Related papers: The electrostatic limit for the 3D Zakharov system
We consider the limiting current from an emitting patch whose size is much smaller than the anode-cathode spacing. The limiting current is formulated in terms of an integral equation. It is solved iteratively, first to numerically recover…
We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…
We study electron motion in electromagnetic (EM) fields in the radiation-dominated regime. It is shown that the electron trajectories become close to some asymptotic trajectories in the strong field limit. The description of the electron…
We derive the differential equation governing the asymptotic quasi-stationary states of the two dimensional plasma immersed in a strong confining magnetic field and of the planetary atmosphere. These two systems are related by the property…
We analyse the development of instability in the framework of nonlinear electrodynamics based on the Maxwell's equations without approach of slowly varying amplitudes and phases. The action is chosen from the Heisenberg-Euler Lagrangian,…
A quantum field has been coupled to a space-time with accelerating expansion. Dynamical modes are destabilised successively at shorter material wavelengths as they metamorphose from oscillators to repellers. Due to degeneracy of energy…
Electron trapping in a finite amplitude Langmuir wave (LW) leads to a frequency shift, \Delta\omega_{TP} < 0, and reduced Landau damping. These may lead to modulational instability. Its growth rate and damping threshold, due to escape of…
It is proved that a convex polyhedral scatterer of impedance type can be uniquely determined by the electric far-field pattern of a non-vanishing incident field. The incoming wave is allowed to bean electromagnetic plane wave, a vector…
Fast magnetosonic waves are among the fundamental oscillation modes of astrophysical plasmas. To study their dynamics, we carry out numerical simulations of the wave turbulence kinetic equation, which describes the evolution of the energy…
An approximate analytic solution is constructed for the 2-d space charge limited emission by a cathode surrounded by non emitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic…
We study relativistically expanding electromagnetic fields of cylindrical geometry. The fields emerge from the side surface of a cylinder and are invariant under translations parallel to the axis of the cylinder. The expansion velocity is…
We consider a one-dimensional cavity composed of two perfect, fixed mirrors and a mobile membrane in between. Assuming that the membrane starts to move from rest and that the membrane moves appreciably in a time-scale much larger than the…
We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of…
We consider the relativistic Vlasov-Maxwell system (RVM) on a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, assuming axisymmetry in the problem. We construct continuous global…
We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the…
The classic problem of the dynamic evolution of Langmuir electron waves in a collisionless plasma and their Landau damping is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies.…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
This article devoted to relativistic dynamics of a charged massive particle in an electroscalar field. It represents a continuation of paper [1] where the authors constructed a non-relativistic theory which describes transverse…
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…
In classical Maxwell's electromagnetism, monopole term of the electric field is proportional to $r^{-2}$, while higher order multipole terms, sourced by anisotropic sources, fall-off faster. However, in nonlinear electromagnetism even a…