Related papers: Optimal velocity fields for instantaneous magnetic…
We study the problem of transporting one probability measure to another via an autonomous velocity field. We rely on tools from the theory of optimal transport. In one space-dimension, we solve a linear homogeneous functional equation to…
The retarded vector potential of a point magnetic dipole with an arbitrary time dependence undergoing accelerated relativistic motions is derived. A novel expression for the angular distribution of the radiated power of an arbitrary moving…
Using relativistic, steady, axisymmetric, ideal magnetohydrodynamics (MHD) we analyze the super-Alfvenic regime of a pulsar wind by means of solving the momentum equation along the flow as well as in the transfield direction. Employing a…
We study an optimal transport problem where, at some intermediate time, the mass is accelerated by either an external force field, or self-interacting. We obtain regularity of the velocity potential, intermediate density, and optimal…
We have carried out high resolution MHD simulations of the nonlinear evolution of Kelvin-Helmholtz unstable flows in 2 1/2 dimensions. The modeled flows and fields were initially uniform except for a thin shear layer with a hyperbolic…
The self-consistent problem of the wave and particle spectrum is formulated and solved for acceleration of particles in a homogeneous magnetic field that varies periodically with time. It follows from the obtained solutions that when…
The intensity peak of a "flying focus" travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an…
In the paper "Optimal control of a Vlasov-Poisson plasma by an external magnetic field - The basics for variational calculus" [arXiv:1708.02464] we have already introduced a set of admissible magnetic fields and we have proved that each of…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…
For a vehicle on an assigned path, we find the minimum-time speed law that satisfies kinematic and dynamic constraints, related to maximum speed and maximum tangential and transversal acceleration. We present a necessary and sufficient…
Unconfined relativistic outflows from rotating, magnetized compact objects are often well-modeled by assuming the field geometry is approximately a split-monopole at large radii. Earlier work has indicated that such an unconfined flow has…
This paper exposes how to obtain a relation that have to be hold for all free--divergence velocity fields that evolve according to Navier--Stokes equations. However, checking the violation of this relation requires a huge computational…
Electromagnetic fields of an accelerated charge are derived from the first principles using Coulomb's law and the relativistic transformations. The electric and magnetic fields are derived first for an instantaneous rest frame of the…
We propose a model of magnetic-field growth in galaxy clusters whereby the field is amplified by a factor of about 10^8 over a cosmologically short time of ~10^8 yr. Our model is based on the idea that the viscosity of the intracluster…
The self-excitation of magnetic field by a spiral Couette flow between two coaxial cylinders is considered. We solve numerically the fully nonlinear, three-dimensional MHD equations for magnetic Prandtl numbers Pm (ratio of kinematic…
We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Amp\`ere type arising from optimal mass transport. Our main result is an exponential rate of convergence for solutions of this…
A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a…
For any smooth bounded domain $\Omega \subset \mathbb{R}^3$, we construct a divergence-free velocity field $u \in L_t^1 W^{1,p}(\Omega)$ for all $p < \infty$, and magnetic fields $B^\epsilon \in L_t^p C^{m}(\Omega)$ for all $p < \infty$ and…
We discuss some Lagrangian and presymplectic models concerning test particles in electromagnetic and gravitational fields, with the aim of describing an upper bound to the acceleration. Some models are based on the relativistic phase space…