper we discuss the behavior of the Oseen-Frank model for nematic liquid crystals in the limit of vanishing thickness. More precisely, in a thin slab~ with~…
The Yang-Mills-Higgs functional on complex line bundles: asymptotics for critical points
Giacomo Canevari, Federico Luigi Dipasquale, Giandomenico Orlandi
We consider a gauge-invariant Ginzburg-Landau functional (also known as Abelian Yang-Mills-Higgs model) on Hermitian line bundles over closed Riemannian manifolds of dimension $n \…
Motion of vortices for the extrinsic Ginzburg-Landau flow for vector fields on surfaces
Giacomo Canevari, Antonio Segatti
We consider the gradient flow of a Ginzburg-Landau functional of the type \[ F_\varepsilon^{\mathrm{extr}}(u):=\frac{1}{2}\int_M \left|D u\right|_g^2 + \left|\mathscr{S} u\right|^2…
Defects in Nematic Shells: a -convergence discrete-to-continuum approach
Giacomo Canevari, Antonio Segatti
In this paper we rigorously investigate the emergence of defects on Nematic Shells with genus different from one. This phenomenon is related to a non trivial interplay between the…
Convergence properties for a generalization of the Caginalp phase field system
Giacomo Canevari, Pierluigi Colli
We are concerned with a phase field system consisting of two partial differential equations in terms of the variables thermal displacement, that is basically the time integration o…