Variational methods for topological patterns arising in physics

Liste des Contributions

1. Solitons and solitonic vortices as mountain passes for the Ginzburg-Landau energy in 2D strips and 3D cylinders

Luc Nguyen (Oxford)

25/11/2025 14:30

We study critical points of the Ginzburg-Landau energy on 2D strips and 3D cylinders. In relation with recent experiments on fermionic and bosonic strips, we prove that there is a critical width of the strip under which the minimizer in some suitable space is the soliton while above it the minimizer is solitonic vortex (aka a vortex which behaves like a soliton in the transverse direction). We...

2. An approach to topological singularities through Mumford-Shah type functionals

Lucia De Luca (Rome)

25/11/2025 15:20

We will present variational approaches to the analysis of topological singularities in the plane, starting from the - nowadays - classical Ginzburg-Landau (GL) model and core-radius (CR) approach. We will introduce a third approach inspired by the Mumford-Shah functional used in the context of image segmentation. Within our framework, the order parameter is an SBV map taking values in the unit...

3. On a nonlinear Schrödinger equation: uniqueness, non-degeneracy and applications to energy minimization

Simona Rota Nodari (Nice)

25/11/2025 16:40

This talk will focus on qualitative properties of normalized ground states for a nonlinear Schrödinger equation with double-power nonlinearity. These ground states are characterized as energy minimizers under a fixed L^2-norm contraint. I will present recent results concerning their existence, and I will discuss their uniqueness in certain regimes of parameters. Joint work with Mathieu Lewin.

4. Domain wall dynamics in notched ferromagnetic nanowires

Gilles Carbou (Pau)

26/11/2025 09:20

We study the dynamics of domain walls in a notched ferro-magnetic nanowire. The model used is the Landau–Lifschitz equation in dimension 1, with a weight representing the notch. We highlight the pinning properties of notches, and the depinning properties of the applied magnetic field. In particular, we establish that when the applied field tends to push the wall far away from the notch,...

5. Stabilization of walls in notched ferromagnetic nanowires

David Sanchez (Toulouse)

26/11/2025 10:40

We present a one-dimensional model of ferromagnetic nanowire featuring notches. We prove the existence of stable wall profiles even under a small applied magnetic field with the walls localized in notches. Moreover, in order to illustrate domain-wall depinning by an applied magnetic field, we prove the non-existence of stationary wall profiles in the presence of a large applied magnetic field.

6. Existence and uniqueness of a domain wall for notched ferromagnetic nanowires

Clémentine Courtes (Strasbourg)

26/11/2025 11:30

In this talk, we study a ferromagnetic nanowire with a defect, represented as a single, unimodal notch. Using a mountain-path argument, we establish the existence and uniqueness of a critical point for the ferromagnetic energy associated with this model. This critical point corresponds to a topological solution (a single domain wall) localized in the vicinity of the notch. This work allows the...

7. The conformal limit for bimerons in easy-plane chiral magnets

Bin Deng (Toulouse)

26/11/2025 14:30

We study minimizers of a reduced micromagnetic energy functional under prescribed unit topological degree. This model arises in thin ferromagnetic films with Dzyaloshinskii-Moriya interaction and easy-plane anisotropy, where these minimizers represent bimeron configurations. We prove their existence, and describe them precisely as perturbations of specific Möbius maps: we establish in...

8. Korn and Poincaré-Korn inequalities: A different perspective

Giovanni Di Fratta (Naples)

26/11/2025 15:20

Korn's inequality and its variants are essential tools in the mathematical analysis of both linear and nonlinear elasticity. They play a central role in establishing existence and regularity results for partial differential equations involving symmetric gradients. In this talk, I will present a conceptually simple derivation of the first and second Korn inequalities for general exponents $1 <...

