Related papers: Analytical Solutions for Beams Passing Apertures w…
Diffraction radiation (DR) is produced when a charged particle passes through an aperture or near a discontinuity in the media in which it is traveling. DR is closely related to transition radiation (TR), which is produced when a charged…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…
It is shown that the diffraction on a polycrystal can be used for investigation and diagnostics of X-ray radiation emitted in a forward direction by relativistic charged particles moving in crystalline or other targets or fields. Methods…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
We present a theoretical model for the propagation of non self-interacting atom laser beams. We start from a general propagation integral equation, and we use the same approximations as in photon optics to derive tools to calculate the atom…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
We propose an efficient method for spatial filtering of light beams by propagating them through 2D (also 3D) longitudinally chirped photonic crystals, i.e. through the photonic structures with fixed transverse lattice period and with the…
We present a general expression for the optical theorem in terms of Localized Waves. This representation is well-known and commonly used to generate Frozen waves, Xwaves, and other propagation invariant beams. We analyze several examples…
Recently, modal expansion methods (MEMs) were developed to accurately predict the extinction and scattering spectra of bare and coated plasmonic particles. However, it remains uncertain whether the accuracy of analytical models is preserved…
Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…
As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for…
Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles, and there are no corresponding solutions for profiles…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
An exact solution has been found for the problem of diffraction radiation appearing when a charged particle moves perpendicularly to a thin finite screen having arbitrary conductivity and frequency dispersion. Expressions describing the…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
The linear intensity profile of multiply scattered light in a slab geometry extrapolates to zero at a certain distance beyond the boundary. The diffusion equation with this "extrapolated boundary condition" has been used in the literature…
We derive the beam tracing and profile evolution for the propagation of any localised beam with arbitrary profile through an inhomogeneous cold plasma. We recover standard Gaussian beam-tracing, with an additional PDE describing the…
In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…
We derived a non-linear 4th-order ordinary differential equation the solutions of which lead to the exact shapes of the cantilever beam. The result of the equation in a non-dimensional form was found to depend on two parameters only: the…