Search results for "Wave equation"
showing 10 items of 74 documents
Using Wave Propagation Simulations and Convolutional Neural Networks to Retrieve Thin Film Thickness from Hyperspectral Images
2021
Ill-posed inversion problems are one of the major challenges when there is a need to combine measurements with the theory and numerical model. In this study, we demonstrate the use of wave propagation simulations to train a convolutional neural network (CNN) for retrieving sub-wavelength thickness profiles of thin film coatings from hyperspectral images. The simulations are produced by solving numerically one-dimensional wave equation with a method based on Discrete Exterior Calculus (DEC). This approach provides a powerful tool to produce large sets of training data for the neural network. CNN was verified by simulated verification sets and measured reflectance spectra, both of which showe…
Biorthonormal-basis method for the vector description of optical-fiber modes
1998
This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.
Generation of even harmonics of sub-THz radiation in bulk GaAs in the presence of a static electric field
2007
The static electric field effects on nonlinear carrier dynamics in low-doped GaAs bulk under the influence of an intense sub-terahertz field are studied by a three-dimensional multivalleys Monte Carlo simulation. The conversion efficiency is calculated by using the appropriate Maxwell equation for the propagation of an electromagnetic wave along a given direction in the medium. Production of odd and even harmonics due to the nonlinearity of the velocity-field relation is investigated.
Exactly solvable relativistic model with the anomalous interaction
2010
A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron'ko-Stroganov model.
Intensive wave power and steel quenching 3-D model for cylindrical sample. Time direct and reverse formulations and solutions
2017
In this paper we develop mathematical models for three dimensional hyperbolic heat equations (wave equation or telegraph equation) with inner source power and construct their analytical solutions for the determination of the initial heat flux for cylindrical sample. As additional conditions the temperature and heat flux at the end time are given. In some cases we give expression of wave energy. In some cases we give expression of wave energy. Some solutions of time inverse problems are obtained in the form of first kind Fredholm integral equation, but others has been obtained in closed analytical form as series. We viewed both direct and inverse problems at the time. For the time inverse pr…
On new ways of group methods for reduction of evolution-type equations
2005
AbstractNew exact solutions of the evolution-type equations are constructed by means of a non-point (contact) symmetries. Also we analyzed the discrete symmetries of Maxwell equations in vacuum and decoupled ones to the four independent equations that can be solved independently.
Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model
2021
Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conserv…
Finite propagation speed for solutions of the wave equation on metric graphs
2012
We provide a class of self-adjoint Laplace operators on metric graphs with the property that the solutions of the associated wave equation satisfy the finite propagation speed property. The proof uses energy methods, which are adaptions of corresponding methods for smooth manifolds.
Recovery of time-dependent coefficients from boundary data for hyperbolic equations
2019
We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.
Relativistic wave equations from supergroup quantization
1983
A formalism of geometric quantization recently introduced which is based on the consideration of Lie groups which are central extensions by U(1) is applied to the relativistic case by using the N-2 super Poincare group with a central charge.