522 research outputs found
Spectral properties of the nonspherically decaying radiation generated by a rotating superluminal source
The focusing of the radiation generated by a polarization current with a
superluminally rotating distribution pattern is of a higher order in the plane
of rotation than in other directions. Consequently, our previously published
asymptotic approximation to the value of this field outside the equatorial
plane breaks down as the line of sight approaches a direction normal to the
rotation axis, i.e., is nonuniform with respect to the polar angle. Here we
employ an alternative asymptotic expansion to show that, though having a rate
of decay with frequency (mu) that is by a factor of order mu^(2/3) slower, the
equatorial radiation field has the same dependence on distance as the
nonspherically decaying component of the generated field in other directions:
it, too, diminishes as the inverse square root of the distance from its source.
We also briefly discuss the relevance of these results to the giant pulses
received from pulsars: the focused, nonspherically decaying pulses that arise
from a superluminal polarization current in a highly magnetized plasma have a
power-law spectrum (i.e., a flux density proportional to mu^alpha) whose index
(alpha) is given by one of the values -2/3, -2, -8/3, or -4
The fundamental role of the retarded potential in the electrodynamics of superluminal sources
We calculate the gradient of the radiation field generated by a polarization
current with a superluminally rotating distribution pattern and show that the
absolute value of this gradient increases as R^(7/2) with distance R within the
sharply focused subbeams constituting the overall radiation beam. This result
not only supports the earlier finding that the azimuthal and polar widths of
these subbeams narrow with distance (as R^(-3) and R^(-1), respectively), but
also implies that the boundary contribution to the solution of the wave
equation governing the radiation field does not always vanish in the limit
where the boundary tends to infinity. There is a fundamental difference between
the classical expressions for the retarded potential and field: while the
boundary contribution for the potential can always be made zero via a gauge
transformation preserving the Lorenz condition, that for the field may be
neglected only if it diminishes with distance faster than the contribution of
the source density in the far zone. In the case of a rotating superluminal
source, however, the boundary term in the retarded solution for the field is by
a factor of order R^(1/2) larger than the source term of this solution in the
limit, which explains why an argument based on the solution of the wave
equation governing the field that neglects the boundary term (such as that
presented by J. H. Hannay) misses the nonspherical decay of the field. Given
that the distribution of the radiation field of an accelerated superluminal
source in the far zone is not known a priori, the only way to calculate the
free-space radiation field of such sources is via the retarded solution for the
potential. Finally, we apply these findings to pulsar observational data: the
more distant a pulsar, the narrower and brighter its giant pulses should be
A new mechanism for generating broadband pulsar-like polarization
Observational data imply the presence of superluminal electric currents in
pulsar magnetospheres. Such sources are not inconsistent with special
relativity; they have already been created in the laboratory. Here we describe
the distinctive features of the radiation beam that is generated by a rotating
superluminal source and show that (i) it consists of subbeams that are narrower
the farther the observer is from the source: subbeams whose intensities decay
as 1/R instead of 1/R^2 with distance (R), (ii) the fields of its subbeams are
characterized by three concurrent polarization modes: two modes that are
'orthogonal' and a third mode whose position angle swings across the subbeam
bridging those of the other two, (iii) its overall beam consists of an
incoherent superposition of such coherent subbeams and has an intensity profile
that reflects the azimuthal distribution of the contributing part of the source
(the part of the source that approaches the observer with the speed of light
and zero acceleration), (iv) its spectrum (the superluminal counterpart of
synchrotron spectrum) is broader than that of any other known emission and
entails oscillations whose spacings and amplitudes respectively increase and
decrease algebraically with increasing frequency, and (v) the degree of its
mean polarization and the fraction of its linear polarization both increase
with frequency beyond the frequency for which the observer falls within the
Fresnel zone. We also compare these features with those of the radiation
received from the Crab pulsar.Comment: 8 pages, 8 figure
Design and development of a novel autonomous moored underwater profiler
The ocean is a dynamic and complex system. Understanding it through observation is critical to predicting and adapting to it. This thesis details a new approach to making vertical profiles at a fixed geographic location. It describes the design of a novel autonomous moored underwater profiler to characterize the water column of the continental shelf. The theory supporting the design is detailed, and the results of laboratory and field tests are presented. The rationale for the system, sub-system, and component design and selection is supported through calculations, and/or validated through bench testing. The resulting prototype is a hybrid of a wire follower type profiler. The profiler is attached to a subsea mooring and it is capable of profiling the entire water column. Using a buoyancy engine and compound pulley system, the unique propulsion system only requires power for the ascent. Performance analysis of the prototype during open water field trials indicated a high potential for the profiler to operate as intended
Inadequacies in the conventional treatment of the radiation field of moving sources
There is a fundamental difference between the classical expression for the
retarded electromagnetic potential and the corresponding retarded solution of
the wave equation that governs the electromagnetic field. While the boundary
contribution to the retarded solution for the {\em potential} can always be
rendered equal to zero by means of a gauge transformation that preserves the
Lorenz condition, the boundary contribution to the retarded solution of the
wave equation governing the {\em field} may be neglected only if it diminishes
with distance faster than the contribution of the source density in the far
zone. In the case of a source whose distribution pattern both rotates and
travels faster than light {\em in vacuo}, as realized in recent experiments,
the boundary term in the retarded solution governing the field is by a factor
of the order of {\em larger} than the source term of this solution in
the limit that the distance of the boundary from the source tends to
infinity. This result is consistent with the prediction of the retarded
potential that part of the radiation field generated by a rotating superluminal
source decays as , instead of , a prediction that is
confirmed experimentally. More importantly, it pinpoints the reason why an
argument based on a solution of the wave equation governing the field in which
the boundary term is neglected (such as appears in the published literature)
misses the nonspherical decay of the field
Morphology of the nonspherically decaying radiation generated by a rotating superluminal source: reply to comment
The fact that the formula used by Hannay in his Comment is "from a standard
text on electrodynamics" neither warrants that it is universally applicable,
nor that it is unequivocally correct. We have explicitly shown [J. Opt. Soc.
Am. A 25, 543 (2008)] that,since it does not include the boundary contribution
toward the value of the field, the formula in question is not applicable when
the source is extended and has a distribution pattern that rotates faster than
light in vacuo. The neglected boundary term in the retarded solution to the
wave equation governing the electromagnetic field forms the basis of
diffraction theory. If this term were identically zero, for the reasons given
by Hannay, the iffraction of electromagnetic waves through apertures on a
surface enclosing a source would have been impossible. If this term were
identically zero, for the reasons given by Hannay, the diffraction of
electromagnetic waves through apertures on a surface enclosing a source would
have been impossible
Rankings for bipartite tournaments via chain editing
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity compete indirectly via matches against players of the opposite kind; examples include education (students/exam questions) and solo sports (golfers/courses). In particular, we look to find rankings via chain graphs, which correspond to bipartite tournaments in which the sets of adversaries defeated by the players on one side are nested with respect to set inclusion. Tournaments of this form have a natural and appealing ranking associated with them. We apply chain editing – finding the minimum number of edge changes required to form a chain graph – as a new mechanism for tournament ranking. The properties of these rankings are investigated in a probabilistic setting, where they arise as maximum likelihood estimators, and through the axiomatic method of social choice theory. Despite some nice properties, two problems remain: an important anonymity axiom is violated, and chain editing is NP-hard. We address both issues by relaxing the minimisation constraint in chain editing, and characterise the resulting ranking methods via a greedy approximation algorith
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