Related papers: Optimal velocity fields for instantaneous magnetic…
We discuss an extension of the velocity Verlet method that accurately approximates the kinetic-energy-conserving charged particle motion that comes from magnetic forcing. For a uniform magnetic field, the method is shown to conserve both…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic…
We study the kinematic dynamo equation on the three-torus and provide a rigorous proof of fast dynamo action for a time-periodic, divergence-free, Lipschitz velocity field. Our construction is based on a stretch-fold-shear mechanism…
A family of rigorous upper bounds on the growth rate of local gyrokinetic instabilities in magnetized plasmas is derived from the evolution equation for the Helmholtz free energy. These bounds hold for both electrostatic and electromagnetic…
We derive an exact, time-dependent analytical magnetic field solution for the inner heliosheath, which satisfies both the induction equation of ideal magnetohydrodynamics in the limit of infinite electric conductivity and the magnetic…
A solution is proposed for finding the vector potential and magnetic field of any distribution of currents with axial symmetry. In this approach, the magnetic field and the vector potential are looked for not by solving a differential…
The ideal magnetohydrodynamic equations are, roughly speaking, a quasi-linear symmetric hyperbolic system of PDEs, but not all the unknowns play the same role in this system. Indeed, in the regime of small magnetic fields, the equations are…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…
A general type of mathematical argument is described, which applies to all the cases in which dynamo maintenance of a steady magnetic field by motion in a uniform density is known to be impossible. Previous work has demonstrated that…
We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in the spacetime tangent bundle and in phase spaces (cotangent bundle). Crucial in order to…
In this paper we consider a measure-theoretical formulation of the training of NeurODEs in the form of a mean-field optimal control with $L^2$-regularization of the control. We derive first order optimality conditions for the NeurODE…
The magnetostatic field distribution in a nonlinear medium amounts to the unique minimizer of the magnetic coenergy over all fields that can be generated by the same current. This is a nonlinear saddlepoint problem whose numerical solution…
Motivated by the Swampland Distance Conjecture, we study distances in field space using the framework of Optimal Transport. The associated optimisation problem naturally leads to a notion of distance in terms of a (generalised) Wasserstein…
We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that if the magnetic field and velocity field are never…
In this paper, we study Liouville type results for the three-dimensional stationary incompressible MHD equations and Hall-MHD equations. Using the energy method and an iteration argument, we establish Liouville type theorems if Lebesgue…
We use particle-in-cell, fully electromagnetic, plasma kinetic simulation to study the effect of external magnetic field on electron scale Kelvin-Helmholtz instability (ESKHI). The results are applicable to collisionless plasmas when e.g.…
We provide for the first time the exact solution of Maxwell's equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the…
Spontaneous magnetic field generation plays important role in laser-plasma interactions. Strong quasi-static magnetic fields affect the thermal conductivity and the plasma dynamics, particularly in the case of ultra intense laser where the…
We propose an algorithm using method of evolving junctions to solve the optimal path planning problems with piece-wise constant flow fields. In such flow fields with a convex Lagrangian in the objective function, we can prove that the…