The Kirchhoff-Love plate model is a widely used in the analysis of thin elastic plates. It is well known that Kirchhoff-Love solutions can be viewed as certain limits of displacements and stresses for elastic plates where the thickness tends to zero. In this paper, we consider the problem from a different point of view and derive computable upper bounds of the difference between the exact three...

The Huygens-Fresnel diffraction integral has been formulated for incident Gaussian laser beams by using the Kirchhoff obliquity factor with the wave front instead of the aperture plane as the surface of integration. Accurate numerical-integration calculations were used to investigate the Fresnel field diffraction region for the much-studied case of a circular aperture. It is shown that the clas...

Equations describing the radiation characteristics of a rigid disk in a finite open baffle are derived using a method similar to that used by Streng for a circular membrane based upon the dipole part of the Kirchhoff–Helmholtz boundary integral formula. In this case, however, a power series solution to the radiation integral is derived in order to eliminate the need for numerical integration. H...

A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler-Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement w...

Due to their very high integration density, echelle grating spectrometers based on silicon nanophotonic platforms have received great attention for their applications in many areas, such as optical sensors, optical communications, and optical interconnections. The design of echelle gratings requires an effective modeling and simulation technique. Though we have used a boundary integral method t...

In this article, we study a Kirchhoff type problem with a positive parameter λ,

In this article, we apply the Nehari manifold method to study the Kirchhoff type equation

Analysis of Electromagnetic Waves in Random Media Liliana Borcea Department of Mathematics, University of Michigan We study Maxwell’s equations in media with small random fluctuations of the electric permittivity, to obtain a detailed mathematical characterization of the statistics of the electric and magnetic fields at long distances of propagation. We introduce a novel wide-angle wave propaga...