Related papers: The Stark problem as a concave toric domain
Quadratic gravity is a UV completion of general relativity, which also solves the hierarchy problem. The presence of 4 derivatives implies via the Ostrogradsky theorem that the $classical$ Hamiltonian is unbounded from below. Here we solve…
Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak solutions with $L^{\infty}$ data. We show that for strong enough…
A novel interpretation is given of Dirac's "wave equation for the relativistic electron" as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different "topological spin"…
We formulate a theory combining the principles of a scalar-tensor gravity and the Rastall proposal of a violation of the usual conservation laws. In the resulting Brans-Dicke-Rastall (BDR) theory the only exact, static, spherically…
We have investigated the bound states of an electron and positron in superstrong magnetic fields typical for neutron stars. The complete relativistic problem of positronium in a strong magnetic field has not been succesfully solved up to…
In the first part of this work we apply Bohr (old or naive quantum atomic) theory for analysis of the remarkable electro-dynamical problem of magnetic monopoles. We reproduce formally exactly some basic elements of the Dirac magnetic…
The classical electromagnetic friction of a charged particle moving with prescribed constant velocity parallel to a planar imperfectly conducting surface is reinvestigated. As a concrete example, the Drude model is used to describe the…
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the…
The linear Stark effect in the MIC-Kepler problem describing the interaction of charged particle with Dirac's dyon is considered. It is shown that constant homogeneous electric field completely removes the degeneracy of the energy levels on…
The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as…
The Nernst-Planck-Navier-Stokes system models electrodiffusion of ions in a fluid. We prove global existence of solutions in bounded domains in three dimensions with either blocking (no-flux) or uniform selective (special Dirichlet)…
The problem of calculation of electromagnetic field energy outside the transparency domain is discussed. It is shown that charged particle contribution to the energy of electromagnetic perturbations in the general case can be described in…
Relativistic strophotron is a system in which fast electrons move along a potential trough produced by quadrupole electric lenses. Equations of motion in the strophotron field are investigated and electron trajectories are found. It is…
We prove the well-posedness of the Cauchy problem on torus to an eletromagnetoelastic system. The physical model consists of three coupled partial differential equations, one of them is a hyperbolic equation describing the elastic medium…
We survey the few exact results on the Stormer problem describing the dynamics of charged particles in the Earth magnetosphere. The analysis of this system leads to the the conclusion that charged particles are trapped in the Earth…
We consider N interacting quantum particles on a one-dimensional lattice, and subjected to an external linear potential. For N = 1, the corresponding Hamiltonian is explicitly diagonalizable, with superexponentially localized eigenstates.…
We consider the system of two material points that interact by elastic forces according to Hooke's law and their motion is restricted to certain curves lying on the plane. The nonintegrability of this system and idea of the proof are…
We consider the motion of compressible Navier-Stokes fluids with the hard sphere pressure law around a rigid obstacle when the velocity and the density at infinity are non zero. This kind of pressure model is largely employed in various…
Observing the Universe, astronomers have concluded that the motion of stars can not be accounted for unless one assumes that most of the mass in the Universe is carried on by a ``dark matter", so far impervious to all attempts at being…