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At least 55 records · Page 3

Theoretical study of the butadiynyl and cyanoethynyl radicals - Support for the identification of C3N in IRC + 10216

Quantum-mechanical calculations, using the matrix Hartree-Fock model, have been performed for the butadiynyl and cyanoethynyl radicals. A rotation constant of 4753 MHz is calculated for C4H, while for C3N the value 4955 MHz is obtained. These may be compared with the rotation constant of 4947.5 MHz derived from the recently observed doublets in the millimeter-wave spectrum of IRC + 10216, suggesting the cyanoethynyl radical as the carrier species of these lines. The electric dipole moment and hyperfine coupling constants of both species are predicted.

Wilson, S.↗

Dynamic simulation of coronal mass ejections

A model is developed for the formation and propagation through the lower corona of the loop-like coronal transients in which mass is ejected from near the solar surface to the outer corona. It is assumed that the initial state for the transient is a coronal streamer. The initial state for the streamer is a polytropic, hydrodynamic solution to the steady-state radial equation of motion coupled with a force-free dipole magnetic field. The numerical solution of the complete time-dependent equations then gradually approaches a stationary coronal streamer configuration. The streamer configuration becomes the initial state for the coronal transient. The streamer and transient simulations are performed completely independent of each other. The transient is created by a sudden increase in the pressure at the base of the closed-field region in the streamer configuration. Both coronal streamers and coronal transients are calculated for values of the plasma beta (the ratio of thermal to magnetic pressure) varying from 0.1 to 100.

Steinolfson, R. S.↗

Irregularities in the secular variation and geodynamic implications; Proceedings of the Session, Cincinnati, OH, May 17, 1984

Consideration is given to: variations in the Gauss coefficients of the geomagnetic potential over the last several hundred years; eccentric geomagnetic dipole drift; and evidence for geomagnetic jerks from 1931 to 1971. Among other topics discussed are: models of the geomagnetic field in western Europe from 1960 to 1980; the external and internal parts of the geomagnetic jerk of 1970; secular variation of the magnetic mean energy density at the source layer depth; and motions at the core surface in the geostrophic approximation. Consideration is also given to: the unpredictability of geomagnetic secular variation; the use of short-term core-mantle coupling and geomagnetic variation impulses as Lagrangian tracers of core motions; and a comparison of two sequential geomagnetic polarity transitions in the upper Olduvai and the lower Jarmillio in the Southern Hemisphere.

Taylor, P.↗

Escape of Flare-Accelerated Particles in Solar Eruptive Events

Impulsive solar energetic particle events are widely believed to be due to the prompt escape into the interplanetary medium of flare-accelerated particles produced by solar eruptive events. According to the standard model for such events, however, particles accelerated by the flare reconnection should remain trapped in the flux rope comprising the coronal mass ejection. The particles should reach the Earth only much later, along with the bulk ejecta. To resolve this paradox, we have extended our previous axisymmetric model for the escape of flare-accelerated particles to fully three-dimentional (3D) geometries. We report the results of magnetohydrodynamic simluations of a coronal system that consists of a bipolar active region embedded in a background global dipole field structured by solar wind. our simulations show that multiple magnetic reconnection episodes occur prior to and during the coronal mass ejection 9CME) eruption and its interplanetary propagation. In addition to the episodes that build up the flux rope, reconnection between the open field and the CME couples the closed coronal to the open interplanetary field. Flare-accelerated particles initially trapped in the CME thereby gain access to the open interplanetary field along a trail blazed by magnetic reconnection. A key difference between these 3D results and our previous calculations is that the interchange reconnection allows accelerated particles to escape from deep within the CME flux rope. We estimate the spatial extent of the particle-escape channels. The relative timings between flare acceleration and release of the energetic particles through CME/open-field coupling are also determined. All our results compare favorably with observations.

