Related papers: Volume enclosed by a flux surface
In this paper we introduce a flow on the spectral data for symmetric CMC surfaces in the $3$-sphere. The flow is designed in such a way that it changes the topology but fixes the intrinsic (metric) and certain extrinsic (periods) closing…
Interactions between magnetic fields advected by matter play a fundamental role in the Universe at a diverse range of scales. A crucial role these interactions play is in making turbulent fields highly anisotropic, leading to observed…
For exact area-preserving twist maps, curves were constructed through the gaps of cantori in \cite{MMP84}, which were conjectured to have minimal flux subject to passing through the points of the cantorus. It was pointed out by \cite{Pol}…
The three-dimensional characterization of magnetic flux-ropes observed in the heliosphere has been a challenging task for decades. This is mainly due to the limitation to infer the 3D global topology and the physical properties from the 1D…
We study an intrinsic volume form defined on a pseudoconvex hypersurface in a complex Calabi-Yau manifold. We compute first and second variation formulae and discuss possible analogues of the affine isoperimetric inequality. In the last…
The magnetic field integrals connected with the momentum resolution are calculated for the ATLAS inner tracking volume in a range of pseudorapidity $|\eta| < 3$ for the cases of `ideal' and inhomogeneous solenoid fields. In the latest case,…
We derive a closed-form expression of the magnetic field of a finite-size current sheet and use it to calculate the field of permanent magnets, which are modeled through their surface current densities. We illustrate the method by…
This study extends the functional perturbation theory~(FPT) of dynamical systems, which was initially developed for investigating the shifts of magnetic field line trajectories within the chaotic edge region of plasma when subjected to…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed…
Instead of investigating the Willmore flow for two-dimensional, closed immersed surfaces directly we turn to its inversion. We give a lower bound on the lifespan of this inverse Willmore flow, depending on the concentration of curvature in…
3D modifications to the well-studied 2D flow topology around an embedded planet have the potential to resolve long-standing problems in planet formation theory. We present a detailed analysis of the 3D isothermal flow field around a 5…
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The…
A material-based, i.e., Lagrangian, methodology for exact integration of flux by volume-preserving flows through a surface has been developed recently in [Karrasch, SIAM J. Appl. Math., 76 (2016), pp. 1178-1190]. In the present paper, we…
This paper shows that the topological structures of particle orbits generated by a generic class of vector fields on spherical surfaces, called {\it the flow of finite type}, are in one-to-one correspondence with discrete structures such as…
We show that a large-scale, weak magnetic field threading a turbulent accretion disk tends to be advected inward, contrary to previous suggestions that it will be stopped by outward diffusion. The efficient inward transport is a consequence…
An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-space filling, or an interval of L-space fillings. In the latter case, which we call "Floer simple," we construct an invariant which computes…
In the context of Synthetic Differential Geometry, we describe the square volume of a ``second-infinitesimal simplex'', in terms of square-distance between its vertices. The square-volume function thus described is symmetric in the…
The conductance of an open quench-disordered two-dimensional (2D) electron system subject to an in-plane magnetic field is calculated within the framework of conventional Fermi liquid theory applied to actually a three-dimensional system of…
In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some…