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In the spectral stability analysis of localized patterns to singular perturbed evolution problems, one often encounters that the Evans function respects the scale separation. In such cases the Evans function of the full linear stability…
360-degrees digitalization of three-dimensional (3D) solids using a projected light-strip is a well established technique. These profilometers project a light-strip over the solid under analysis while the solid is rotated a full revolution.…
We describe new exact results for a model of ionization of a bound state, induced by an oscillating potential. In particular we have obtained exact expressions, in the form of readily computable rapidly convergent sums, for the energy…
Polarization in ferroelectrics, described by the Landau-Ginzburg Hamiltonian, is considered, based on a multi-dimensional Fokker-Planck equation. This formulation describes the time evolution of the probability distribution function over…
Reaction-nonlinear diffusion partial differential equations can exhibit shock-fronted travelling wave solutions. Prior work by Yi et. al. (2021) has demonstrated the existence of such waves for two classes of regularisations, including…
The proton charge and magnetization density distributions can be related to the well known Sachs electromagnetic form factors $G_{E,M}({\bm q}^{2})$ through Fourier transforms, only in the Breit frame. The Breit frame however moves with…
Five methods of calculating electrical field distributions in one dimensional wave-guide arrays are reviewed. We analytically solve the scalar Helmholtz Equation and, based on the computed Bloch functions and associated bands of propagation…
Dense plasma environment affects the electronic structure of ions via variations of the microscopic electrical fields, also known as plasma screening. This effect can be either estimated by simplified analytical models, or by…
Consider the problem when $X_1,X_2,..., X_n$ are distributed on a circle following an unknown distribution $F$ on $S^1$. In this article we have consider the absolute general set-up where the density can have local features such as…
We consider an alternative explanation of newly found growth of neutral pion transition form factor with virtuality of one of photon. It is based on Sudakov suppression of quark-photon vertex. Some applications to scattering and…
Streamer discharges are the primary mode of electric breakdown of air in lightning and high voltage technology. Streamer channels branch many times, which determines the developing tree-like discharge structure. Understanding these branched…
We develop a first-principles computational method for investigating the dielectric screening in extended systems using the self-consistent Sternheimer equation and localized non-orthogonal basis sets. Our approach does not require the…
The analysis of wave propagation in linear, passive media is usually done by considering a single real frequency (the monochromatic limit) and also often a single plane wave component (plane wave limit), separately. For gain media, we…
A general expression for the double differential cross section of fluorescence radiation following photorecombination (PRF) of polarized electrons and polarized ions is derived by using usual atomic theory methods and is represented in the…
The Fraunhofer diffraction of quantum particles from materials with sharp electron-density edges or symmetric bond structures is ubiquitous. In contrast, diffraction from atoms with characteristic asymptotically-diffused electron…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance…
Using the time-dependent Ginzburg-Landau equations we study the propagation of planar fronts in superconductors, which would appear after a quench to zero applied magnetic field. Our numerical solutions show that the fronts propagate at a…
Recently Bar-Ziv and Moses discovered a dynamical shape transformation induced in cylindrical lipid bilayer vesicles by the action of laser tweezers. We develop a hydrodynamic theory of fluid bilayers in interaction with the surrounding…
I present some simple exactly solvable models of spin diffusion caused by synchrotron radiation noise in storage rings. I am able to use standard stochastic differential equation and Fokker-Planck methods and I thereby introduce, and…