Three-Dimensional Biorthogonal Divergence-Free and Curl-Free Wavelets with Free-Slip Boundary

This paper deals with the construction of divergence-free and curl-free wavelets on the unit cube, which satisfies the free-slip boundary conditions. First, interval wavelets adapted to our construction are introduced. Then, we provide the biorthogonal divergence-free and curl-free wavelets with free-slip boundary and simple structure, based on the characterization of corresponding spaces. Moreover, the bases are also stable

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Wavelet Analysis on the Sphere

The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials

Rigorous electromagnetic calculations in radiometry

Until recently, accurate estimates in radiometry using geometrical optics were justified because of the use of optical frequencies and large apertures. Nevertheless in modern radiometry, due to the increased interest in longer wavelengths and the improvement of experimental accuracy, geometrical optics cannot provide accurate enough estimates for experimental purposes. Initially the accuracy was improved by using the Fresnel approximation for the calculation of physical flux. Obviously this approach includes all the common approximations of scalar diffraction theories, namely scalar field, infinitely thin aperture and perfectly absorbing screen. Therefore, a more accurate model is introduced that accounts for the vector nature of light, finite thickness for the aperture and infinite conducting screen which is a good approximation because of the use of longer wavelengths. The application of this model, as well as abandoning the single wavelength approximation, results in deviations from scalar theory of 1% for a typical radiometric configuration

13th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, CA, March 17-21, 1997, Conference Proceedings Volumes I & II

Includes Volumes 1 &