Related papers: Numerically Analytical Methods of Solution of the …
Shallow water surface flows commonly entrain sediments, resulting in scouring and/or deposition of the underlying substrate that may strongly influence the pattern of subsequent flow. These coupled phenomena, which can be investigated…
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
Radiative emission from an open-ended unflanged planar dielectric waveguide is studied for the case of TM polarization on the basis of an iterative scheme. The first step of the scheme leads to approximate values for the reflection…
The diffraction of a time-harmonic plane wave on collinear finite defects in a square lattice is studied. This problem is reduced to a matrix Wiener-Hopf equation. This work adapts the recently developed iterative Wiener-Hopf method to this…
With the increasing use of ultrashort laser pulses and nanoscale-materials, one is regularly confronted to situations in which the properties of the media supporting propagation are not varying slowly with time (or space). Hence, the usual…
Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping optics, and the highly nonlinear…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
Using the FDTD method, we investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel air cylinders in a dielectric medium. The corresponding frequency band structure is computed using the standard…
We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear…
We present three complementary methods to study stationary nonlinear solutions in one-dimensional nonlinear metal-dielectric structures. Two of them use an approximate treatment of the Kerr type nonlinear term taking into account only the…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlocal diffusion operators in the basis of spherical harmonics,…
We investigate a one-dimensional nonlinear wave system which arises from a variational principle modeling a type of cholesteric liquid crystals. The problem treated here is the Cauchy problem for the same wave speed case with initial data…
We consider a linearly polarized electromagnetic wave incident on an opaque screen with square aperture of edge a. An application of Faraday's law to a loop parallel to the screen, on the side away from the source, shows that the wave must…
The set of non-linear equations describing the Standard Model kinematics of the top quark antiqark production system in the dilepton decay channel has at most a four-fold ambiguity due to two not fully reconstructed neutrinos. Its most…
Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different…
We study light scattering by a hedgehog-like and linear disclination topological defects in a nematic liquid crystal by a metric approach. Light propagating near such defects feels an effective metric equivalent to the spatial part of the…
A problem of diffraction of a symmetrical transverse magnetic mode $ \text{TM}_{0l} $ by an open-ended cylindrical waveguide corrugated inside is considered. A depth and a period of corrugations are supposed to be much less than the…
The approach allowing is considered to represent the solutions such as stationary lonely waves of various nonlinear wave the equations as system of the ordinary differential equations in variable action - angle.