Masson, S.↗

The steady global corona

The formation of the steady coronal structure which consists of coronal streamers and holes is seen in terms of a model employing numerical solutions of time-dependent, dissipationless, magnetohydrodynamic equations of motion applicable to the meridional plane. A coronal streamer consists of closed magnetic field lines near the solar surface with overlying and adjacent open field lines, and the atmosphere, which is stationary in the closed region, flows outward in the open region, or coronal hole. The steady coronal structure is obtained by starting the numerical calculation with a state comprising a polytropic, hydrodynamical solution to the steady-state radial equation of motion coupled with a dipole magnetic field. Global coronal configurations are calculated for values of the plasma beta which vary from 0.1 to 100. It is found that the height and lateral extension of the closed region are only weakly dependent on the data.

Steinolfson, R. S.↗

What we have learned from the magnetosphere

Three significant discoveries resulting from recent studies of earth's magnetosphere are discussed: (1) the central role of magnetic-field-line reconnection in determining the topology, geometry, and dynamics of the magnetosphere; (2) the realization that auroral arcs result from coupling of solar-wind stresses to the ionosphere and neutral atmosphere; and (3) the role of plasma turbulence in affecting both the microscopic state and macroscopic observables of the magnetospheric plasma. Magnetic-field-line reconnection is described in terms of Dungey's (1961) model of the magnetosphere, a simple picture of magnetic-substorm evolution is outlined, and questions concerning the reconnection rate are considered. The production of aurorae by field-aligned electron beams is examined, and an analogy is made between earth's magnetosphere and that of a pulsar with aligned dipole and spin axes. Plasma-turbulence problems are reviewed which concern anomalously fast electron and proton losses from the Van Allen belts, whistler-electron interactions, and anomalous resistance in auroral arcs. The Pioneer 10 encounter with Jupiter's magnetosphere is briefly noted.

Kennel, C. F.↗

A Study of the Free Oscillations of the Earth

Published observations on the toroidal oscillations of the earth are critically reviewed. A supplementary analysis of the record obtained by the Lamont strain seismometer is presented. Eleven toroidal modes are identified, and it is concluded that the periods are known to within 1 per cent. A perturbation scheme involving the ratio of the angular velocity of the earth to the resonant frequency is used in calculating the effects due to the rotation of the earth on the resonant frequency. The free oscillations are viewed as a superposition of traveling waves. In a nonrotating system two traveling waves combine to produce a stationary standing wave. In a rotating system, the rotation distinguishes between waves that travel in the direction of rotation and those that travel in the opposite direction. Rotation removes a degeneracy and results in a splitting of a spectral peak of order l into 2 times l plus 1 peaks. The fractional displacement in frequency for the lowest-order toroidal oscillations is 1/206 and of the same order as the Q of the peak, so that splitting will probably not be observed in the toroidal oscillations. Viewed locally, rotation causes a particle to precess about a direction parallel to the axis of rotation. This precession will cause a variation of amplitude with time if the motion is recorded by an instrument with an anisotropic response function. Care is therefore needed in studying the time decay of a given spectral peak. Rotation also couples the normal coordinates so that a motion that is initially purely horizontal will develop a vertical component. It is expected that vertical seismometers should record particle motion with the toroidal frequencies. The perturbations of the toroidal oscillations due to core-mantle interaction are treated in detail. An exact expression is obtained for the rate of energy dissipated by a finitely conducting plate oscillating across a magnetic field. The energy dissipated at the core-mantle boundary due to viscous and hydromagnetic coupling is shown to be insignificant as compared with the energy dissipated within the mantle. The toroidal magnetic field leaking into the lower mantle combines with the dipole field, resulting in a stress on the mantle, tending to stiffen the lower boundary. The stress is of sufficient magnitude to produce a displacement toward higher frequency in the lower-order toroidal oscillations. Observations on the (sub 0) T (sub 2) oscillations lead to an estimate of the toroidal magnetic field in the lower mantle. A calculation of elastic energy in the low-order oscillations suggests a value of 10 (sup 18) ergs per cycles per hour for the energy density at low frequencies in the Chilean earthquake. Each mode of oscillation has a characteristic radial distribution of elastic energy associated with it. This distribution determines which parts of the earth contribute most heavily in determining a particular resonant frequency. The distribution of energy for the lower 17 modes for a homogeneous and a Gutenberg model earth is calculated. The resonant frequencies for models of the earth based on the Gutenberg and Lehmann distribution of elastic properties are presented. It is shown that the Gutenberg model earth fits the observations more closely than the Lehmann model and that a slight alteration of the Gutenberg model gives a significantly better fit to the observations. The alteration involves a lower shear-wave velocity in the lower mantle while the Gutenberg velocity distribution is maintained in the upper mantle. Various studies of the earth's oscillations coupled with surface-wave investigations substantiate Gutenberg's hypothesis of a layer of low velocity in the upper mantle. The physical conditions required for the formation of a region of low velocity are examined in detail. The results confirm Birch's earlier statement that a temperature gradient in excess of 6 degrees to 7 degrees per kilometer is needed to produce a decrease in velocity. The low-velocity layer does not require that the temperature approach or exceed the melting temperature. If tile upper mantle is homogeneous, the region of lower velocity should commence at the base of the crust and extend to 150 kilometers under the oceans and about 100 kilometers under continental regions. The distribution of thermal conductivity and radioactivity consistent with the low-velocity layer is also considered.

