Asymptotic Distances Research Articles

On the asymptotic frequency behavior of uniform GTD in the shadow region of a smooth convex surface

A number of canonical plane-wave and line-source solutions involving circular cylinders have led to a widely accepted uniform geometrical theory of diffraction (GTD) formulation for the scattered electromagnetic field in the shadow region of a smooth convex surface. The current solution does not constitute a properly formulated asymptotic high-frequency theory in the sense that it becomes increasingly inaccurate with increasing frequency. This inaccuracy results from transition-function dominance in the deep shadow region over the Pekeris caret function that is used. An improved formulation that circumvents this difficulty by avoiding use of a transition function is derived via a straightforward extension of the canonical line-source solution given by Jones (1963). This new solution takes the form of Keller-type modes with modified diffraction coefficients that result in convergence at the shadow boundary provided that the source and observation point are not both located at asymptotic distances from the scatterer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The theory of magnetohydrodynamic wave generation by localized sources. II - Collisionless dissipation of wave packets

The dispersion equation of Barnes (1966) is used to study the dissipation of asymptotic wave packets generated by localized periodic sources. The solutions of the equation are linear waves, damped by Landau and transit-time processes, in a collisionless warm plasma. For the case of an ideal MHD system, most of the waves emitted from a source are shown to cancel asympotically through destructive interference. The modes transporting significant flux to asymptotic distances are found to be Alfven waves and fast waves with theta (the angle between the magnetic field and the characteristics of the far-field waves) of about 0 and about pi/2.

Coulomb-gauge electrodynamics analysis of two-photon exchange in electron-atom scattering.

We analyze all the time-ordered two-photon-exchange Feynman diagrams for electron-atom scattering in the Coulomb gauge. This includes the exchange of Coulomb as well as transverse photons. At threshold energy, we recover the two-photon exchange potential previously obtained by Feinberg and Sucher using covariant field-dispersion-theory technique. The present calculation is an analog of the classical work of Casimir and Polder on the two-photon exchange between a pair of neutral atoms and bridges a gap between the covariant field-dispersion-theory calculation and other nonrelativistic calculations. The Casimir effect is manifested in the first nonadiabatic potential which changes from a ${R}^{\mathrm{\ensuremath{-}}6}$ dependence to a ${R}^{\mathrm{\ensuremath{-}}7}$ dependence at asymptotic distances (R&gt;a/\ensuremath{\alpha}). We calculate terms up to the order of (${\mathrm{hlambda}}_{e}$/R${)}^{2}$ or, equivalently, of order (a/R${)}^{4}$ compared to the classical electric dipole polarization potential, and include the lowest-order energy dependence beyond the threshold. The neglected terms are of order ${\ensuremath{\alpha}}^{2}$ or smaller at asymptotic distances. The present results are valid also for positron-atom scattering.

The nature of confined states

We show that in spite of charge confinement in the Schwinger model1 and its nonconfinement in (QED)4, the charged states in the two theories have many features in common. A convenient infrared regularization procedure is introduced to facilitate the study of large-distance behaviors in the Schwinger model, particularly those properties that are relevant to the question of when a charged state is physical. One difference that emerges between the two theories is that when a charged state in the Schwinger model is made physical while its energy is kept bounded, the charge goes off to infinity. The end-product could be considered neutral if the charge is defined as the limit of local measurements. On the other hand, if one attempts to change a local charged state in the Schwinger model into a physical state by transporting the localization region to asymptotic distances, the state may end up in either a θ-sector or the corresponding (θ+π)-sector, depending on the direction of transport. A possible generalization of this θ-mixing property to quark-like states in QCD is commented upon.

Überschallknall und Widerstand eines vorne spitzen Rotationskörpers in einer schweregeschichteten Atmosphäre

J. L. Ryhming [5] concluded that the minimum-boom body for given bow-shock wave drag and maximum body thickness is also the minimum drag body due to the bow shock for a given maximum body thickness. Here it is shown that the above conclusion is only valid for asymptotic distances. The geometry of the minimum-boom body depends on the distance for which one wants to minimize the sonic boom.