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We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes…
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamical accessible frameworks. This is…
Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for 3D dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric…
A new method to obtain the radial profile of the magnetic perturbation in a toroidal force-free plasma having circular cross section is developed. The method is quite general and can be applied to any circular low-beta plasma once suitable…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
The adiabatic limit of a recently proposed dynamical extension of Taylor relaxation, \emph{multi-region relaxed magnetohydrodynamics} (MRxMHD) is summarized, with special attention to the appropriate definition of relative magnetic…
This paper considers magnetohydrodynamics (MHD) and some of its applications from the perspective of differential geometry, considering the dynamics of an ideal fluid flow and magnetic field on a general three-dimensional manifold, equipped…
We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta…
In the present work, we study the geometric structures of the Rotating Shallow Water Magnetohydrodynamics (RSW-MHD) equations through a Lie group invariant Euler-Poincar\'e variational principle. In this geometric framework, we derive new,…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
Isotropic homogeneous hydromagnetic turbulence is studied using numerical simulations at resolutions of up to 1024^3 meshpoints. It is argued that, in contrast to the kinematic regime, the nonlinear regime is characterized by a spectral…
Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In…
Magnetic geodesics describe the trajectory of a particle in a Riemannian manifold under the influence of an external magnetic field. In this article, we use the heat flow method to derive existence results for such curves. We first…
In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which…
Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric…
Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark-gluon plasma in heavy-ion collisions to matters in supernovas, compact…
This article provides a pedagogically oriented introduction to geometric (Clifford) calculus on pseudo-Riemannian manifolds. Unlike usual approaches to the topic, which rely on embedding the geometric algebra either within a tensor algebra…
We elaborate on nonmetric geometric flow theory and metric-affine gravity with applications in modern cosmology. Two main motivations for our research follow from the facts that 1) cosmological models for $f(Q)$ modified gravity theories,…