33 citations · 82 across the 28 of their papers we have counts for
30 papers · 1 filter
Singular Limits for Three-Dimensional Global Minimizers of Ginzburg--Landau-Type Functionals: Uniform Estimates and Singular Sets
Giacomo Canevari, Haotong Fu, Wei Wang
We study the asymptotic behavior of global minimizers of a Ginzburg--Landau-type functional with general compact vacuum manifold on bounded domains in ,…
The formation of gradient-driven singular structures of codimension one and two in two-dimensions: The case study of ferronematics. Part~{II}: Refined structure of the energy-concentration set
Giacomo Canevari, Federico Luigi Dipasquale, Bianca Stroffolini
In this paper, we continue our study, started in~\cite{CDS1}, of a two-dimensional variational model for ferronematics -- composite materials formed by dispersing magnetic nanopart…
Asymptotics of Minimizers for Ginzburg--Landau-type Functionals in High Dimensions
Giacomo Canevari, Haotong Fu, Wei Wang
We investigate local minimizers of Ginzburg--Landau-type functionals in dimension that satisfy logarithmic energy bounds, assuming the potential has a vacuum manifold wit…
Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics
Giacomo Canevari, Federico Luigi Dipasquale, Bianca Stroffolini
We consider Sobolev maps from a planar domain into a closed Riemannian manifold and their BV liftings via a double covering of the target. We establish a sharp lower bound on the j…
A not-so-strange term coming from somewhere
Giacomo Canevari, Kirill Cherednichenko, Arghir Zarnescu
We consider Laplace's equation in a periodically perforated domain with Robin boundary conditions on the holes, where the Robin coefficient is scaled proportionally to the inverse…
-convergence of the -Dirichlet energy for manifold-valued maps
Giacomo Canevari, Van Phu Cuong Le, Ramon Oliver-Bonafoux +1
We prove a -convergence result for the -Dirichlet energy functional defined on maps from a smooth bounded domain to , a -con…
The formation of gradient-driven singular structures of codimension one and two in two-dimensions: The case study of ferronematics. Part~I: Energy estimates and compactness results
Giacomo Canevari, Federico Luigi Dipasquale, Bianca Stroffolini
We study a two-dimensional variational model for ferronematics -- composite materials formed by dispersing magnetic nanoparticles into a liquid crystal matrix. The model features t…
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 \…
A free discontinuity model for smectic thin films
John M. Ball, Giacomo Canevari, Bianca Stroffolini
We attempt to describe surface defects in smectic A thin films by formulating a free discontinuity problem - that is, a variational problem in which the order parameter is allowed…
Two-dimensional Ferronematics, Canonical Harmonic Maps and Minimal Connections
Giacomo Canevari, Apala Majumdar, Bianca Stroffolini +1
We study a variational model for ferronematics in two-dimensional domains, in the "super-dilute" regime. The free energy functional consists of a reduced Landau-de Gennes energy fo…
The Yang-Mills-Higgs functional on complex line bundles: -convergence and the London equation
Giacomo Canevari, Federico Luigi Dipasquale, Giandomenico Orlandi
We consider the Abelian Yang-Mills-Higgs functional, in the non-self dual scaling, on a complex line bundle over a closed Riemannian manifold of dimension . This functiona…
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…
Dynamics of Ginzburg-Landau vortices for vector fields on surfaces
Giacomo Canevari, Antonio Segatti
In this paper we consider the gradient flow of the following Ginzburg-Landau type energy \[ F_\varepsilon(u) := \frac{1}{2}\int_{M}\vert D u\vert_g^2 +\frac{1}{2\varepsilon^2}\left…
Hölder regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit
Giacomo Canevari, Jamie M. Taylor
We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with application…
Topological singular set of vector-valued maps, II: -convergence for Ginzburg-Landau type functionals
Giacomo Canevari, Giandomenico Orlandi
We prove a -convergence result for a class of Ginzburg-Landau type functionals with -well potentials, where is a closed and -connected submanif…
Polydispersity and surface energy strength in nematic colloids
Giacomo Canevari, Arghir Zarnescu
We consider a Landau-de Gennes model for a polydisperse, inhomogeneous suspension of colloidal inclusions in a nematic host, in the dilute regime. We study the homogenised limit an…
The Well Order Reconstruction Solution for Three-Dimensional Wells, in the Landau-de Gennes theory
Giacomo Canevari, Joseph Harris, Apala Majumdar +1
We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solutions (WORS) as a function of the well size, characterized by , and…
Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation
Giacomo Canevari, Arghir Zarnescu
We consider a Landau-de Gennes model for a suspension of small colloidal inclusions in a nematic host. We impose suitable anchoring conditions at the boundary of the inclusions, an…
Improved partial regularity for manifold-constrained minimisers of subquadratic energies
Giacomo Canevari, Giandomenico Orlandi
We consider minimising -harmonic maps from three-dimensional domains to the real projective plane, for . These maps arise as least-energy configurations in variational mo…
Minimizers of a Landau-de Gennes Energy with a Subquadratic Elastic Energy
Giacomo Canevari, Apala Majumdar, Bianca Stroffolini
We study a modified Landau-de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of…
Order Reconstruction for Nematics on Squares with Isotropic Inclusions: A Landau-de Gennes Study
Yiwei Wang, Giacomo Canevari, Apala Majumdar
We prove the existence of a well order reconstruction solution (WORS) type Landau-de Gennes critical point on a square domain with an isotropic concentric square inclusion, with ta…
Topological singular set of vector-valued maps, I: Applications to manifold-constrained Sobolev and BV spaces
Giacomo Canevari, Giandomenico Orlandi
We introduce an operator on vector-valued maps which has the ability to capture the relevant topological information carried by . In particular, this operator i…
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…