Making electromagnetic wavelets

Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by deforming and merging two branch cuts. This determines a unique field on the interior of the spheroid which gives the boundary conditions for the surface charge-current density necessary to radiate the wavelets. These sources are computed, including the impulse response of the antenna.Comment: 29 pages, 4 figures; minor corrections and addition

Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: (\vec \nabla \rho_p- \vec \nabla \rho_n)^2 G_d(\rho)+ (\vec \nabla \rho_p- \vec \nabla \rho_n)\cdot(\vec J_p-\vec J_n) G_{so(\rho)+(\vec J_p-\vec J_n)^2 G_J(\rho) pertaining to different proton and neutron densities. Our calculation treats systematically the effects from $1\pi$-exchange, iterated $1\pi$-exchange, and irreducible $2\pi$-exchange with intermediate $\Delta$-isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions $G_d(\rho)$, $G_{so}(\rho)$ and $G_J(\rho)$ which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.Comment: 12 pages, 5 figure

Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector spin-orbit terms

We extend a recent calculation of the nuclear energy density functional in the systematic framework of chiral perturbation theory by computing the isovector spin-orbit terms: $(\vec \nabla \rho_p- \vec \nabla \rho_n)\cdot(\vec J_p-\vec J_n) G_{so}(k_f)+ (\vec J_p-\vec J_n)^2 G_J(k_f)$. The calculation includes the one-pion exchange Fock diagram and the iterated one-pion exchange Hartree and Fock diagrams. From these few leading order contributions in the small momentum expansion one obtains already a good equation of state of isospin-symmetric nuclear matter. We find that the parameterfree results for the (density-dependent) strength functions $G_{so}(k_f)$ and $G_J(k_f)$ agree fairly well with that of phenomenological Skyrme forces for densities $\rho > \rho_0/10$. At very low densities a strong variation of the strength functions $G_{so}(k_f)$ and $G_J(k_f)$ with density sets in. This has to do with chiral singularities $m_\pi^{-1}$ and the presence of two competing small mass scales $k_f$ and $m_\pi$. The novel density dependencies of $G_{so}(k_f)$ and $G_J(k_f)$ as predicted by our parameterfree (leading order) calculation should be examined in nuclear structure calculations.Comment: 9 pages, 3 figure, published in: Physical Review C68, 014323 (2003

The Color Splitting System for TV Cameras - XYZ Prism

One of the dominant aspects, which prejudices the quality of color image reproduction, is the first operation in TV chain - scanning. Up to this day, the color splitting system, working in RGB colorimetric system, is still entirely used. The existence of negative parts of the color matching functions r(l), g(l), b(l) causes complications by optical separation of partial pictures R, G, B in classic scanning system. It leads to distortion of reproduction of color images. However, the specific technical and scientific applications, where the color carries the substantial part of information (cosmic development, medicine), demand high fidelity of color reproduction. This article submits the results of the design of the color splitting system working in XYZ colorimetric system (next only XYZ prism). Shortly the way to obtain theoretical spectral reflectances of partial filters of XYZ prism is described. Further, these filters are approximated by real optical interference filters and the geometry of XYZ prism is established. Finally, the results of the colorimetric distortion test of proposed scanning system are stated

Chiral 3π\pi-exchange NN-potentials: Results for dominant next-to-leading order contributions

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams with one insertion from the second order chiral effective pion-nucleon Lagrangian proportional to the low-energy constants $c_{1,2,3,4}$. The resulting isoscalar central potential vanishes identically. In most cases these $3\pi$-exchange potentials are larger than the ones generated by the diagrams involving only leading order vertices due to the large values of $c_{3,4}$ (which mainly represent virtual $\Delta$-excitation). A similar feature has been observed for the chiral $2\pi$-exchange. We also give suitable (double-integral) representations for the spin-spin and tensor potentials generated by the leading-order diagrams proportional to $g_A^6$ involving four nucleon propagators. In these cases the Cutkosky rule cannot be used to calculate the spectral-functions in the infinite nucleon mass limit since the corresponding mass-spectra start with a non-vanishing value at the $3\pi$-threshold. Altogether, one finds that chiral $3\pi$-exchange leads to small corrections in the region $r\geq 1.4$ fm where $1\pi$- and chiral $2\pi$-exchange alone provide a very good strong NN-force as shown in a recent analysis of the low-energy pp-scattering data-base.Comment: 11 pages, 7 figures, to be published in The Physical Review

A wave-envelope of sound propagation in nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. The solution recovers the solution based on the method of multiple scales for slowly varying duct geometry. A computer program was developed based on the wave-envelope analysis for general mean flows. Results are presented for the reflection and transmission coefficients as well as the acoustic pressure distributions for a number of conditions: both straight and variable area ducts with and without liners and mean flows from very low to high subsonic speeds are considered

Transmission of sound through nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined, circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. Although the theory is described for circular ducts, it is applicable to other duct configurations - annular, two dimensional, and rectangular. The theory is described for the linear problem, but the technique is general and has the advantage of being applicable to the nonlinear case as well as the linear case. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave. A computer program was developed. The mean flow model consists of a one dimensional flow in the core and a quarter-sine profile in the boundary layer. Results are presented for the reflection and transmission coefficients in ducts with varying slopes and carrying different mean flows

Complex-Distance Potential Theory and Hyperbolic Equations

An extension of potential theory in R^n is obtained by continuing the Euclidean distance function holomorphically to C^n. The resulting Newtonian potential is generated by an extended source distribution D(z) in C^n whose restriction to R^n is the delta function. This provides a natural model for extended particles in physics. In C^n, interpreted as complex spacetime, D(z) acts as a propagator generating solutions of the wave equation from their initial values. This gives a new connection between elliptic and hyperbolic equations that does not assume analyticity of the Cauchy data. Generalized to Clifford analysis, it induces a similar connection between solutions of elliptic and hyperbolic Dirac equations. There is a natural application to the time-dependent, inhomogeneous Dirac and Maxwell equations, and the `electromagnetic wavelets' introduced previously are an example.Comment: 25 pages, submited to Proceedings of 5th Intern. Conf. on Clifford Algebras, Ixtapa, June 24 - July 4, 199

Colorimetry and TV Colour Splitting Systems

The colorimetric standard of the present-day television system goes back to the American NTSC system from 1953. In this RGB colorimetric system it is not possible, for basic reasons, to produce a scanning device which will provide signals suitable for controlling any displayed unit. From the very beginning of the television system the scanning device has produced inevitable colour deformation. The range of reproductive colours is not fully utilized either by a contemporary Cathode Ray Tube display unit or by a Liquid Crystal Display. In addition, the range is not sufficient for true reproduction of colours. Specific technical and scientific applications in which colour bears a substantial part of the information (cosmic development, medicine) demand high fidelity colour reproduction. The colour splitting system, working in the RGB colorimetric system, continues to be universally used. This article submits the results of a design for a colour splitting system working in the XYZ colorimetric system (hereafter referred to as the XYZ prism). A way to obtain theoretical spectral reflectances of partial XYZ prism filters is briefly described. These filters are then approximated by real optical interference filters and the geometry of the XYZ prism is established

Violation of the Leggett-Garg Inequality in Neutrino Oscillations

The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than $6{\sigma}$ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.Comment: Updated to match published version. 6 pages, 2 figure