Related papers: Optimal velocity fields for instantaneous magnetic…
We consider a Dirac electron in the presence of an exponentially decaying magnetic field. We obtain exact energy eigenvalues with a zero-energy state and the corresponding eigenfunctions. We also calculate the probability density and…
The eigenspinor approach uses the classical amplitude of the algebraic Lorentz rotation connecting the lab and rest frames to study the relativistic motion of particles. It suggests a simple covariant extension of the common definition of…
The existence of a weak galactic magnetic field has been repeatedly confirmed by observational data. The origin of this field has not as yet been explained in a fully satisfactory way and represents one of the main challenges of the…
Introducing nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. We address the problem of optimizing vortex pinning landscape for randomly distributed metallic…
For a simple spherically symmetric mean-field dynamo model we investigate the possibility of determining the radial dependence of the coefficient $\alpha$. Growth rates for different magnetic field modes are assumed to be known by…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
In this paper we study an optimal shape design problem for the first eigenvalue of the fractional $p-$laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is…
Several lines of evidence suggest that protogalactic and galactic environments manage to grow magnetic field very rapidly. This makes the theoretical problem of achieving rapid growth of magnetic fields in such environments difficult.…
A nonlinear differential equation about optimal shapes for blades of a fan. A boundary value differential problem from engineering, geometrical or physical bonds. A relation between linear profiles and constant speed along the side under…
For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the…
We show that smooth solutions to the Euler equation on the half-plane can exhibit double-exponential growth of their vorticity gradients. We also determine the maximal possible growth rate and construct solutions that saturate it. These are…
In order to understand the conditions which lead a highly magnetized, relativistic plasma to become unstable, and in such cases how the plasma evolves, we study a prototypical class of magnetostatic equilibria where the magnetic field…
A novel, interesting class of scalar-tensor gravity theories is those with a limit on the field motion, where the scalar field either goes to a constant acceleration or stops accelerating and goes to a constant velocity. We combine these…
We study semi-analytical time-dependent solutions of the relativistic magnetohydrodynamic (MHD) equations for the fields and the fluid emerging from a spherical source. We assume uniform expansion of the field and the fluid and a polytropic…
By writing the flow equations for the continuum Legendre effective action (a.k.a. Helmholtz free energy) with respect to a particular form of smooth cutoff, and performing a derivative expansion up to some maximum order, a set of…
We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…
The magnetic Dirichlet-to-Neumann map encodes the voltage-to-current measurements under the influence of a magnetic field. In the case of surfaces, we provide precise spectral asymptotics expansion (up to arbitrary polynomial power) for the…
A general framework for solving the Boltzmann equation for a 2-dimensional electron gas (2DEG) in random magnetic fields is presented, when the random fields are included in the driving force. The formalism is applied to some recent…
This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. Boundary conditions are…
We study a retarded potential solution of a massless scalar field in curved space-time. In a special ansatz for a particle at rest whose magnitude of the (scalar) charge is changing with time, we found an exact analytic solution. The…