Related papers: Exact closed-form solutions for Lamb's problem (II…
We consider the physically relevant fully compressible setting of the Rayleigh Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to the gravitational force. Under suitable restrictions…
The fundamental problem of optical wave propagation is the determination of the field at an observation point, given a disturbance specified over some finite aperture. In both vacuum and inhomogeneous media, the solution of this problem is…
We present a new direct approach to obtain the Green's function of the Oseen equations, also known as the oseenlet. This approach is different in that it does not assume an initial form of the solution to begin with. The final solution is…
Using spacetime Gaussian test functions, we find closed-form expressions for the smeared Wightman function, Feynman propagator, retarded and advanced Green's functions, causal propagator and symmetric propagator of a massless scalar field…
We consider an approximate solution for the one-dimensional semilinear singularly-perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of…
We consider the numerical treatment of one of the most popular finite strain models of the viscoelastic Maxwell body. This model is based on the multiplicative decomposition of the deformation gradient, combined with Neo-Hookean…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
We use the effective-mass approximation and the density-functional theory with the local-density approximation for modeling two-dimensional nano-structures connected phase-coherently to two infinite leads. Using the non-equilibrium Green's…
Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to…
We demonstrate that the corrections to the classical Kelvin image theory due to finite electron screening length $\lambda$, recently discussed by Roulet and Saint Jean, Am. J. Phys. 68(4) 319, is amenable to an exact closed form solution in…
This paper examines the propagation of time-harmonic waves in a two-dimensional triangular lattice with a lattice constant $a = 1$. The sources are positioned along line segments within the lattice. Specifically, we investigate the discrete…
The one dimensional wave equation serves as a basic model for imaging modalities such as seismic which utilize acoustic data reflected back from a layered medium. In 1955 Peterson et al. described a single scattering approximation for the…
The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
We developed the formal connection of the field theoretical Bethe-Salpeter equation including the ladder approximation with its representation on the light-front for a bosonic model. We use the light-front Green's function for the…
The nonequilibrium photon Green function for a bounded medium surrounded by vacuum is analyzed on the basis of the Dyson equation. As its components, the field-field fluctuations as well as the spectral function split up into parts related…
Beamforming methods for sound source localization are usually based on free-field Green's functions to model the sound propagation between source and microphone. This assumption is known to be incorrect for many industrial applications and…
The spectral decomposition of the elastic wave operator in a layered isotropic half-space is derived by means of standard functional analytic methods. Particular attention is paid to the coupled $P$-$SV$ waves. The problem is formulated…
Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectra is…
The Hubbard model is exactly solved for two particles with opposite spins on d-dimensional hypercubes. It is shown that the spectrum can be separated into two parts: a trivial (U-independent) part resulting from symmetries of hypercubes and…