Related papers: A topological approach to magnetic nulls
The appearance of eruptive space plasma processes, e.g., in eruptive flares as observed in the solar atmosphere, is usually assumed to be caused by magnetic reconnection. The process of magnetic reconnection is often connected with singular…
Topology describes global quantities invariant under continuous deformations, such as the number of elementary excitations at a phase boundary, without detailing specifics. Conversely, differential laws are needed to understand the physical…
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…
Detection of a separator line that connects magnetic nulls and the determination of the dynamics and plasma environment of such a structure can improve our understanding of the three-dimensional (3D) magnetic reconnection process. However,…
Nodal topological lattice is a form of magnetic crystal with topologically non-trivial spin texture, which further exhibits a periodic array of nodes with vanishing magnetization. Electronic structure for conduction electrons strongly…
We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred…
Using high spatial and temporal data from the \emph{Solar Dynamics Observatory} (\emph{SDO}) and the \emph{Interface Region Imaging Spectrograph} (\emph{IRIS}), several observational signatures of magnetic reconnection in the course of…
Stability and reconnection of magnetic fields play a fundamental role in natural and man-made plasma. In these applications the field's topology determines the stability of the magnetic field. Here I will describe the importance of one…
Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic…
We study the evolution of turbulent magnetic fields from a topological point of view, invoking commonplace mathematical tools from general topology and dynamical systems theory which connect magnetic field evolution to time reversal…
Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search of hopfions in real physical systems is going on for nearly half a…
Using the notion of magnetic curvature recently introduced by the first author, we extend E. Hopf's theorem to the setting of magnetic systems. Namely, we prove that if the magnetic flow on the s-sphere bundle is without conjugate points,…
We study the polar magnetism near an activity maximum when these regions change their polarity, from which it is expected that its magnetism should be less affected by the global field. To fully characterise the magnetic field vector, we…
The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and…
Switching of magnetic vortex cores involves a topological transition characterized by the presence of a magnetization singularity, a point where the magnetization vanishes (Bloch point). We analytically derive the shape of the Bloch point…
We construct examples of smooth periodic solutions to the Magnetohydrodynamic equations in dimension 2 with positive resistivity for which the topology of the magnetic lines changes under the flow. By Alfv\'en's theorem this is known to be…
A Weyl semimetal has Weyl nodes that always come in pairs with opposite chiralities. Notably, different ways of connection between nodes are possible and would lead to distinct topologies. Here we identify their differences in many respects…
Magnetic reconnection occurs when two plasmas having co-planar but anti-parallel magnetic fields meet. At the contact point, the field is locally annihilated and the magnetic energy can be released into the surrounding plasma. Theory and…
The question whether magnetic fields play an important role in the processes of molecular cloud and star formation has been debated for decades. Recent observations have revealed a simple picture that may help illuminate these questions:…
Small steady-state deformational oscillations of a drop of a viscous magnetic liquid in a non-stationary uniform magnetic field are theoretically investigated for low Reynolds numbers. The drop is suspended in another viscous magnetic…