Related papers: The third order helicity of magnetic fields via li…
Most general third-order $3d$ linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the…
We show a combinatorial formula for a lower bound of the dimension of the non-unipotent monodromy part of the first Milnor cohomology of a hyperplane arrangement satisfying some combinatorial conditions. This gives exactly its dimension if…
Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories…
The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable…
Revealing the spin excitations of complex quantum magnets is key to developing a minimal model that explains the underlying magnetic correlations in the ground state. We investigate the low-energy magnons in $\alpha$-RuCl$_3$ by combining…
An analytical representation of the interstellar magnetic field in the vicinity of the heliosphere is derived. The three-dimensional field structure close to the heliopause is calculated as a solution of the induction equation under the…
Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants which are the magnetic helicity and the generalized helicity. New exact relations are derived for homogeneous…
It is by now well-known that a Lorentz force law and the homogeneous Maxwell equations can be derived from commutation relations among Euclidean coordinates and velocities, without explicit reference to momentum, action or variational…
We search for observational signatures of magnetic helicity in data from all-sky radio polarization surveys of the Milky Way Galaxy. Such a detection would help confirm the dynamo origin of the field and may provide new observational…
We summarize the emergence of non-commutative/non-associative structures in Dirac's generalization of Maxwell theory, focusing mostly on the magnetic field analogue of the non-geometric R-flux string model. The cohomological interpretation…
The helicity of a magnetic field is a fundamental property that is conserved in ideal MHD. It can be explored in the stellar context by mapping large-scale magnetic fields across stellar surfaces using Zeeman-Doppler imaging. A recent study…
We present a numerical and analytical study of incompressible homogeneous conducting fluids using a helical Fourier representation. We analytically study both small- and large-scale dynamo properties, as well as the inverse cascade of…
We compute the noncommutative de Rham cohomology for the finite-dimensional q-deformed coordinate ring $C_q[SL_2]$ at odd roots of unity and with its standard 4-dimensional differential structure. We find that $H^1$ and $H^3$ have three…
We explain the (non)helical dynamo process using a field-structure model based on magnetic induction equation in an intuitive way. We show how nonhelical kinetic energy converts into magnetic energy and cascades toward smaller eddies in a…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We present the conservative dynamics of compact binaries to third order in the post-Minkowskian approximation in a theory that extends general relativity by a massless scalar field coupled to the Gauss-Bonnet invariant. We employ the…
This paper resolves the global regularity problem for the three-dimensional incompressible magnetohydrodynamics (MHD) equations in the upper half-space with slip boundary conditions, in the presence of a background magnetic field. Motivated…
In the Dirac operator framework we characterize and estimate the ground state energy of relativistic hydrogenic atoms in a constant magnetic field and describe the asymptotic regime corresponding to a large field strength using relativistic…
Formulations of magnetic monopoles in a Hilbert-space formulation of quantum mechanics require Dirac's quantization condition of magnetic charge, which implies a large value that can easily be ruled out for elementary particles by standard…
We prove that for any infinite field homology stability for the third integral homology of the special linear groups $SL(n,F)$ begins at $n=3$. When $n=2$ the cokernel of the map from the third homology of $SL(2,F)$ to the third homology of…