Related papers: General mathematical analysis on multiple solution…
Numerous natural and technological phenomena are governed by resonances. In nanophotonics, resonances often result from the interaction of several optical elements. Controlling these resonances is an excellent opportunity to provide light…
We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
We present an approximate analytic expression for thermonuclear reaction rate of charged particles when the cross section contains a single narrow or wide resonance described by a Breit-Wigner shape. The resulting expression is uniformly…
Three types of boundary integral equation (BIE) methods are employed to obtain closed-form solutions of a wave-scattering problem which are compared to the exact, closed-form (reference), solution deriving from the separation-of-variables…
In the course of devising a simple method for extraction of the S-matrix poles from the data, an additional fundamental resonance property emerged. It is a reaction invariant quantity, and since it is directly related to the Breit-Wigner…
The refraction index and matter potential depend on neutrino energy and this dependence has a resonance character associated to the production of the mediator in the $s-$channel. For light mediators and light particles of medium…
Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
Closed formulas in terms of double sums of Clebsch-Gordan coefficients are computed for the evaluation of bra-ket spherical harmonic overlap integrals of a wide class of trigonometric functions. These analytical expressions can find useful…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fifth paper, the usual structural analysis of plates on an elastic foundation…
We explore the feasibility of interference alignment in signal vector space -- based only on beamforming -- for K-user MIMO interference channels. Our main contribution is to relate the feasibility issue to the problem of determining the…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
Considering the concept of "{\it nonlinear coherent states}", we will study the interference effects by introducing the {\it "superposition of two classes of nonlinear coherent states"} which are $\frac{\pi}{2}$ out of phase. The formalism…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
Scattering resonances play a crucial role in understanding wave behavior in various physical systems. While significant progress has been made in analyzing resonances in high-contrast and nonlinear media, a general characterization of…
We present a subdivision method to solve systems of congruence equations. This method is inspired in a subdivision method, based on Bernstein forms, to solve systems of polynomial inequalities in several variables and arbitrary degrees. The…
We theoretically and numerically investigate resonant optical properties of composite structures consisting of several subwavelength resonant diffraction gratings separated by homogeneous layers. Using the scattering matrix formalism, we…
Spin-1 resonances are naturally present in composite Higgs frameworks. We first review a model independent approach to parametrize a single additional heavy triplet and then we consider more realistic models arising in composite Higgs…
A general theory of nonlinear signal-noise interactions for wavelength division multiplexed fiber-optic coherent transmission systems is presented. This theory is based on the regular perturbation treatment of the nonlinear Schrodinger…