MacDonald, Gordon J. F.↗

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗

Role of Tropical Atlantic SST Variability as a Modulator of El Nino Teleconnections

The present study suggests that the off-equatorial North Atlantic (NATL) SST warming plays a significant role in modulating El Niño teleconnection and its impact on the North Atlantic and European regions. The El Niño events accompanied by NATL SST warming exhibit south-north dipole pattern over the Western Europe to Atlantic, while the ENSO teleconnection pattern without NATL warming exhibits a Rossby wave-like pattern confined over the North Pacific and western Atlantic. Especially, the El Niño events with NATL warming show positive (negative) geopotential-height anomalies over the North Atlantic (Western Europe) which resemble the negative phase of the NAO. Consistently, it is shown using a simple statistical model that NATL SSTA in addition to the tropical Pacific SSTA leads to better prediction on regional climate variation over the North Atlantic and European regions. This role of NATL SST on ENSO teleconnection is also validated and discussed in a long term simulation of coupled global circulation model (CGCM).

Teleconnection↗

A new model for the high-frequency decametric radiation from Jupiter

It is generally accepted that the Jupiter decametric noise bursts occur at frequencies directly related to the electron gyrofrequencies in the Jupiter ionosphere, and it is frequently suggested that the radiation occurs at the gyrofrequency. The recent Pioneer 10 measurement of a 4-G-(R sub 5) cubed dipole moment provides some basis for a more detailed analysis of the local wave mode involved in the radiation. The direct measurement of a relatively small planetary dipole moment suggests that phenomena associated with local ionospheric wave modes having frequencies higher than local gyrofrequencies should be considered for at least some of the emissions. A possible explanation for certain intense high-frequency Jupiter noise bursts is discussed which is based on a wave-wave coupling mechanism that involves the radiation field and the (n + 1/2) gyrofrequency electrostatic modes.

Scarf, F. L.↗

Arylethynyl Substituted 9,lO-Anthraquinones: Tunable Stokes Shifts by Substitution and Solvent Polarity

