78 citations · 624 across the 43 of their papers we have counts for
27 papers · 1 filter
Variational principles for the interaction of liquid crystals and electric fields in the Oseen--Frank model
Giovanni Di Fratta, Valeriy Slastikov, Arghir Zarnescu
We develop a rigorous variational framework for uniaxial nematic liquid crystals interacting with an external electric field in the one-constant Oseen--Frank approximation. Equilib…
The Ginzburg-Landau system with general potential: maximum principle and gradient estimates
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We study critical points of the Ginzburg-Landau energy functional $$\mathcal{F}_\varepsilon[u] = \int_Ω\Big[ \frac{1}{2}|\nabla u|^2 + \frac{1}{2\varepsilon^2} W(1 - |u|^2)\Big]\,d…
Skyrmion stacking in stray field-coupled ultrathin ferromagnetic multilayers
N. J. Dubicki, V. V. Slastikov, A. Bernand-Mantel +1
This paper explores the energy landscape of ferromagnetic multilayer heterostructures that feature magnetic skyrmions -- tiny whirls of spins with non-trivial topology -- in each m…
Existence of higher degree minimizers in the magnetic skyrmion problem
Cyrill B. Muratov, Theresa M. Simon, Valeriy V. Slastikov
We demonstrate existence of topologically nontrivial energy minimizing maps of a given positive degree from bounded domains in the plane to in a variational model des…
Reduced theory of symmetric and antisymmetric exchange interactions in nanowires
Giovanni Di Fratta, Filipp N. Rybakov, Valeriy Slastikov
We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a wire generated by a regular simple curve and defined in the space of -val…
Reduced energies for thin ferromagnetic films with perpendicular anisotropy
G. Di Fratta, C. B. Muratov, V. V. Slastikov
We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring…
Curved thin-film limits of chiral Dirichlet energies
Giovanni Di Fratta, Valeriy Slastikov
We investigate the curved thin-film limit of a family of perturbed Dirichlet energies in the space of Sobolev maps defined in a tubular neighborhood of an -dimension…
Magnetic skyrmions under confinement
Antonin Monteil, Cyrill B. Muratov, Theresa M. Simon +1
We present a variational treatment of confined magnetic skyrmions in a minimal micromagnetic model of ultrathin ferromagnetic films with interfacial Dzylashinksii-Moriya interactio…
On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces
Giovanni Di Fratta, Alberto Fiorenza, Valeriy Slastikov
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of -valued maps defined in cylindrical surfaces. The model nat…
Symmetry properties of minimizers of a perturbed Dirichlet energy with a boundary penalization
Giovanni Di Fratta, Antonin Monteil, Valeriy Slastikov
We consider -valued maps on a domain minimizing a perturbation of the Dirichlet energy with vertical penalization in and horizontal penaliz…
Transverse domain walls in thin ferromagnetic strips
M. Morini, C. B. Muratov, M. Novaga +1
We present a characterization of the domain wall solutions arising as minimizers of an energy functional obtained in a suitable asymptotic regime of micromagnetics for infinitely l…
Spin-diffusion model for micromagnetics in the limit of long times
Giovanni Di Fratta, Ansgar Jüngel, Dirk Praetorius +1
In this paper, we consider spin-diffusion Landau-Lifshitz-Gilbert equations (SDLLG), which consist of the time-dependent Landau-Lifshitz-Gilbert (LLG) equation coupled with a time-…
Symmetry and multiplicity of solutions in a two-dimensional Landau-de Gennes model for liquid crystals
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We consider a variational two-dimensional Landau-de Gennes model in the theory of nematic liquid crystals in a disk of radius . We prove that under a symmetric boundary conditio…
Variational principles of micromagnetics revisited
Giovanni Di Fratta, Cyrill B. Muratov, Filipp N. Rybakov +1
We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution…
Landau-de Gennes corrections to the Oseen-Frank theory of nematic liquid crystals
Giovanni Di Fratta, Jonathan Robbins, Valeriy Slastikov +1
We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At…
On a sharp Poincaré-type inequality on the 2-sphere and its application in micromagnetics
Giovanni Di Fratta, Valeriy Slastikov, Arghir Zarnescu
The main aim of this note is to prove a sharp Poincaré-type inequality for vector-valued functions on , that naturally emerges in the context of micromagnetics of sph…
Edge domain walls in ultrathin exchange-biased films
Ross G. Lund, Cyrill B. Muratov, Valeriy V. Slastikov
We present an analysis of edge domain walls in exchange-biased ferromagnetic films appearing as a result of a competition between the stray field at the film edges and the exchange…
Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
For , we consider the Ginzburg-Landau functional for -valued maps defined in the unit ball with the vortex boundary data on $\partial…
On the uniqueness of minimisers of Ginzburg-Landau functionals
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for -valued maps under a suitable convexity assumpti…
One-dimensional in-plane edge domain walls in ultrathin ferromagnetic films
Ross G. Lund, Cyrill B. Muratov, Valeriy V. Slastikov
We study existence and properties of one-dimensional edge domain walls in ultrathin ferromagnetic films with uniaxial in-plane magnetic anisotropy. In these materials, the magnetiz…
Liquid crystal defects in the Landau-de Gennes theory in two dimensions-beyond the one-constant approximation
Georgy Kitavtsev, Jonathan M Robbins, Valeriy Slastikov +1
We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general -radially symmetric boundary conditions. We show that for generic elas…
Existence of travelling-wave solutions representing domain wall motion in a thin ferromagnetic nanowire
Ross G. Lund, J. M. Robbins, Valeriy Slastikov
We study the dynamics of a domain wall under the influence of applied magnetic fields in a one-dimensional ferromagnetic nanowire, governed by the Landau--Lifshitz--Gilbert equatio…
Instability of point defects in a two-dimensional nematic liquid crystal model
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We study a class of symmetric critical points in a variational Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3\times…
Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We investigate stability properties of the radially symmetric solution corresponding to the vortex defect (so called "melting hedgehog") in the framework of the Landau - de Gennes…