Diffraction Theory by Means of Singular Integral Equations. VIIUniform High-Frequency Asymptotics for the Diffraction of Plane Waves by a Slit

We consider the diffraction of plane waves by a slit between two semi-infinite halfplanes for arbitrary angles of incidence and DIRICHLET boundary condition (electric field strength parallel to the edges). By a function-theoretic technique, which treats the angles of observation and incidence on an equal footing, we derive a high-frequency asymptotic expansion for the far field amplitude, uniformly valid over the whole range of both angles. Our expansion in terms of products of generalized FRESNEL integrals is compared with the known limiting cases of normal and grazing incidence both analytically and numerically including a comparison with MATHIEU -series results.     

Gravitative Selbstkräfte und Strahlungsverluste klassischer Spinteilchen (erste Näherung)

The solutions ofEinstein's linearised field equations for a pol-dipol-like massdistribution are regularised at the position of the arbitrarily moving source by means ofRiesz' method of analytic continuation. Selfforce and selftorque resulting from the spin particle's gravitational proper field are computed Lorentz-covariantly. The selfforce devides into the radiation reaction caused by lightlike emission of field momentum and the exchange-force due to fluctuation of the convective field momentum. Gravitational momentum emission is gauge invariant while the convective field momentum combines with the particle's mechanical momentum to a gauge invariant quantity. Corresponding considerations apply to the selftorque. (Gauge invariance refers to gauge transformations induced by arbitrary infinitesimal deviations from Cartesian coordinates into the Lorentz-covariant theory of gravitation.)     

Zur Theorie einer Klasse von Beugungsproblemen mittels singulärer Integralgleichungen. V Hochfrequenz-Beugung ebener elektromagnetischer Wellen an einer ideal leitenden Kreisblende

The high-frequency diffraction of a plane electromagnetic wave by a circular aperture in a infinite plane conducting screen is considered at normal incidence. The asymptotic solution of the singular integral equation for the Fourier-transform of the current density on the screen is found by means of elementary function-theoretic methods. Five terms of the high-frequency development of the transmission coefficient are given.     

High-Speed Scattering of Charged and Uncharged Particles in General Relativity

After a brief consideration of the high-speed scattering of two point charges we thoroughly discuss high-speed scattering for a charged particle by a fixed mass and of two uncharged particles of comparable masses. We use perturbation technique over Minkowski spacetime in the de Donder gauge and solve the field equations and the resulting equations of motion (which take the reaction of the particles' quasistatic self-field into account) by iteration. The obtained energy-momentum conservation laws allow the computation of second-order corrections for the scattering angle and the cross section. The asymptotic structure of the far-field indicates synchrotron radiation (electromagnetic and gravitational, respectively) which causes an energy loss whose reaction on the motion is briefly considered in the low-velocity limit including bound motion. (For neutral particles this is a third-order effect).     

Zur Theorie einer Klasse von Beugungsproblemen mittels singulärer Integralgleichungen. IV Hochfrequente Schallbeugung an der Kreisblende: numerische Ergebnisse

The six-term developments of the far-field amplitude and the transmission coefficient formerly given for the high-frequency diffraction of a plane sound wave by a circular aperture in an infinite plane sound-soft screen at normal incidence are corrected and numerically evaluated.     

Selbstwechselwirkung von Gravitationsfeldern schnell bewegter Pol-Dipolquellen

We construct retarded solutions of the second order Lorentz-covariant approximation of Einstein's field equations for rapidly moving pole-dipole-like mass distributions. As the conventional Green's function method breaks down here, the integration is accomplished by a new regularization procedure based on analytic continuation of properly cut integrals. It is pointed out that there is no self-interaction for a pole-particle, in contradistinction to a spin-particle, where the self-interaction manifests itself in a back-scattering of gravitational radiation (producing a wave tail).     

High magnetic shear gain in a liquid sodium stable Couette flow experiment: a prelude to an α-Ω dynamo

The Ω phase of the liquid sodium α-Ω dynamo experiment at New Mexico Institute of Mining and Technology in cooperation with Los Alamos National Laboratory has demonstrated a high toroidal field B(?) that is ?8×B(r), where B(r) is the radial component of an applied poloidal magnetic field. This enhanced toroidal field is produced by the rotational shear in stable Couette flow within liquid sodium at a magnetic Reynolds number Rm?120. Small turbulence in stable Taylor-Couette flow is caused by Ekman flow at the end walls, which causes an estimated turbulence energy fraction of (δv/v)(2)～10(-3).