2-Arylethynyl- and 2,6- and 2,7-diarylethynyl-substituted 9,lO-anthraquinones were synthesized via Sonogashira coupling reactions of 2-bromo-, 2,6-dibromo-, and 2,7-dibromo-9,10- anthraquinone with para-substituted phenylacetylenes. While the redox properties of those compounds are almost insensitive to substitution, their absorption maxima are linearly related to the Hammett constants with different slopes for electron donors and electron acceptors. ABI compounds are photoluminescent both in solution (quantum yields of emission <= 6 %), and as solids. The emission spectra have the characteristics of charge-transfer bands with large Stokes shifts (100-250 nm). The charge-transfer character of the emitting state is supported by large dipole moment differences between the ground and the excited state as concluded on the basis of molecular modeling and Lippert-Mataga correlations of the Stokes shifts with solvent polarity. Maximum Stokes shifts are attained by both electron-donating and -withdrawing groups. This is explained by a destabilization of the HOMO by electron donors and a stabilization of the LUMO by electron acceptors. X-ray crystallographic analysis of, for example, 2,7-bisphenylethynfl- 9,lO-anthraquinone reveals a monoclinic P21In space group and no indication for pi-overlap that would promote quenching, thus explaining emission from the solid state. Representative reduced forms of the title compounds were isolated as stable acetates of the corresponding dihydrs-9,10- anthraquinones. The emission of these compounds is blue-shifted relative to the parent oxidized forms and is attributed to internal transitions in the dihydro-9,lO-anthraquinone core.

Yang, Jinhua↗

MHD Modeling of the Solar Wind with Turbulence Transport and Heating

We have developed a magnetohydrodynamic model that describes the global axisymmetric steady-state structure of the solar wind near solar minimum with account for transport of small-scale turbulence associated heating. The Reynolds-averaged mass, momentum, induction, and energy equations for the large-scale solar wind flow are solved simultaneously with the turbulence transport equations in the region from 0.3 to 100 AU. The large-scale equations include subgrid-scale terms due to turbulence and the turbulence (small-scale) equations describe the effects of transport and (phenomenologically) dissipation of the MHD turbulence based on a few statistical parameters (turbulence energy, normalized cross-helicity, and correlation scale). The coupled set of equations is integrated numerically for a source dipole field on the Sun by a time-relaxation method in the corotating frame of reference. We present results on the plasma, magnetic field, and turbulence distributions throughout the heliosphere and on the role of the turbulence in the large-scale structure and temperature distribution in the solar wind.

Goldstein, M. L.↗

Corequake and shock heating model of the 5 March 1979 gamma-ray burst

Ramaty et al. (1980) have proposed a model of a neutron-star corequake and subsequent shock heating of the atmosphere to account for the gamma-ray burst of March 5, 1979. This model is elaborated by examining the overall energetics and characteristics of the radiation-dominated gas shocks under the assumption of thermodynamic equilibrium, taking into account the electron-positron pair production behind the shock. Using values for the density typical of those expected for neutron-star crusts (100-10,000 g/cu cm) and shock velocities characteristic of the sound speed (40,000-100,000), shock luminosities are obtained comparable to those required if the burst originated in the LMC. In addition, the fraction of energy deposited in electron-positron pairs is in good agreement with observation. Uneven shock heating between the polar and equatorial regions of the neutron star due to the presence of a dipole magnetic field, coupled with a rotation rate of 8 s, can also naturally account for the pulsating phase of the burst.

Ellison, D. C.↗

Ab initio characterization of ClOOH - Implications for atmospheric chemistry

The equilibrium structure, dipole moment, harmonic vibrational frequencies, and infrared intensities of ClOOH are determined using the CCSD(T) (singles and doubles coupled-cluster theory plus a perturbational estimate of the effects of connected triple excitations) electronic structure method in conjunction with a TZ2P (triple xi plus double polarization) basis set. The heat of formation of CIOOH is determined (using two different isodesmic reactions) to be +1.5 +/- 1 kcal/mol at 0 K or +0.2 +/- 1 kcal/mol at 298.15 K. Using the computed heat of formation, we examined the stability of ClOOH with respect to the ClO + OH, ClOO + H, and HOO + Cl dissociation limits. Since ClOOH is found to be quite stable, it is argued that the chemistry of ClOOH should be included in any accurate modeling of the stratosphere.

