Related papers: Axisymmetric solutions in the geomagnetic directio…
We study parameterized elliptic systems on symmetric domains with additional system symmetries. We prove the existence of continua of nontrivial solutions bifurcating from the constant branch determined by a critical point of the potential,…
We consider positive solutions, possibly unbounded, to the semilinear equation $-\Delta u=f(u)$ on continuous epigraphs bounded from below. Under the homogeneous Dirichlet boundary condition, we prove new monotonicity results for $u$, when…
We have used Monte Carlo simulations to investigate the magnetic properties of asymmetric dots as a function of their geometry. The asymmetry of round dots is produced by cutting off a fraction of the dot and is characterized by an…
We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…
Charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation is derived. The metric associated with this solution is an axially symmetric metric which is characterized by…
We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved…
We calculate axisymmetric oscillations of rotating neutron stars composed of the surface fluid ocean, solid crust, and fluid core, taking account of a dipole magnetic field as strong as $B_S\sim 10^{15}$G at the surface. The adiabatic…
Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density…
We investigate the stability of test-particle equilibrium orbits in axisymmetric, but otherwise arbitrary, gravitational and electromagnetic fields. We extend previous studies of this problem to include a toroidal magnetic field. We find…
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…
We study the behaviour near a boundary point a of any positive solution of a nonlinear elliptic equations with forcing term which vanishes on the boundary except at a. Our results are based upon a priori estimates for solutions and…
This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits…
Internal-external field separation is crucial for many aspects of geomagnetism, aiming at distinguishing contributions of the magnetic field generated within the Earth (or any other planet) from those produced in the exterior. When data is…
The MHD instabilities can generate complex field topologies even if the initial field configuration is a very simple one. We consider the stability properties of magnetic configurations containing a toroidal and an axial field. In this…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
This paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that each bounded positive solution of the convolution equation…
Axisymmetric stellar wind solutions are presented, obtained by numerically solving the ideal magnetohydrodynamic (MHD) equations. Stationary solutions are critically analysed using the knowledge of the flux functions. These flux functions…
We continue our previous application of supersymmetric quantum mechanical methods to eigenvalue problems in the context of some deformed canonical commutation relations leading to nonzero minimal uncertainties in position and/or momentum.…
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional (3D) axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical…