5,992 research outputs found
Stored energies for electric and magnetic current densities
Electric and magnetic current densities are an essential part of
electromagnetic theory. The goal of the present paper is to define and
investigate stored energies that are valid for structures that can support both
electric and magnetic current densities. Stored energies normalized with the
dissipated power give us the Q factor, or antenna Q, for the structure. Lower
bounds of the Q factor provide information about the available bandwidth for
passive antennas that can be realized in the structure. The definition that we
propose is valid beyond the leading order small antenna limit. Our starting
point is the energy density with subtracted far-field form which we obtain an
explicit and numerically attractive current density representation. This
representation gives us the insight to propose a coordinate independent stored
energy. Furthermore, we find here that lower bounds on antenna Q for structures
with e.g. electric dipole radiation can be formulated as convex optimization
problems. We determine lower bounds on both open and closed surfaces that
support electric and magnetic current densities.
The here derived representation of stored energies has in its electrical
small limit an associated Q factor that agrees with known small antenna bounds.
These stored energies have similarities to earlier efforts to define stored
energies. However, one of the advantages with this method is the above
mentioned formulation as convex optimization problems, which makes it easy to
predict lower bounds for antennas of arbitrary shapes. The present formulation
also gives us insight into the components that contribute to Chu's lower bound
for spherical shapes. We utilize scalar and vector potentials to obtain a
compact direct derivation of these stored energies. Examples and comparisons
end the paper.Comment: Minor updates to figures and tex
Stored Electromagnetic Energy and Antenna Q
Decomposition of the electromagnetic energy into its stored and radiated
parts is instrumental in the evaluation of antenna Q and the corresponding
fundamental limitations on antennas. This decomposition is not unique and there
are several proposals in the literature. Here, it is shown that stored energy
defined from the difference between the energy density and the far field energy
equals the new energy expressions proposed by Vandenbosch for many cases. This
also explains the observed cases with negative stored energy and suggests a
possible remedy to them. The results are compared with the classical explicit
expressions for spherical regions where the results only differ by ka that is
interpreted as the far-field energy in the interior of the sphere. Numerical
results of the Q-factors for dipole, loop, and inverted L-antennas are also
compared with estimates from circuit models and differentiation of the
impedance. The results indicate that the stored energy in the field agrees with
the stored energy in the Brune synthesized circuit models whereas the
differentiated impedance gives a lower value for some cases. The corresponding
results for the bandwidth suggest that the inverse proportionality between
bandwidth and Q depends on the relative bandwidth or equivalent the threshold
of the reflection coefficient. The Q from the differentiated impedance and
stored energy are most useful for relative narrow and wide bandwidths,
respectively
Stored energies in electric and magnetic current densities for small antennas
Electric and magnetic currents are essential to describe electromagnetic
stored energy, as well as the associated quantities of antenna Q and the
partial directivity to antenna Q-ratio, D/Q, for general structures. The upper
bound of previous D/Q-results for antennas modeled by electric currents is
accurate enough to be predictive, this motivates us here to extend the analysis
to include magnetic currents. In the present paper we investigate antenna Q
bounds and D/Q-bounds for the combination of electric- and magnetic-currents,
in the limit of electrically small antennas. This investigation is both
analytical and numerical, and we illustrate how the bounds depend on the shape
of the antenna. We show that the antenna Q can be associated with the largest
eigenvalue of certain combinations of the electric and magnetic polarizability
tensors. The results are a fully compatible extension of the electric only
currents, which come as a special case. The here proposed method for antenna Q
provides the minimum Q-value, and it also yields families of minimizers for
optimal electric and magnetic currents that can lend insight into the antenna
design.Comment: 27 pages 7 figure
Disentangling the Hercules stream
Using high-resolution spectra of nearby F and G dwarf stars, we have
investigated the detailed abundance and age structure of the Hercules stream.
