Related papers: Differential Geometric and Topological methods wit…
Two examples of the use of differential geometry in plasma physics are given: The first is the computation and solution of the constraint equations obtained from the Riemann metric isometry of the twisted flux tube. In this case a…
Two theorems on the Riemannian geometrical constraints on vortex magnetic filaments acting as dynamos in (MHD) flows are presented. The use of Gauss-Mainard-Codazzi equations allows us to investigate in detail the influence of curvature and…
In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum…
Analogue black holes in non-Riemannian effective spacetime of moving vortical plasmas described by moving magnetohydrodynamic (MHD) flows. This example is an extension of acoustic torsion recently introduced in the literature (Garcia de…
Plasma toroidal metric singularities in helical devices and tokamaks, giving rise to magnetic surfaces inside the plasma devices are investigated in two cases. In the first we consider the case of a rotational plasma on an helical device…
The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia).…
In the conventional formulation of general relativity, gravity is represented by the metric curvature of Riemannian geometry. There are also alternative formulations in flat affine geometries, wherein the gravitational dynamics is instead…
Equations of ideal magnetohydrodynamics (MHD) play an important role in the studies of turbulence, astrophysics, and plasma physics. These equations possess remarkable geometric structures and symmetries. Indeed, they admit a geodesic…
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…
The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is used to construct variational principles for symmetric equilibrium configurations of magnetized plasma including flow. In particular, helical symmetry is considered…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
Magnetohydrodynamic (MHD) waves are routinely observed in the solar atmosphere. These waves are important in the context of solar physics as it is widely believed they can contribute to the energy budget of the solar atmosphere and are a…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian…
We derive new models of stochastic Hall magnetohydrodynamics (MHD) by using a symmetry-reduced stochastic Euler-Poincar\'e variational principle. The new stochastic Hall MHD theory has potential applications for uncertainty quantification…
We analyze the properties of foliations in presence of non-metricity, deriving the generalized Gauss-Codazzi relations in full generality. These results are employed to study the teleparallel framework of non-metric geometry, obtaining…
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic…
We study the geometry of a codimension-one foliation with a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies along the leaves of the foliation.…
In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct…
Riemannian geometrical tools, such as Ricci collineations and Killing symmetries, so often used in Einstein general theory of gravitation are here applied to plasma physics to build magnetic surfaces from Einstein plasma metrics used in…