Can a Turing Player identify itself?

We show that the problem of whether two Turing Machines are functionally equivalent is undecidable and explain why this is significant for the theory of repeated play and evolution

The radar cross section of dielectric disks

A solution is presented for the backscatter (nonstatic) radar cross section of dielectric disks of arbitrary shape, thickness and dielectric constant. The result is obtained by employing a Kirchhoff type approximation to obtain the fields inside the disk. The internal fields induce polarization and conduction currents from which the scattered fields and the radar cross section can be computed. The solution for the radar cross section obtained in this manner is shown to agree with known results in the special cases of normal incidence, thin disks and perfect conductivity. The solution can also be written as a product of the reflection coefficient of an identically oriented slab times the physical optics solution for the backscatter cross section of a perfectly conducting disk of the same shape. This result follows directly from the Kirchhoff type approximation without additional assumptions

Review of measurements of the RF spectrum of radiation from lightning

Measurements reported in the literature of the spectrum of electromagnetic radiation from lightning in the frequency range from 1 kHz to 1 GHz are reviewed. Measurements have been made either by monitoring the power received at individual frequencies using a narrow bandwidth recording device tuned to the frequencies under investigation or by recording the transient (time dependent) radiation with a wide bandwidth device and then Fourier transforming the waveform to obtain a spectrum. Measurements of the first type were made extensively in the 1950's and 1960's and several composite spectra have been deduced by normalizing the data of different investigators to common units of bandwidth and distance. The composite spectra tend to peak near 5 kHz and then decrease roughly as (frequency) to the -1, up to nearly 100 MHz where scatter in the data make the behavior uncertain. Measurements of the second type have been reported for return strokes, the stepped leader and for some intracloud processes. The spectrum of first return strokes obtained in this manner is very similar to the composite spectra obtained from the narrow-band measurements

Sources of the strongest RF radiation from lightning

Experiments performed at the Kennedy Space Center, Florida during TRIP-78 identified sources of the strongest RF radiation from lightning in the HF-VHF frequency range. Measurements were made of electric field changes associated with RF radiation using a field change system triggered on the output of an RF detector. The field changes associated with the strongest RF radiation are very fast (10 - 20 microseconds), bipolar pulses having an initial negative going half-cycle followed by a positive overshoot. These fast pulses consistently produced more RF radiation than was associated with return strokes, and their shape was remarkably consistent, independent of frequency

Internal Excitation in Molecular Collisions

Theory and analysis of relative motion and internal excitation in molecular collision

The temporal structure of RF radiation from lightning

Radiation from lightning in the RF band from 3-300 MHz has been examined. Simultaneous measurements were made of the RF radiation from lightning together with records of fast and slow field changes. Continuous analogue recordings were made with a system having 300 kHz of bandwidth in the RF channels. The temporal history of RF radiation of these frequencies consists of a sequence of discrete pulses. The data reveal a distinct pattern in the radiation which is independent of frequency and depends on the type of lightning flash: Cloud-to-ground flashes are characterized by an abrupt beginning associated with the stepped leader, whereas cloud-to-cloud flashes begin with a slower train of noise pulses more typical of the end of both types of flash. An exception to this pattern is cloud-to-ground flashes preceded by a breakdown phase, in which case the radiation begins like a cloud-to-cloud flash

Comparison of finite source and plane wave scattering from corrugated surfaces

The choice of a plane wave to represent incident radiation in the analysis of scatter from corrugated surfaces was examined. The physical optics solution obtained for the scattered fields due to an incident plane wave was compared with the solution obtained when the incident radiation is produced by a source of finite size and finite distance from the surface. The two solutions are equivalent if the observer is in the far field of the scatterer and the distance from observer to scatterer is large compared to the radius of curvature at the scatter points, condition not easily satisfied with extended scatterers such as rough surfaces. In general, the two solutions have essential differences such as in the location of the scatter points and the dependence of the scattered fields on the surface properties. The implication of these differences to the definition of a meaningful radar cross section was examined

Comparison of sigma(o) obtained from the conventional definition with sigma(o) appearing in the radar equation for randomly rough surfaces

A comparison is made of the radar cross section of rough surface calculated in one case from the conventional definition and obtained in the second case directly from the radar equation. The validity of the conventional definition representing the cross section appearing in the radar equation is determined. The analysis is executed in the special case of perfectly conducting, randomly corrugated surfaces in the physical optics limit. The radar equation is obtained by solving for the radiation scattered from an arbitrary source back to a colocated antenna. The signal out of the receiving antenna is computed from this solution and the result put into a form recognizeable as the radar equation. The conventional definition is obtained by solving a similar problem but for backscatter from an incident planewave. It is shown that these tow forms for sigma are the same if the observer is far enough from the surface

RF radiation from lightning correlated with aircraft measurements during storm hazards-82

During the Storm Hazards Experiment 1982, the Goddard Space Flight Center monitored radiation from lightning from a site at the Wallops Flight Facility, Wallops Island, VA. Measurements were made while the NASA F106 penetrated thunderstorms to obtain data on lightning strikes to the aircraft. The objective of the ground-based measurements was to help determine if the events recorded by the F106 were part of lightning discharges. During the experiment, 53 cases were obtained in which events were recorded aboard the aircraft while reliable quality RF radiation was recorded on the ground. These cases came from 12 different storms occurring from June through August 1982. The data confirms that the aircraft was measuring events which were part of lightning and indicates that the events recorded on the aircraft tend to occur early in the flash

The scatter of obliquely incident plane waves from a corrugated conducting surface

A physical optics solution is presented for the scattering of plane waves from a perfectly conducting corrugated surface in the case of waves incident from an arbitrary direction and for an observer far from the surface. This solution was used to compute the radar cross section of the surface in the case of backscatter from irregular (i.e., stochastic) corrugations and to point out a correction to the literature on this problem. A feature of the solution is the occurrence of singularities in the scattered fields which appear to be a manifestation of focussing by the surface at its stationary points. Whether or not the singularities occur in the solution depends on the manner in which one restricts the analysis to the far field