We find that the stars in the stream have a wide range of stellar ages,
metallicities, and element abundances. By comparing to existing samples of
stars in the solar neighbourhood with kinematics typical of the Galactic thin
and thick disks we find that the properties of the Hercules stream distinctly
separate into the abundance and age trends of the two disks. Hence, we find it
unlikely that the Hercules stream is a unique Galactic stellar population, but
rather a mixture of thin and thick disk stars. This points toward a dynamical
origin for the Hercules stream, probably caused by the Galactic bar.Comment: Accepted for publication in ApJ Letter
Calibration of the CH and CN Variations Among Main Sequence Stars in M71 and in M13
An analysis of the CN and CH band strengths measured in a large sample of M71
and M13 main sequence stars by Cohen (1999a,b) is undertaken using synthetic
spectra to quantify the underlying C and N abundances. In the case of M71 it is
found that the observed CN and CH band strengths are best matched by the
{\it{identical}} C/N/O abundances which fit the bright giants, implying: 1)
little if any mixing is taking place during red giant branch ascent in M71, and
2) a substantial component of the C and N abundance inhomogeneities is in place
before the main sequence turn-off. The unlikelihood of mixing while on the main
sequence requires an explanation for the abundance variations which lies
outside the present stars (primordial inhomogeneities or intra-cluster self
enrichment). For M13 it is shown that the 3883\AA CN bands are too weak to be
measured in the spectra for any reasonable set of expected compositions. A
similar situation exists for CH as well. However, two of the more luminous
program stars do appear to have C abundances considerably greater than those
found among the bright giants thereby suggesting deep mixing has taken place on
the M13 red giant branch.Comment: 14 pages, 4 figures, accepted for publication by A
Optimal Planar Electric Dipole Antenna
Considerable time is often spent optimizing antennas to meet specific design
metrics. Rarely, however, are the resulting antenna designs compared to
rigorous physical bounds on those metrics. Here we study the performance of
optimized planar meander line antennas with respect to such bounds. Results
show that these simple structures meet the lower bound on radiation Q-factor
(maximizing single resonance fractional bandwidth), but are far from reaching
the associated physical bounds on efficiency. The relative performance of other
canonical antenna designs is compared in similar ways, and the quantitative
results are connected to intuitions from small antenna design, physical bounds,
and matching network design.Comment: 10 pages, 15 figures, 2 tables, 4 boxe
Scaling Limits for Internal Aggregation Models with Multiple Sources
We study the scaling limits of three different aggregation models on Z^d:
internal DLA, in which particles perform random walks until reaching an
unoccupied site; the rotor-router model, in which particles perform
deterministic analogues of random walks; and the divisible sandpile, in which
each site distributes its excess mass equally among its neighbors. As the
lattice spacing tends to zero, all three models are found to have the same
scaling limit, which we describe as the solution to a certain PDE free boundary
problem in R^d. In particular, internal DLA has a deterministic scaling limit.
We find that the scaling limits are quadrature domains, which have arisen
independently in many fields such as potential theory and fluid dynamics. Our
results apply both to the case of multiple point sources and to the
Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in
v2: added "least action principle" (Lemma 3.2); small corrections in section
4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version);
expanded section 6.
Tracing the Galactic thick disk to Solar metallicities
We show that the Galactic thick disk reaches at least solar metallicities,
and that it experienced strong chemical enrichment during a period of ~3 Gyr,
ending around 8-9 Gyr ago. This finding puts further constraints on the
relation and interface between the thin and thick disks, and their formation
processes. Our results are based on a detailed elemental abundance analysis of
261 kinematically selected F and G dwarf stars in the solar neighborhood: 194
likely members of the thick disk and 67 likely members of the thin disk, in the
range -1.3<[Fe/H]<+0.4.Comment: Accepted for publication in ApJ Letter
The resultant on compact Riemann surfaces
We introduce a notion of resultant of two meromorphic functions on a compact
Riemann surface and demonstrate its usefulness in several respects. For
example, we exhibit several integral formulas for the resultant, relate it to
potential theory and give explicit formulas for the algebraic dependence
between two meromorphic functions on a compact Riemann surface. As a particular
application, the exponential transform of a quadrature domain in the complex
plane is expressed in terms of the resultant of two meromorphic functions on
the Schottky double of the domain.Comment: 44 page
C and N Abundances in Stars At the Base of the Red Giant Branch in M5
We present an analysis of a large sample of moderate resolution Keck LRIS
spectra of subgiant (V \sim 17.2) and fainter stars in the Galactic globular
cluster M5 (NGC 5904) with the goal of deriving C and N abundances.
Star-to-star stochastic variations with significant range in both [C/Fe] and
[N/Fe] are found at all luminosities extending to the bottom of the RGB at M_V
\sim +3. Similar variations in CH appear to be present in the main sequence
turnoff spectra. There is no sign of a change in the behavior of C and N with
evolutionary stage over the full range in luminosity of the RGB and SGB. The C
and N abundances appear strongly anti-correlated, as would be expected from the
CN-cycle processing of stellar material. Yet the present stars are considerably
fainter than the RGB bump, the point at which deep mixing is believed to set
in. On this basis, while the observed abundance pattern is consistent with
proton capture nucleosynthesis, we infer that the site of the reactions is
likely not within the present sample, but rather in a population of more
massive (2 -- 5 M(Sun)) now defunct stars. The range of variation of the N
abundances is very large and the sum of C+N increases as C decreases. To
reproduce this requires the incorporation not only of CN but also of
ON-processed material. Furthermore, the existence of this correlation is quite
difficult to reproduce with an external mechanism such as ``pollution'' with
material processed in a more massive AGB star, which mechanism is fundamentally
stochastic in nature. We therefore suggest that although the internal mixing
hypothesis has serious flaws,new theoretical insights are needed and it should
not be ruled out yet. (abridged)Comment: Slightly updated version to conform to that accepted by the A
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