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The method of flow equations is applied to QED on the light front. Requiring that the particle number conserving terms in the Hamiltonian are considered to be diagonal and the other terms off-diagonal an effective Hamiltonian is obtained…
This paper presents an improved version of the previously proposed self-consistent drift-diffusion-reaction model correcting for non-physical behavior at longer time scales. To this end a novel boundary condition is employed that takes into…
In this letter we propose a Turing model of the formation of patterns of visible light emission intensity in atmospheric pressure gas discharges. The electron density and the electron temperature take the roles of activator and inhibitor…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
One of the difficulties associated with the scattering problems arising in connection with integrable systems is that they are frequently non-self-adjoint, making it difficult to determine where the spectrum lies. In this paper, we consider…
The discharge structure of inductively coupled plasma is studied via fluid simulation and analytic theory collaboration. At low pressure, the discharge is stratified by the double layer, which is modelled as dipole moment. The parabolic…
Spectral methods are well suited for solving hydrodynamic problems in which the self-gravity of the flow needs to be considered. Because Poisson's equation is linear, the numerical solution for the gravitational potential for each…
The diffusion and flow of amorphous materials, such as glasses and granular materials, has resisted a simple microscopic description, analogous to defect theories for crystals. Early models were based on either gas-like inelastic collisions…
Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated . Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are…
New non-stationary non-contracted form of the erosive radially-slotted discharge as a thin round sheet with the current of the azimuth direction have been discovered, its existence beings stipulated by a radial transport-wave fluxes.…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…
We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Amp{\`e}re model proposed in [3]. The main…
We study various aspects of the scattering of generalized compact oscillons in the signum-Gordon model in (1+1) dimensions. Using covariance of the model we construct traveling oscillons and study their interactions and the dependence of…
We discuss the method of self-consistent bounds for dissipative PDEs with periodic boundary conditions. We prove convergence theorems for a class of dissipative PDEs, which constitute a theoretical basis of a general framework for…
We investigate path-wise observables in experiments on driven colloids in a periodic light field to dissect selected intricate transport features, kinetics, and transition-path time statistics out of thermodynamic equilibrium. These…
We consider a plasma that is created by a high voltage difference, which is known as a Townsend gas discharge. The plasma is confined to the region between two concentric spheres, one of which is a cathode and the other an anode.…
There is a classic alternative to the Franck-Hertz experiment designed to show more than a recurrence of the first excited state. Instead of being subjected to a rising potential between source and accelerating grid, electrons are now…
Ultracold condensates provide a unique platform for exploring soliton physics. Motivated by the recent experiments realizing the sine-Gordon model in a split one-dimensional (1D) BEC, we demonstrate that this system naturally supports…
A theory of the separation of a system of indirect excitons into a condensed and a gaseous phases with the formation of regular patterns of alternating phases in inhomogeneous external fields is developed. The theory is applied to the study…
Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. The present paper focuses on the…