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

Observation of coherent π0\pi^0 electroproduction on deuterons at large momentum transfer

The first experimental results for coherent $\pi^0$-electroproduction on the deuteron, $e+d\to e+d +\pi^0$, at large momentum transfer, are reported. The experiment was performed at Jefferson Laboratory at an incident electron energy of 4.05 GeV. A large pion production yield has been observed in a kinematical region for 1.1$<Q^2<$1.8 GeV$^2$, from threshold to 200 MeV excitation energy in the $d\pi^0$ system. The $Q^2$-dependence is compared with theoretical predictions.Comment: 26 page

The nature of turbulence in OMC1 at the star forming scale: observations and simulations

Aim: To study turbulence in the Orion Molecular Cloud (OMC1) by comparing observed and simulated characteristics of the gas motions. Method: Using a dataset of vibrationally excited H2 emission in OMC1 containing radial velocity and brightness which covers scales from 70AU to 30000AU, we present the transversal structure functions and the scaling of the structure functions with their order. These are compared with the predictions of two-dimensional projections of simulations of supersonic hydrodynamic turbulence. Results: The structure functions of OMC1 are not well represented by power laws, but show clear deviations below 2000AU. However, using the technique of extended self-similarity, power laws are recovered at scales down to 160AU. The scaling of the higher order structure functions with order deviates from the standard scaling for supersonic turbulence. This is explained as a selection effect of preferentially observing the shocked part of the gas and the scaling can be reproduced using line-of-sight integrated velocity data from subsets of supersonic turbulence simulations. These subsets select regions of strong flow convergence and high density associated with shock structure. Deviations of the structure functions in OMC1 from power laws cannot however be reproduced in simulations and remains an outstanding issue.Comment: 12 pages, 8 figures, accepted A&A. Revised in response to referee. For higher resolution, see http://www.astro.phys.au.dk/~maikeng/sim_paper

Chemical Abundances of the S star GZ Peg

The chemical compositions of stars from the Asymptotic Giant Branch are still poorly known due to the low temperatures of their atmospheres and therefore the presence of many molecular transitions hampering the analysis of atomic lines. One way to overcome this difficulty is by the study of lines in regions free from molecular contamination. We have chosen some of those regions to study the chemical abundance of the S-type star GZ Peg. Stellar parameters are derived from spectroscopic analysis and a metallicity of -0.77 dex is found. Chemical abundances of 8 elements are reported and an enhancement of s-process elements is inferred, typical to that of an S-type star.Comment: 5 figures, 3 tables. accepted for publication in the Publications of the Astronomical Society of Australi

A method for detection of structure

Context. In order to understand the evolution of molecular clouds it is important to identify the departures from self-similarity associated with the scales of self-gravity and the driving of turbulence. Aims. A method is described based on structure functions for determining whether a region of gas, such as a molecular cloud, is fractal or contains structure with characteristic scale sizes. Methods. Using artificial data containing structure it is shown that derivatives of higher order structure functions provide a powerful way to detect the presence of characteristic scales should any be present and to estimate the size of such structures. The method is applied to observations of hot H2 in the Kleinman-Low nebula, north of the Trapezium stars in the Orion Molecular Cloud, including both brightness and velocity data. The method is compared with other techniques such as Fourier transform and histogram techniques. Results. It is found that the density structure, represented by H2 emission brightness in the K-band (2-2.5micron), exhibits mean characteristic sizes of 110, 550, 1700 and 2700AU. The velocity data show the presence of structure at 140, 1500 and 3500AU. Compared with other techniques such as Fourier transform or histogram, the method appears both more sensitive to characteristic scales and easier to interpret.Comment: Astronomy and Astrophysics, in pres

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.

Observations of spatial and velocity structure in the Orion Molecular Cloud

Observations are reported of H2 IR emission in the S(1) v=1-0 line at 2.121 microns in the Orion Molecular Cloud, OMC1, using the GriF instrument on the Canada-France-Hawaii Telescope. GriF is a combination of adaptive optics and Fabry-Perot interferometry, yielding a spatial resolution of 0.15" to 0.18" and a velocity discrimination as high as 1 km/s. Thanks to the high spatial and velocity resolution of the GriF data, 193 bright H2 emission regions can be identified in OMC1. The general characteristics of these features are described in terms of radial velocities, brightness and spatial displacement of maxima of velocity and brightness, the latter to yield the orientation of flows in the plane of the sky. Strong spatial correlation between velocity and bright H2 emission is found and serves to identify many features as shocks. Important results are: (i) velocities of the excited gas illustrate the presence of a zone to the south of BN-IRc2 and Peak 1, and the west of Peak 2, where there is a powerful blue-shifted outflow with an average velocity of -18 km/s. This is shown to be the NIR counterpart of an outflow identified in the radio from source I, a very young O-star. (ii) There is a band of weak velocity features (<5 km/s) in Peak 1 which may share a common origin through an explosive event, in the BN-IRc2 region, with the fast-moving fingers (or bullets) to the NW of OMC1. (iii) A proportion of the flows are likely to represent sites of low mass star formation and several regions show multiple outflows, probably indicative of multiple star formation within OMC1. The high spatial and velocity resolution of the GriF data show these and other features in more detail than has previously been possible.Comment: 27 pages, 19 figures, submitted to A&A Version 2: Several additions, including a section on protostellar candidates in OMC1, have been made based on the referee's suggestions v3: corrected typograph

Head-on collisions of boson stars

We study head-on collisions of boson stars in three dimensions. We consider evolutions of two boson stars which may differ in their phase or have opposite frequencies but are otherwise identical. Our studies show that these phase differences result in different late time behavior and gravitational wave output