180 citations · 1.3k across the 65 of their papers we have counts for
34 papers · 1 filter
Euler's elastica functional as a large mass limit of a two-dimensional non-local isoperimetric problem
Cyrill B. Muratov, Matteo Novaga, Theresa M. Simon
We consider a large mass limit of the non-local isoperimetric problem with a repulsive Yukawa potential in two space dimensions. In this limit, the non-local term concentrates on t…
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…
An optimal design problem for a charge qubit
Dario Mazzoleni, Cyrill B. Muratov, Berardo Ruffini
In this paper we introduce a simple variational model describing the ground state of a superconducting charge qubit. The model gives rise to a shape optimization problem that aims…
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…
Thomas-Fermi theory of out-of-plane charge screening in graphene
Vitaly Moroz, Cyrill B. Muratov
This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas-Fermi theory. We est…
A variational model of charged drops in dielectrically matched binary fluids: the effect of charge discreteness
Cyrill B. Muratov, Matteo Novaga, Philip Zaleski
This paper addresses the ill-posedness of the classical Rayleigh variational model of conducting charged liquid drops by incorporating the discreteness of the elementary charges. I…
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…
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…
Conducting flat drops in a confining potential
Cyrill B. Muratov, Matteo Novaga, Berardo Ruffini
We study a geometric variational problem arising from modeling two-dimensional charged drops of a perfectly conducting liquid in the presence of an external potential. We character…
A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree harmonic maps from to
Anne Bernand-Mantel, Cyrill B. Muratov, Theresa M. Simon
We characterize skyrmions in ultrathin ferromagnetic films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular…
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…
Emergence of non-trivial minimizers for the three-dimensional Ohta-Kawasaki energy
Hans Knüpfer, Cyrill Muratov, Matteo Novaga
This paper is concerned with the diffuse interface Ohta-Kawasaki energy in three space dimensions, in a periodic setting, in the parameter regime corresponding to the onset of non-…
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…
A nonlocal isoperimetric problem with dipolar repulsion
Cyrill B. Muratov, Thilo Simon
We study a geometric variational problem for sets in the plane in which the perimeter and a regularized dipolar interaction compete under a mass constraint. In contrast to previous…
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…
A universal thin film model for Ginzburg-Landau energy with dipolar interaction
Cyrill B. Muratov
We present an analytical treatment of a three-dimensional variational model of a system that exhibits a second-order phase transition in the presence of dipolar interactions. Withi…
Magnetic domains in thin ferromagnetic films with strong perpendicular anisotropy
Hans Knüpfer, Cyrill B. Muratov, Florian Nolte
We investigate the scaling of the ground state energy and optimal domain patterns in thin ferromagnetic films with strong uniaxial anisotropy and the easy axis perpendicular to the…
On equilibrium shapes of charged flat drops
Cyrill B. Muratov, Matteo Novaga, Berardo Ruffini
Equilibrium shapes of two-dimensional charged, perfectly conducting liquid drops are governed by a geometric variational problem that involves a perimeter term modeling line tensio…
Uniqueness of one-dimensional Néel wall profiles
Cyrill B. Muratov, Xiaodong Yan
We study the domain wall structure in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Using the re…
On well-posedness of variational models of charged drops
Cyrill B. Muratov, Matteo Novaga
Electrified liquids are well known to be prone to a variety of interfacial instabilities that result in the onset of apparent interfacial singularities and liquid fragmentation. In…
One-dimensional domain walls in thin ferromagnetic films with fourfold anisotropy
Ross G. Lund, Cyrill B. Muratov
We study the properties of domain walls and domain patterns in ultrathin epitaxial magnetic films with two orthogonal in-plane easy axes, which we call fourfold materials. In these…
Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations
C. B. Muratov, X. Zhong
We study the long time behavior of positive solutions of the Cauchy problem for nonlinear reaction-diffusion equations in with bistable, ignition or monostable nonli…
Eventual self-similarity of solutions for the diffusion equation with nonlinear absorption and a point source
Peter V. Gordon, Cyrill B. Muratov
This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superli…