Related papers: Unique Topological Characterization of Braided Mag…
Newly emerging magnetic flux can show a complicated linked or interwoven topology of the magnetic field. The complexity of this linkage or knottedness of magnetic flux is related to the free energy stored in the magnetic field. Magnetic…
Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…
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…
A key question in understanding the observed magnetic field topologies of cool stars is the link between the small- and the large-scale magnetic field and the influence of the stellar parameters on the magnetic field topology. We examine…
We use the Hopf mapping to construct a magnetic configuration consisting of closed field lines, each of which is linked with all the other ones. We obtain in this way a solution of the equations of magnetohydrodynamics of an ideal…
Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation consisting entirely of invariant submanifolds. A regular leaf,…
Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near ideal MHD are reviewed in two parts. The first part gives a physically complete description of the frozen in field topology, taking magnetic flux…
Magnetic flux plays an important role in compactifications of field and string theories in two ways, it generates a multiplicity of chiral fermion zero modes and it can break supersymmetry. We derive the complete four-dimensional effective…
In this paper we define and study the moduli space of metric-graph-flows in a manifold M. This is a space of smooth maps from a finite graph to M, which, when restricted to each edge, is a gradient flow line of a smooth (and generically…
The design of a magnetic field source that can switch from a high field to a low field configuration by rotation by $90^\circ$ of a set of iron pieces is investigated using topology optimization. A Halbach cylinder is considered as the…
The transport on top of a periodic two-dimensional hexagonal magnetic pattern of (i) a single macroscopic steel sphere, (ii) a doublet of wax/magnetite composite spheres, and (iii) an immiscible mixture of ferrofluid droplets with a…
Fast magnetic reconnection is defined by the topology of the magnetic field lines changing on a timescale that is approximately an order of magnitude longer than the topology-conserving ideal-evolution timescale. Fast reconnection is an…
Topological textures in magnetically ordered materials are important case studies for fundamental research with promising applications in data science. They can also serve as photonic elements to mold electromagnetic fields endowing them…
The singularities of an irrotational magnetic field are lines of electric current. This property derives from the relationship between vector fields and the topology of the underlying three-space and allows for a definition of {cosmic…
We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The…
The paper reviews the notion of $n+\frac{1}{2}$D non-autonomous Hamiltonian systems, portraying their dynamics as the flow of the Reeb field related to a closed two-form of maximal rank on a cosymplectic manifold, and naturally decomposing…
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…
We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applications, we settle the speculation over their topological…
A Laplacian eigenfunction on a two-dimensional manifold dictates some natural partitions of the manifold; the most apparent one being the well studied nodal domain partition. An alternative partition is revealed by considering a set of…
Classification of matter through topological phases and topological edge states between distinct materials has been a subject of great interest recently. While lattices have been the main setting for these studies, a relatively unexplored…