Related papers: Asymptotic windings, surface helicity and their ap…
The entropy functional introduced by Colding and Minicozzi plays a fundamental role in the analysis of mean curvature flow. However, unlike the hypersurface case, relatively little about the entropy is known in the higher-codimension case.…
Helicity measures complexity in the field. Magnetic helicity is given by a volume integral over the scalar product of magnetic field {\bf B} and its vector potential {\bf A}. A direct computation of magnetic helicity in the solar atmosphere…
We consider a variational model describing the shape of liquid drops and crystals under the influence of gravity, resting on a horizontal surface. Making use of anisotropic symmetrization techniques, we establish existence, convexity and…
Magnetic helicity is an invariant of ideal magnetohydrodynamics (MHD) that encodes information on the topology of magnetic field lines. It has long been appreciated that magnetic topology is an important constraint for the evolution of…
Helicity is a topological invariant that measures the linkage and knottedness of lines, tubes and ribbons. As such, it has found myriads of applications in astrophysics and solar physics, in fluid dynamics, in atmospheric sciences, and in…
Toroidal topologies and helicity are pervasive in nature and hold basic importance in scientific research. In particular, the interplay between these features gives rise to fascinating toroidal helical electromagnetic excitations. Here, we…
We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples tangential and normal forces and thus generates lift. We consider materials that deform easily, due to either geometry (e.g. a shell) or…
We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces.…
Simplicial surfaces describe the incidence relations between vertices, edges and faces of triangulated 2-dimensional manifolds in a purely combinatorial way. By considering only the incidences of edges and faces, simplicial surfaces are…
Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer geometry, we generalise the spectral results of an original…
The term "surface polarization" is introduced to describe the in-plane polarization existing at the surface of an insulating crystal when the in-plane surface inversion symmetry is broken. Here, the surface polarization is formulated in…
This article presents an improvement and extension of the heuristic first presented by Hougardy, Lutz, and Zelke in 2010 for realizing triangulated orientable surfaces with few vertices by a simplex-wise linear embedding. The improvement…
Initiated by the work of Uhlenbeck in late 1970s, we study questions about the existence, multiplicity and asymptotic behavior for minimal immersions of closed surface in some hyperbolic three-manifold, with prescribed conformal structure…
The concept of closed trapped surface is of paramount importance in General Relativity and other gravitational theories. However, it is a purely geometrical object. With the aim of bringing this concept to closer attention by the…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
Magnetic helicity flux gives information about the topology of a magnetic field passing through a boundary. In solar physics applications, this boundary is the photosphere and magnetic helicity flux has become an important quantity in…
In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. 18(4), 2018) a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic…
We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total (relative) magnetic helicity is already recognized as…
The surface Hamiltonian for a spin zero particle that is pinned to a surface by letting the thickness of a layer surrounding the surface go to zero -- assuming a strong normal force -- is constructed. The new approach we follow to achieve…
Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical…