8 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…
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…
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…
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…