Related papers: Magnetic Geodesics via the Heat Flow
Thermodynamics of magnetic materials is discussed in practical, lab-oriented terms. In the common experimental configuration in which the external magnetic field comes from a solenoidal coil connected to a power supply, magnetic work is…
We discuss the heat content asymptotics associated with the heat flow out of a smooth compact manifold in a larger compact Riemannian manifold. Although there are no boundary conditions, the corresponding heat content asymptotics involve…
In this paper we analyze the problem of the geodesic connectedness of subsets of Riemannian manifolds. By using variational methods, the geodesic connectedness of open domains (whose boundaries can be not differentiable and not convex) of a…
In this work we study the geodesic flow on nilmanifolds associated to graphs. We are interested in the construction of first integrals to show complete integrability on some compact quotients. Also examples of integrable geodesic flows and…
We extend two results from the theory of geodesic flows to the magnetic setting on manifolds of arbitrary dimension. First, we investigate the magnetic ray transform and establish a tensor tomography result. Second, we define and analyze…
In this article, we study the the harmonic map heat flow from a manifold with conic singularities to a closed manifold. In particular, we have proved the short time existence and uniqueness of solutions as well as the existence of global…
Geodesics for a 5D magnetized Schwarzschild-like solution are analyzed by reducing the problem to the motion of a test particle in an effective potential. In absence of magnetic field comparison is established with Schwarzschild's geometry.…
Hydrodynamics of plasma in the random magnetic field is considered, which is characterized by the second moment of magnetic induction. Equations of ideal magnetic hydrodynamics in such field are received for an adiabatic process. It is…
We present a concise definition of an electromagnetic curve on a Riemannian manifold and illustrate the explicit case of the motion of a charged particle on the unit sphere under the influence of a uniform magnetic field.
Hamilton flows on K\"ahler manifold for which all trajectories are $H$-planar curves (complex analog of geodesics) are considered. These flows are called $H$-planar. The equation which has to obey the Hamiltonian of $H$-planar Hamilton flow…
This paper presents a model for quasi two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes. A method is presented that allows to take 3D effects…
The problem of reconstruction of a flow of conducting incompressible fluid generating a given magnetic mode is considered. We use the magnetic induction equation to derive ordinary differential equations along the magnetic field lines,…
A physically consistent approach is considered for defining an external magnetic field as needed in computational fluid dynamics problems involving magnetohydrodynamics (MHD). The approach results in simple analytical formulae that can be…
An expression for the internal energy of a fluid element in a weakly coupled, magnetized, anisotropic plasma is derived from first principles. The result is a function of entropy, particle density and magnetic field, and as such plays the…
A useful inductive bias for temporal data is that trajectories should stay close to the data manifold. Traditional flow matching relies on straight conditional paths, and flow matching methods which learn geodesics rely on RBF kernels or…
We study mean curvature flows in a warped product manifold defined by a closed Riemannian manifold and $\mathbb{R}$. In such a warped product manifold, we can define the notion of a graph, called a geodesic graph. We prove that the curve…
A solution to the heat equation between Riemannian manifolds, where the domain is compact and possibly has boundary, will not leave a compact and locally convex set before the image of the boundary does.
An explanation of stability of fireballs is proposed based on quantum effects in a thin surface layer of negatively charged plasma surrounding a positive kernel of a fireball. We construct a quantization of the geodesic flow on the sphere…
We prove several results concerning the existence of surfaces of section for the geodesic flows of closed orientable Riemannian surfaces. The surfaces of section $\Sigma$ that we construct are either Birkhoff sections, meaning that they…
We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of…