Related papers: Magnetic Geodesics via the Heat Flow

We present a framework that allows us to clearly identify the geometric features underlying the phenomenon of superconductivity in two dimensional materials. In particular, we show that any such medium whose response to an externally…

Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible,…

Non-solitonic examples of the application of geometrical and topological methods in plasma physics and magnetohydrodynamics (MHD) are given. The first example considers the generalization of magnetic helicity to gravitational torsion loop.…

We estimate the heat kernel on a closed Riemannian manifold $M$, with $dim(M)\geq 3$, evolving under the Ricci-harmonic map flow and the result depends on some constants arising from a Sobolev imbedding theorem. In a special case, when the…

In this paper, we consider the heat flow for p-pseudoharmonic maps from a closed Sasakian manifold M into a compact Riemannian manifold N. We prove global existence and asymptotic convergence of the solution for the p-pseudoharmonic map…

We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to…

The generation of magnetic field in an electrically conducting fluid generally involves the complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process is of great importance in geophysics, planetary…

It is well known that magnetic fields constrain motions of charged particles, impeding the diffusion of charged particles perpendicular to magnetic field direction. This modification of transport processes is of vital importance for a wide…

It has recently been shown theoretically that the time-dependent heat conduction equation is form-invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped…

Initial results from the Madison Dynamo Experiment provide details of the inductive response of a turbulent flow of liquid sodium to an applied magnetic field. The magnetic field structure is reconstructed from both internal and external…

In this paper, we establish the existence of periodic orbits of a twisted geodesic flow on all low energy levels and in all dimensions whenever the magnetic field form is symplectic and spherically rational. This is a consequence of a more…

Hot Jupiters can experience mass loss driven by heating from UV radiation from their host stars, and this flow is often controlled by magnetic fields. More specifically, near the planetry surface, the magnetic pressure dominates the ram…

Geometric flows have proved to be a powerful geometric analysis tool, perhaps most notably in the study of 3-manifold topology, the differentiable sphere theorem, Hermitian-Yang-Mills connections and canonical Kaehler metrics. In the…

Let $\Omega$ be an open set in a geodesically complete, non-compact, $m$-dimen-sional Riemannian manifold $M$ with non-negative Ricci curvature, and without boundary. We study the heat flow from $\Omega$ into $M-\Omega$ if the initial…

In this paper, we prove that for any given closed contact manifold, there exists an infinite-dimensional space of Riemannian metrics which can be identified with the space of bundle metrics on the induced contact distribution. For each such…

The theory of cold, relativistic, magnetohydrodynamic outflows is generalized by the inclusion of an intense radiation source. In some contexts, such the breakout of a gamma-ray burst jet from a star, the outflow is heated to a high…

Using the generally covariant magnetofluid formalism for a hot plasma, a new curvature (of space time) driven mechanism for generating seed vorticity/magnetic field is presented. The "battery" owes its origin to the interaction between…

We study the transition in dimensionality of a three-dimensional magnetohydrodynamic flow forced only mechanically, when the strength of a magnetic guiding field is gradually increased. We use numerical simulations to consider cases in…

Many practical applications exploit an external local magnetic field -- magnetic obstacle -- as an essential part of their constructions. Recently, it has been demonstrated that the flow of an electrically conducting fluid influenced by an…

We develop appropriate notions of Maslov index and spectral flow for electromagnetic geodesics within a fixed energy level and prove a Morse Index type theorem in this context. This is then applied to the problem of electromagnetic…