Related papers: Topological and statistical properties of nonlinea…
Polarization data from high mass star formation regions (W51 e2/e8, Orion BN/KL) are used to derive statistical properties of the plane of sky projected magnetic field. Structure function and auto-correlation function are calculated for…
While the topological order in two dimensions has been studied extensively since the discover of the integer and fractional quantum Hall systems, topological states in 3 spatial dimensions are much less understood. In this paper, we propose…
The nonlinear force-free field (NLFFF) modeling has been extensively used to infer the three-dimensional (3D) magnetic field in the solar corona. One of the assumptions in the NLFFF extrapolation is that the plasma beta is low, but this…
The work in this article is inspired by a classical problem: the statistical physical properties of a closed polymer loop that is wound around a rod. Historically the preserved topology of this system has been addressed through…
Topological semimetals can be classified by the connectivity and dimensionality of the band cross- ing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimet- al are 0D points, whereas the band…
The relative magnetic helicity is a quantity that is often used to describe the level of entanglement of non-isolated magnetic fields, such as the magnetic field of solar active regions.The aim of this paper is to investigate how different…
We study the relative helicity of active region (AR) NOAA~12673 during a ten-hour time interval centered around a preceding X2.2 flare (SOL2017-09-06T08:57) and also including an eruptive X9.3 flare that occurred three hours later…
Magnetic flux rope (MFR) plays an important role in solar activities. A quantitative assessment of the topology of an MFR and its evolution is crucial for a better understanding of the relationship between the MFR and the associated…
We develop a statistical mechanical framework, based on a variational approximation, to describe closed loop plectonemes. This framework incorporates weak helix structure dependent forces into the determination of the free energy and…
For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, the free energy is one of the main indicators used in space weather forecasts to…
Floer theory was originally devised to estimate the number of 1-periodic orbits of Hamiltonian systems. In earlier works, we constructed Floer homology for homoclinic orbits on two dimensional manifolds using combinatorial techniques. In…
The SDO/HMI instruments provide photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation…
We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the…
We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot K in its m-fold cyclic branched cover Sigma^m(K), and we give computations when m=2 for over fifty three-bridge knots…
We describe quasi-Hopf twist deformations of flat closed string compactifications with non-geometric R-flux using a suitable cochain twist, and construct nonassociative deformations of fields and differential calculus. We report on our new…
Global magnetic field extrapolations are now revealing the huge complexity of the Sun's corona, and in particular the structure of the boundary between open and closed magnetic flux. Moreover, recent developments indicate that magnetic…
While it is well known that three dimensional quantum many-body systems can support non-trivial braiding statistics between particle-like and loop-like excitations, or between two loop-like excitations, we argue that a more fundamental…
The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian…
Given a known radial magnetic field distribution on the Sun's photospheric surface, there exist well-established methods for computing a potential magnetic field in the corona above. Such potential fields are routinely used as input to…
The corona is a layer of hot plasma that surrounds the Sun, traces out its complex magnetic field, and ultimately expands into interplanetary space as the supersonic solar wind. Although much has been learned in recent decades from advances…