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Using a variational method, we recently determined an electromagnetic “signature” for characterizing a straight wire in free space. The signature consists of the first five resonant frequencies and their widths, more compactly expressed as the first five complex-valued resonant frequencies. Here we apply the variational method to the much more complicated case of determining the same signature for a straight wire or wire pair on a flat interface between a homogeneous earth and air. To calculate the resonances we obtain an integral equation for the current on a wire on the interface between two dielectric media. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current in an equivalent thin strip on the interface has non-zero solutions. The variational method extracts good approximations to these complex-valued resonant frequencies, without having to solve the integral equation. A table of resonances is given for the case of a relative dielectric constant of the earth equal to 4 and for three values of the ratio of wire radius to wire half-length.

With an interest in finding wires and distinguishing them from other electrically conducting objects, we have looked for an electromagnetic “fingerprint” in terms of resonances of a straight wire of length 2h and radius a. The resonances of the wire are formulated using the theory of the linear antenna, leading to an integral equation for the current on the wire. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current on the wire has non-zero solutions. By applying a variational technique we obtain approximate numerical solutions for the resonant frequencies and their widths. A table of the first five resonances is given for several ratios of wire half-length h to wire radius a. In a subsequent paper we propose to extend the method described here to deal with wires on an earth-air interface, for example as used to command the detonation of improvised explosive devices.

The backscattering of an electromagnetic missile from a perfectly conducting curved obstacle is investigated. The obstacle is assumed to have zero curvature just at the point of reflection of the incident pulse. The asymptotic dependence of the backscattered energy is sought, as the distance separating the obstacle from the source of the incident pulse tends to infinity. The backscattered energy is found to depend on the rate at which the energy spectral density of the current pulse at the source decays with increasing frequency, as well as on the degree of flatness of the obstacle at the point of reflection.

The scattered energy flux due to an electromagnetic missile incident upon an infinite circular conducting cylinder is analyzed. The flux obtained directly from Maxwell’s equations is compared with that of a geometrical‐optics description, generalizable to a broad class of convex objects with nonzero, bounded surface curvature.

The problem of wave scattering by a broken corner is considered. This is a linear problem whose analysis, however, is reduced—in a sense described below—to a nonlinear ordinary matrix differential equation. For scattering from a strip, a Painleve equation, was derived some time ago. The present work shows that matrix Painleve equations also arise naturally in physical problems.

A coordinate frame is considered as an arrangement of clocks that meet certain criteria of synchronization. Einstein’s ideal clock is compared with the behavior required for clocks to maintain synchrony in the group of coordinate frames that leaves Maxwell’s equations invariant. The required clock rates differ from the rate of Einstein’s clock. An ideal adjustable clock is defined as an Einstein clock augmented by variable “gearing” that can offset its rate. Ongoing adjustment of these clocks enables them to meet all synchronization criteria in the group of coordinate frames. The need for adjustment is due to the well known invariance of Maxwell’s equations under a group of coordinate transformations larger than the Lorentz group, and has nothing to do with imperfections in clocks. It is shown that the adjustments needed by ideal adjustable clocks to maintain synchrony can be measurably separated from additional adjustments that may be needed to compensate for random imperfections. The necessity for adjustment brings with it the necessity for ongoing measurement of the light signals whose exchange defines synchronization. Implications are discussed, both for the interpretation of Maxwell’s equations and for the role of measuring instruments. S 1984 Academic

GABA receptor binding to mammalian neuronal membranes has been classified into at least 2 subtypes—GABA A and GABA B binding sites. In catfish brain GABA A receptor sites have previously been demonstrated. Evidence is now presented that under appropriate conditions which rule out GABA A receptor binding, [ 3 H]GABA binds to membranes prepared from catfish brain. This binding is bicuculline-insensitive but differs enough from mammalian GABA B binding to cast some doubt on the idea that GABA B receptors exist in catfish brain. Specific binding was detected that was saturable and exhibited a dissociation constant of 4μM. (±)Baclofen, a potent inhibitor in rat brain, was a weak inhibitor, producing a maximum of 43% inhibition. This inhibitory effect could be enhanced, however, in the presence of 320 μM isoguvacine. [ 3 H]GABA binding was unaffected by bicuculline. Thus bicuculline-insensitive GABA binding sites exist in catfish brain but they differ in a number of ways from the GABA B receptor site found in mammals. Furthermore, a third [ 3 H]GABA binding site appears to exist that is both baclofen- and bicuculline-insensitive, yet is inhibited by high concentrations of isoguvacine, a known GABA A agonist.

A new method is introduced to find properties of wave and other fields. The relationship between the geometry of the strip and the symmetry of the Helmholtz equation is shown and leads to previously undiscovered properties of the field. The field pattern of the strip is shown to have a particularly simple form and, moreover, to be completely determined by symmetry‐like principles.

The objective of this review is to discuss the state of the art at a difficult stage in the development of a subject‐field—when attempts are being made to translate the results of research into operational services of value to practitioners. Judged by the criterion of practical relevance, the application of computers in the law is a subject which, over the past fifteen years, has promised much, but fulfilled little. This is a sweeping generalization—but, as a generalization, it has some justification.