9. TBA

Adriana Garroni (Rome)

26/11/2025 16:40

TBA

10. A variational model for two-dimensional ferronematics - Part I

Bianca Stroffolini (Naples)

27/11/2025 09:20

This talk is the first of two parts, presented jointly with Federico Luigi Dipasquale. Ferronematics are composite materials characterised by the coupling between magnetic particles and nematic liquid crystals. In these talks, we will present some results on a two-dimensional model for ferronematics in confined geometries. The model is based on the coupling between a polar order parameter –...

11. Ferronematics: Asymptotics for critical points

Federico Dipasquale (Naples)

27/11/2025 10:40

We consider a variational model for ferronematics --- composite materials formed by dispersing magnetic nanoparticles into a liquid crystal matrix. The model features two coupled order parameters: a Landau-de Gennes $Q$-tensor for the liquid crystal component and a magnetisation vector field $M$, both of them governed by a Ginzburg-Landau-type energy. The energy includes a singular coupling...

12. Convergent finite element methods for the Ericksen model of nematic liquid crystals

Michele Ruggeri (Bologna)

27/11/2025 11:30

The Ericksen model describes nematic liquid crystals (LCs) in terms of a unit-length vector field (director) and a scalar function (degree of orientation). Compared to the classical Oseen-Frank model, it allows for the description of a larger class of defects. Equilibrium states of the LC are given by admissible pairs that minimize an energy functional, which consists of the sum of...

13. Some progress on the Aviles-Giga conjecture

Xavier Lamy (Toulouse)

27/11/2025 14:30

The Aviles-Giga energy is a phase transition model related to liquid crystals, micromagnetics and elasticity. Sharp interface limits of bounded energy are weak solutions of the 2D eikonal equation: unit vector fields $m$ with zero divergence (in the sense of distributions). Partial information about the limit energy cost of a given solution $m$ is encoded in a family of signed measures called...

14. Aviles-Giga type functionals calibrated with the help of currents

Roger Moser (Bath)

27/11/2025 15:20

For vector fields in a two-dimensional domain, consider a Modica-Mortola (or Allen-Cahn) type functional. We do not make any specific assumptions on the wells of the potential function (so there may be multiple single-point wells or one or several more complex wells), but we do assume that the divergence of the vector fields is quite strongly penalised or even vanishes identically. This then...

15. The binormal flow with Lipschitz non-closed curves data

Valeria Banica (Paris)

27/11/2025 16:40

The binormal flow is a geometric flow of curves in R^3, that models vortex filament dynamics in fluids and superfluids, and is also related to the continuous classical Heisenberg ferromagnet equation. The result presented in this talk is the construction of weak solutions for non-closed Lipschitz curves data, and it extends the result of Bob Jerrard and Didier Smets obtained in 2015 for closed...

16. Energy of semi-coherent interfaces

Emanuele Spadaro (Rome)

28/11/2025 09:20

In this talk I will discuss models for analyzing inter-crystalline
boundaries that arise from differences in atomic spacing. In the case of
semi-coherent interfaces, where the misfit between crystal lattices is small, the interfaces can be resolved into sequences of edge dislocations,
leading to an interfacial energy that exhibits Read–Shockley-type superlinear scaling as a function of the misfit.

17. Phase-field approximation of sharp-interface energies accounting for lattice symmetry

Vito Crismale (Rome)

28/11/2025 10:40

The talk concerns a phase field approximation for sharp interface energies, defined on partitions, as appropriate for modeling grain boundaries in polycrystals. The label takes value in O(d)/G, where G is the point group of a lattice. The limiting surface energy behaves for small angles as s|log s|, according to the Read and Shockley law. These functionals can be used for image reconstruction...

18. A "not so strange" term in the homogenisation of a problem with Robin boundary conditions

Giacomo Canevari (Verona)

28/11/2025 11:30

We consider Laplace's equation in a periodically perforated domain, with Robin boundary conditions on the holes and a Robin coefficient inversely proportional to the total surface area of the holes. We show that, in a critical regime, the homogenised equation contains an additional zero-order term, which is defined in terms of a suitable eigenvalue problem and depends nonlinearly on the Robin...