Lee, Timothy J.↗

A correlated ab initio study of linear carbon-chain radicals CnH (n = 2-7)

Linear carbon-chain radicals CnH for n = 2-7 have been studied with correlation consistent valence and core-valence basis sets and the coupled cluster method RCCSD(T). Equilibrium structures, rotational constants, and dipole moments are reported and compared with available experimental data. The ground state of the even-n series changes from 2 sigma+ to 2 pi as the chain is extended. For C4H, the 2 sigma+ state was found to lie only 72 cm-1 below the 2 pi state in the estimated complete basis set limit for valence correlation. The C2H- and C3H- anions have also been characterized.

NASA Discipline Exobiology↗

Unstable Air-Sea Interaction in the Extratropical North Atlantic

The possibility of coupled modes in the extratropical North Atlantic has fascinated the climate community since 1960's. A significant aspect of such modes is an unstable air-sea interaction, also called positive feedback, where disturbances between the atmosphere and ocean grow unbound. If a delayed response exists before the negative feedback takes effect, an oscillatory behaviour will develop. Here we explore the relationship between heat flux (positive upward) and sea surface temperature (SST). Positive feedback is characterized by a cross-correlation between the two where correlation maintains a negative sign whether SST or heat flux leads. We use model results and observations to argue that in the North Atlantic there exist regions with positive feedback. The two main locations coincide with the well-known north-south SST dipole where anomalies of opposite sign occupy areas east of Florida and north-east of Newfoundland. We show that oceanic dynamics, wave propagation and advection, give rise to oceanic anomalies in these regions. Subsequently these anomalies are amplified by atmosphere- ocean interaction: thus a positive feedback.

Hakkinen, Sirpa↗

Impacts of Stratospheric Ozone Recovery on Southern Ocean Temperature and Heat Budget

The impacts of stratospheric ozone recovery on Southern Ocean surface and interior temperature, heat content, heat uptake, and heat transport are investigated by contrasting two ensemble chemistry-climate model simulations in 2005–2099: one with fixed ozone depleting substances (ODSs) and another with decreasing ODSs. In our simulations ozone recovery significantly affects Southern Ocean temperature, with large latitudinal and vertical variations. Ozone recovery causes a dipole change of the full-depth ocean heat content (OHC) with an increase south of 60°S and a decrease between 45°S and 60°S. Integrated over latitudes south of 40°S, OHC decreases in response to ozone recovery. This ocean heat loss is shown to be driven by weakened poleward ocean heat transport (OHT) across 40°S, which is partly canceled by enhanced heat uptake. The weakening of poleward OHT into the Southern Ocean is caused by the ozone-induced equatorward shift of the meridional overturning circulation.

stratospheric ozone↗

Modeling of the Magnetosphere-Ionosphere-Atmosphere System

This grant covered the transition period between the ISTP/GGS main mission MAMI work (NAGW5-1097) to the extended mission of GGS/SolaxMax. During this period we concentrated on the following subjects: (1) Ionospheric modeling and in particular the coupling of the ionosphere and the magnetosphere require knowledge of the ionospheric conductances. We have an algorithm to derive these conductances from POLAR UVI or POLAR VIS images. The image analysis requires carefully calibrated measurements, separation of auroral brightness from scattered solar EUV and emissions caused by photoelectrons, and modeling of the auroral conditions, Under this grant we evaluated the various sources of uncertainty that contribute to the conductance calculation by comparing different model approaches and we conducted sensitivity studies. A joint modeling effort between our ionospheric models and a global MHD magnetospheric model with S. Slinker and J. Fedder lead to improved parameterizations for the MHD model. The predictions of that new model were validated using data from ground based instruments, POLAR UVI images, and DMSP satellites. These findings were presented at the GEM meeting in Snowmass, and at the Huntsville modeling workshop in Guntersville. A manuscript for publication is in preparation. A study to evaluate the thermospheric effects of large substorms and storms was con- ducted with the TIE-GCM model. Of particular interest are compositional changes of the thermosphere in the southern hemisphere. Southern hemisphere effects are stronger than those on the northern hemisphere because of the larger offset of the magnetic dipole from the rotational axis. These results were presented at the Huntsville modeling workshop in Guntersville.

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