Related papers: Unique Topological Characterization of Braided Mag…
A key feature of topological insulators is the robustness of the electron energy spectrum. At a surface of a topological insulator, Dirac point is protected by the characteristic symmetry of the system. The breaking of the symmetry opens a…
We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$ respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy) classes, up to full twists. We examine the dynamics…
In this paper we seek to understand the timescale on which the photospheric motions on the Sun braid coronal magnetic field lines. This is a crucial ingredient for determining the viability of the braiding mechanism for explaining the high…
We construct two classes of the magnetohydrostatic equilibria of the axisymmetric flux tubes with twisted magnetic fields in the stratified solar atmosphere that span from the photosphere to the transition region. We built the models by…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
We study strongly correlated fractional topological phases on a two-sphere threaded by a magnetic dipole field with globally vanishing flux. Solving the Dirac equation in this background produces spheroidal wavefunctions forming a highly…
We report the creation and real-space observation of magnetic structures with well-defined topological properties and a lateral size as low as about 150 nm. They are generated in a thin ferrimagnetic film by ultrashort single optical laser…
The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic field topology at different surface…
Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main…
Observations of magnetic clouds, within interplanetary coronal mass ejections (ICMEs), are often well described by flux rope models. Most of these assume either a cylindrical or toroidal geometry. In some cases, these models are also…
A fast method is presented for computing the topological entropy of braids on the torus. This work is motivated by the need to analyze large braids when studying two-dimensional flows via the braiding of a large number of particle…
Maxwell's equations allow for some remarkable solutions consisting of pulsed beams of light which have linked and knotted field lines. The preservation of the topological structure of the field lines in these solutions has previously been…
We use direct numerical simulations to study the evolution, or relaxation, of magnetic configurations to an equilibrium state. We use the full single-fluid equations of motion for a magnetized, non-resistive, but viscous fluid; and a…
We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that…
Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. While most studies are based on the topological band insulators, the topological state in strongly correlated low-dimensional systems…
We study the relaxation of a topologically non-trivial vortex braid with zero net helicity in a barotropic fluid. The aim is to investigate the extent to which the topology of the vorticity field -- characterized by braided vorticity field…
Magneto-optical imaging of thick stress-free lead samples reveals two distinct topologies of the intermediate state. Flux tubes are formed upon magnetic field penetration (closed topology) and laminar patterns appear upon flux exit (open…
The deep connections between braids and dynamics by way of the Nielsen-Thurston classification theorem have led to a wide range of practical applications. Braids have been used to detect coherent structures and mixing regions in oceanic…